(THOL.mp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(THOL.exE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ V1)))) @ V1)))))))
(THOL.exI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))))))))
(THOL.ext,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.eq @ (^[V2]: (V0 @ V2))) @ (^[V2]: (V1 @ V2)))))))))
(THOL.iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.implies @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ ((cHOL.implies @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(THOL.sym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ V0)))))))
(TNat.le0,(call @ (^[V0]: ((cNat.ord_nat_inst.less_eq_nat @ cNat.zero_nat_inst.zero_nat) @ V0))))
(TSet.UnE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V1)) @ V3)) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V2)) @ V3)) @ V3))))))))))))
(TFun.bijI,(call @ (^[V0]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top))))))
(TFun.id_o,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ cFun.id) @ V0)) @ V0))))
(TFun.injD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TFun.injI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2))) @ ((cHOL.eq @ V1) @ V2))))))) @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)))))
(TFun.o_id,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ V0) @ cFun.id)) @ V0))))
(THOL.allE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (V0 @ V3)))) @ ((c==> @ ((c==> @ (V0 @ V1)) @ V2)) @ V2)))))))))
(THOL.allI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: (V0 @ V1)))))))
(THOL.cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V3)))))))))))))
(THOL.ex1E,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V0 @ V3)) @ ((cHOL.eq @ V3) @ V2))))) @ V1))))) @ V1)))))))
(THOL.ex1I,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cHOL.eq @ V2) @ V1))))) @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2))))))))))
(THOL.exCI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ (cHOL.All @ (^[V2]: (cHOL.Not @ (V0 @ V2))))) @ (V0 @ V1))) @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))))))))
(THOL.if_P,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ V0) @ ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ V1)))))))))
(THOL.iffE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V1) @ V0)) @ V2))) @ V2)))))))))
(THOL.iffI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(THOL.impE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ V0) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(THOL.impI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(THOL.notE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ V0)) @ ((c==> @ V0) @ V1)))))))
(THOL.notI,(call @ (^[V0]: ((c==> @ ((c==> @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(THOL.refl,(call @ (^[V0]: ((cHOL.eq @ V0) @ V0))))
(THOL.spec,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ (V0 @ V1)))))))
(THOL.swap,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ V0)) @ ((c==> @ ((c==> @ (cHOL.Not @ V1)) @ V0)) @ V1)))))))
(THOL.theI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cHOL.eq @ V2) @ V1))))) @ (V0 @ (cHOL.The @ (^[V2]: (V0 @ V2)))))))))))
(TInt.negD,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V1))))))))))
(TMap.domD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cMap.dom @ V1))) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ (V1 @ V0)) @ (cOption.option.Some @ V2))))))))))
(TMap.domI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (cOption.option.Some @ V2))) @ ((cSet.member @ V1) @ (cMap.dom @ V0))))))))))
(TMap.ranI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (cOption.option.Some @ V2))) @ ((cSet.member @ V2) @ (cMap.ran @ V0))))))))))
(TNat.gr0I,(call @ (^[V0]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cHOL.False)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)))))
(TSet.IntE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TSet.IntI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V0) @ V2)) @ ((cSet.member @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2)))))))))))
(TSet.PowD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Pow @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet.PowI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cSet.member @ V0) @ (cSet.Pow @ V1))))))))
(TSet.UnCI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cSet.member @ V0) @ V2))) @ ((cSet.member @ V0) @ ((cLattices.sup_class.sup @ V2) @ V1))))))))))
(TSet.UnI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TSet.UnI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ ((cLattices.sup_class.sup @ V2) @ V1))))))))))
(TSet.bexE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Bex @ V0) @ (^[V3]: (V1 @ V3)))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((c==> @ (V1 @ V3)) @ V2))))) @ V2)))))))))
(TSet.bexI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ ((cSet.Bex @ V2) @ (^[V3]: (V0 @ V3))))))))))))
(TFun.o_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ (^[V2]: (V0 @ (V1 @ V2)))))))))
(TFun.surjD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (V0 @ V2))))))))))
(TFun.surjE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ (V0 @ V3))) @ V2)))) @ V2)))))))))
(TFun.surjI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ (V1 @ V2))) @ V2)))) @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)))))))
(THOL.TrueE,(call @ (^[V0]: ((c==> @ cHOL.True) @ ((c==> @ V0) @ V0)))))
(THOL.TrueI,cHOL.True)
(THOL.allE',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (V0 @ V3)))) @ ((c==> @ ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V3]: (V0 @ V3)))) @ V2))) @ V2)))))))))
(THOL.conjE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ ((c==> @ V1) @ V2))) @ V2)))))))))
(THOL.conjI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ V1) @ ((cHOL.conj @ V0) @ V1))))))))
(THOL.disjE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.disj @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ V2)) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(THOL.eq_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cHOL.eq @ V1) @ V2))))))))))
(THOL.eq_ac_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cHOL.eq @ V1) @ V2))) @ ((cHOL.eq @ V1) @ ((cHOL.eq @ V0) @ V2))))))))))
(THOL.eq_ac_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ V0)))))))
(THOL.iffCE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ ((c==> @ V1) @ V2))) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ ((c==> @ (cHOL.Not @ V1)) @ V2))) @ V2))))))))))
(THOL.iffD1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(THOL.iffD2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ V1) @ V0)))))))
(THOL.impCE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V2)) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(THOL.impE',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.implies @ V0) @ V1)) @ V0)) @ V2))))))))))
(THOL.notE',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ V0)) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V0)) @ V1)))))))
(THOL.notI2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ (cHOL.Not @ V1))) @ ((c==> @ ((c==> @ V0) @ V1)) @ (cHOL.Not @ V0))))))))
(THOL.subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (V2 @ V0)) @ (V2 @ V1))))))))))
(THOL.theI',(call @ (^[V0]: ((c==> @ (cHOL.Ex1 @ (^[V1]: (V0 @ V1)))) @ (V0 @ (cHOL.The @ (^[V1]: (V0 @ V1))))))))
(THOL.theI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cHOL.eq @ V3) @ V1))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V2 @ V3))))) @ (V2 @ (cHOL.The @ (^[V3]: (V0 @ V3))))))))))))))
(THOL.trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.eq @ V0) @ V2))))))))))
(TInt.int_0,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ cNat.zero_nat_inst.zero_nat)) @ cInt.zero_int_inst.zero_int))
(TInt.int_1,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ cNat.one_nat_inst.one_nat)) @ cInt.one_int_inst.one_int))
(TInt.nat_0,((cHOL.eq @ (cInt.nat @ cInt.zero_int_inst.zero_int)) @ cNat.zero_nat_inst.zero_nat))
(TInt.nat_1,((cHOL.eq @ (cInt.nat @ cInt.one_int_inst.one_int)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))
(TInt.nat_2,((cHOL.eq @ (cInt.nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cNat.Suc @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))
(TNat.lessE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ (cNat.Suc @ V0))) @ V2)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ (cNat.Suc @ V3))) @ V2))))) @ V2))))))))))
(TNat.lessI,(call @ (^[V0]: ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V0)))))
(TNum.Suc_1,((cHOL.eq @ (cNat.Suc @ cNat.one_nat_inst.one_nat)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TSet.DiffE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V2))) @ V3))) @ V3)))))))))))
(TSet.DiffI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V2))) @ ((cSet.member @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2)))))))))))
(TSet.IntD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cSet.member @ V0) @ V1)))))))))
(TSet.IntD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cSet.member @ V0) @ V2)))))))))
(TSet.Un_ac_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ V1) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TSet.Un_ac_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TSet.Un_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TSet.Un_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TSet.ballE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.Ball @ V0) @ (^[V4]: (V1 @ V4)))) @ ((c==> @ ((c==> @ (V1 @ V2)) @ V3)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V0))) @ V3)) @ V3))))))))))))
(TSet.ballI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: (V1 @ V2)))))))))
(TSet.bexCI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cHOL.Not @ (V1 @ V3))))) @ (V1 @ V2))) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.Bex @ V0) @ (^[V3]: (V1 @ V3))))))))))))
(TSet.bspec,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (V1 @ V3)))) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))))))))
(TSet.strip_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: (V1 @ V2)))))))))
(TSet.strip_2,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: (V0 @ V1)))))))
(TSet.strip_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(TFun.bij_id,(((cFun.bij_betw @ cFun.id) @ cOrderings.top_class.top) @ cOrderings.top_class.top))
(TFun.id_def,((cHOL.eq @ cFun.id) @ (^[V0]: V0)))
(TFun.inj_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TFun.set.id,((cHOL.eq @ (cSet.vimage @ cFun.id)) @ cFun.id))
(THOL.Ex_def,(call @ (^[V0]: ((c== @ (cHOL.Ex @ V0)) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ V1)))) @ V1)))))))
(THOL.FalseE,(call @ (^[V0]: ((c==> @ cHOL.False) @ V0))))
(THOL.If_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cHOL.If @ V0) @ V1) @ V2)) @ (cHOL.The @ (^[V3]: ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V0) @ cHOL.True)) @ ((cHOL.eq @ V3) @ V1))) @ ((cHOL.implies @ ((cHOL.eq @ V0) @ cHOL.False)) @ ((cHOL.eq @ V3) @ V2)))))))))))))
(THOL.ccontr,(call @ (^[V0]: ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ cHOL.False)) @ V0))))
(THOL.disjCI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V1)) @ ((cHOL.disj @ V1) @ V0)))))))
(THOL.disjI1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((cHOL.disj @ V0) @ V1)))))))
(THOL.disjI2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((cHOL.disj @ V1) @ V0)))))))
(THOL.ex1_eq_2,(call @ (^[V0]: (cHOL.Ex1 @ (^[V1]: ((cHOL.eq @ V0) @ V1))))))
(THOL.ex1_eq_1,(call @ (^[V0]: (cHOL.Ex1 @ (^[V1]: ((cHOL.eq @ V1) @ V0))))))
(THOL.impCE',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ V2)) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V2)) @ V2))))))))))
(THOL.imp_ex,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.implies @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ V1)))))))))
(THOL.not_ex,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.Ex @ (^[V1]: (V0 @ V1))))) @ (cHOL.All @ (^[V1]: (cHOL.Not @ (V0 @ V1))))))))
(THOL.or_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.disj @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cHOL.implies @ V0) @ V2)) @ ((cHOL.implies @ ((cHOL.implies @ V1) @ V2)) @ V2))))))))))
(THOL.rev_mp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((cHOL.implies @ V0) @ V1)) @ V1)))))))
(THOL.ssubst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (V2 @ V1)) @ (V2 @ V0))))))))))
(THOL.the1I2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))) @ (V1 @ (cHOL.The @ (^[V2]: (V0 @ V2)))))))))))
(TMap.domIff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cMap.dom @ V1))) @ (cHOL.Not @ ((cHOL.eq @ (V1 @ V0)) @ cOption.option.None))))))))
(TMap.dom_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cMap.dom @ (^[V3]: (((cHOL.If @ (V0 @ V3)) @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ (cMap.dom @ V1)) @ (cSet.Collect @ (^[V3]: (V0 @ V3))))) @ ((cLattices.inf_class.inf @ (cMap.dom @ V2)) @ (cSet.Collect @ (^[V3]: (cHOL.Not @ (V0 @ V3))))))))))))))
(TNat.max_0L,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.max @ cNat.zero_nat_inst.zero_nat) @ V0)) @ V0))))
(TNat.max_0R,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V0))))
(TNat.min_0L,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.min @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TNat.min_0R,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat))))
(TPure.termI,(call @ (^[V0]: (cPure.term @ V0))))
(TSet.ComplD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cHOL.Not @ ((cSet.member @ V0) @ V1))))))))
(TSet.ComplE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ V2)) @ V2)))))))))
(TSet.ComplI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cSet.member @ V0) @ V1)) @ cHOL.False)) @ ((cSet.member @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TSet.DiffD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cSet.member @ V0) @ V1)))))))))
(TSet.DiffD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((c==> @ ((cSet.member @ V0) @ V2)) @ V3)))))))))))
(TSet.Int_ac_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TSet.Int_ac_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V1) @ V0)))))))
(TSet.Int_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TSet.Int_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TSet.UNIV_I,(call @ (^[V0]: ((cSet.member @ V0) @ cOrderings.top_class.top))))
(TSet.Un_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cHOL.disj @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.Un_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cHOL.disj @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.bex_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cHOL.disj @ ((cSet.Bex @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Bex @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.emptyE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.bot_class.bot)) @ V1))))))
(TSet.imageE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cSet.image @ (^[V4]: (V1 @ V4))) @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V4))) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ V3))))) @ V3)))))))))))
(TSet.imageI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ (V2 @ V0)) @ ((cSet.image @ V2) @ V1))))))))))
(TSet.rangeE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cSet.image @ (^[V3]: (V1 @ V3))) @ cOrderings.top_class.top))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V3))) @ V2)))) @ V2)))))))))
(TSet.rangeI,(call @ (^[V0]: (call @ (^[V1]: ((cSet.member @ (V0 @ V1)) @ ((cSet.image @ V0) @ cOrderings.top_class.top)))))))
(TSet.set_mp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TATP.fEx_def,(call @ (^[V0]: ((cHOL.eq @ (cATP.fEx @ V0)) @ (cHOL.Ex @ V0)))))
(TATP.fEx_law,(call @ (^[V0]: ((cHOL.eq @ (cATP.fNot @ (cATP.fEx @ V0))) @ (cATP.fAll @ (cATP.fComp @ V0))))))
(TFun.bij_def,(call @ (^[V0]: ((cHOL.eq @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.conj @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))))))
(TFun.comp_id,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ V0) @ cFun.id)) @ V0))))
(TFun.id_comp,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ cFun.id) @ V0)) @ V0))))
(TFun.inj_fun,(call @ (^[V0]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ (^[V1]: (^[V2]: (V0 @ V1)))) @ cOrderings.top_class.top)))))
(TFun.inj_onD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V0 @ V2)) @ (V0 @ V3))) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cHOL.eq @ V2) @ V3))))))))))))))
(TFun.inj_onI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((c==> @ ((cHOL.eq @ (V1 @ V2)) @ (V1 @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))) @ ((cFun.inj_on @ V1) @ V0)))))))
(TFun.o_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.comp @ V0) @ V1) @ V2)) @ (V0 @ (V1 @ V2))))))))))
(TFun.o_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ V0) @ ((cFun.comp @ V1) @ V2))) @ ((cFun.comp @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TFun.surj_id,((cHOL.eq @ ((cSet.image @ cFun.id) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(THOL.All_def,(call @ (^[V0]: ((c== @ (cHOL.All @ V0)) @ ((cHOL.eq @ V0) @ (^[V1]: cHOL.True))))))
(THOL.Ex1_def,(call @ (^[V0]: ((c== @ (cHOL.Ex1 @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ (V0 @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ ((cHOL.eq @ V2) @ V1)))))))))))
(THOL.Let_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.Let @ V0) @ V1)) @ (V1 @ V0)))))))
(THOL.and_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.conj @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cHOL.implies @ V0) @ ((cHOL.implies @ V1) @ V2))) @ V2)))))))))
(THOL.conj_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ ((cHOL.conj @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V1) @ V2))))))))))
(THOL.conj_ac_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V1) @ V2))) @ ((cHOL.conj @ V1) @ ((cHOL.conj @ V0) @ V2))))))))))
(THOL.conj_ac_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V1) @ V0)))))))
(THOL.disj_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ ((cHOL.disj @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V1) @ V2))))))))))
(THOL.disj_ac_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.disj @ V1) @ ((cHOL.disj @ V0) @ V2))))))))))
(THOL.disj_ac_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ V1) @ V0)))))))
(THOL.eqTrueE,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ V0) @ cHOL.True)) @ V0))))
(THOL.eqTrueI,(call @ (^[V0]: ((c==> @ V0) @ ((cHOL.eq @ V0) @ cHOL.True)))))
(THOL.eq_True,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.True)) @ V0))))
(THOL.ex_comm,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(THOL.ex_ex1I,(call @ (^[V0]: ((c==> @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (V0 @ V2)) @ ((cHOL.eq @ V1) @ V2)))))))) @ (cHOL.Ex1 @ (^[V1]: (V0 @ V1))))))))
(THOL.if_True,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cHOL.If @ cHOL.True) @ V0) @ V1)) @ V0))))))
(THOL.if_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ (cHOL.Not @ V1)) @ ((cHOL.eq @ V4) @ V5))) @ ((cHOL.eq @ (((cHOL.If @ V0) @ V2) @ V4)) @ (((cHOL.If @ V1) @ V3) @ V5))))))))))))))))))
(THOL.iff_exI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.eq @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(THOL.imp_all,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.implies @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ V1)))))))))
(THOL.not_all,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.All @ (^[V1]: (V0 @ V1))))) @ (cHOL.Ex @ (^[V1]: (cHOL.Not @ (V0 @ V1))))))))
(THOL.not_def,(call @ (^[V0]: ((c== @ (cHOL.Not @ V0)) @ ((cHOL.implies @ V0) @ cHOL.False)))))
(THOL.not_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ V0) @ (cHOL.Not @ V1))))))))
(THOL.not_imp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.implies @ V0) @ V1))) @ ((cHOL.conj @ V0) @ (cHOL.Not @ V1))))))))
(THOL.not_not,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(THOL.not_sym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))))))))
(THOL.notnotD,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(THOL.uncurry,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.implies @ V0) @ ((cHOL.implies @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.conj @ V0) @ V1)) @ V2)))))))))
(TInt.Neg_def,((cHOL.eq @ cInt.Neg) @ cNum.neg_numeral_class.neg_numeral))
(TInt.Pos_def,((cHOL.eq @ cInt.Pos) @ cNum.numeral_class.numeral))
(TInt.dup_def,(call @ (^[V0]: ((cHOL.eq @ (cInt.dup @ V0)) @ ((cInt.plus_int_inst.plus_int @ V0) @ V0)))))
(TInt.inj_int,((cFun.inj_on @ cNat.semiring_1_class.of_nat) @ cOrderings.top_class.top))
(TInt.int_Suc,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V0))) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ (cNat.semiring_1_class.of_nat @ V0))))))
(TInt.int_def,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (cInt.Abs_Integ @ ((cProduct_Type.Pair @ V0) @ cNat.zero_nat_inst.zero_nat))))))
(TInt.nat.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ cHOL.eq) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))))))
(TInt.nat_def,((c== @ cInt.nat) @ (((cFun.map_fun @ cInt.Rep_Integ) @ cFun.id) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)))))))
(TInt.nat_int,(call @ (^[V0]: ((cHOL.eq @ (cInt.nat @ (cNat.semiring_1_class.of_nat @ V0))) @ V0))))
(TInt.sub_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.sub @ V0) @ V1)) @ ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TInt.zle_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TList.Nil_tl,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cList.list.Nil) @ (cList.tl @ V0))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))))))
(TList.drop_0,(call @ (^[V0]: ((cHOL.eq @ ((cList.drop @ cNat.zero_nat_inst.zero_nat) @ V0)) @ V0))))
(TList.hd_def,((c== @ cList.hd) @ (^[V0]: (((cList.list.list_rec @ cHOL.undefined) @ (^[V1]: (^[V2]: (^[V3]: V1)))) @ V0))))
(TList.hd_map,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.hd @ ((cList.map @ V1) @ V0))) @ (V1 @ (cList.hd @ V0)))))))))
(TList.hd_rev,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.hd @ (cList.rev @ V0))) @ (cList.last @ V0))))))
(TList.hd_upt,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ (cList.hd @ ((cList.upt @ V0) @ V1))) @ V0)))))))
(TList.listsE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cList.list.Cons @ V0) @ V1)) @ (cList.lists @ V2))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V2)) @ ((c==> @ ((cSet.member @ V1) @ (cList.lists @ V2))) @ V3))) @ V3)))))))))))
(TList.map.id,((cHOL.eq @ (cList.map @ cFun.id)) @ cFun.id))
(TList.map_tl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ V0) @ (cList.tl @ V1))) @ (cList.tl @ ((cList.map @ V0) @ V1))))))))
(TList.nth_tl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ (cList.tl @ V1)))) @ ((cHOL.eq @ ((cList.nth @ (cList.tl @ V1)) @ V0)) @ ((cList.nth @ V1) @ (cNat.Suc @ V0)))))))))
(TList.take_0,(call @ (^[V0]: ((cHOL.eq @ ((cList.take @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cList.list.Nil))))
(TList.tl_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.tl @ V0)) @ cList.list.Nil)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))))))
(TList.tl_def,((c== @ cList.tl) @ (^[V0]: (((cList.list.list_rec @ cList.list.Nil) @ (^[V1]: (^[V2]: (^[V3]: V2)))) @ V0))))
(TList.wf_lex,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ (cList.lex @ V0))))))
(TList.wf_set,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wf @ (cList.set @ V0))) @ (cTransitive_Closure.acyclic @ (cList.set @ V0))))))
(TMap.dom_def,(call @ (^[V0]: ((cHOL.eq @ (cMap.dom @ V0)) @ (cSet.Collect @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (V0 @ V1)) @ cOption.option.None))))))))
(TMap.ran_def,(call @ (^[V0]: ((cHOL.eq @ (cMap.ran @ V0)) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (cOption.option.Some @ V1))))))))))
(TMeson.abs_B,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (^[V2]: (V0 @ (V1 @ V2)))) @ ((cMeson.COMBB @ V0) @ V1)))))))
(TMeson.abs_C,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (^[V2]: ((V0 @ V2) @ V1))) @ ((cMeson.COMBC @ V0) @ V1)))))))
(TMeson.abs_I,((c== @ (^[V0]: V0)) @ cMeson.COMBI))
(TMeson.abs_K,(call @ (^[V0]: ((c== @ (^[V1]: V0)) @ (cMeson.COMBK @ V0)))))
(TMeson.abs_S,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (^[V2]: ((V0 @ V2) @ (V1 @ V2)))) @ ((cMeson.COMBS @ V0) @ V1)))))))
(TNat.Let_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.Let @ (cNat.Suc @ V0)) @ V1)) @ (V1 @ (cNat.Suc @ V0))))))))
(TNat.Nat_def,((c== @ cNat.Nat) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ cNat.Zero_Rep)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cNat.Suc_Rep @ V2))) @ (V0 @ V2))))))))))
(TNat.Suc_def,(call @ (^[V0]: ((cHOL.eq @ (cNat.Suc @ V0)) @ (cNat.Abs_Nat @ (cNat.Suc_Rep @ (cNat.Rep_Nat @ V0)))))))
(TNat.Suc_leD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.Suc_leI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)))))))
(TNat.add_leE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ V3))) @ V3)))))))))))
(TNat.inj_Suc,(call @ (^[V0]: ((cFun.inj_on @ cNat.Suc) @ V0))))
(TNat.le_0_eq,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.le_SucE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.Suc @ V1))) @ ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ (cNat.Suc @ V1))) @ V2)) @ V2))))))))))
(TNat.le_SucI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.Suc @ V1))))))))
(TNat.le_add1,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)))))))
(TNat.le_add2,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V0)))))))
(TNat.le_cube,(call @ (^[V0]: ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V0) @ V0))))))
(TNat.le_refl,(call @ (^[V0]: ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V0))))
(TNat.not_gr0,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0))) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TNum.add_One,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One)) @ (cNum.inc @ V0)))))
(TNum.add_inc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ V0) @ (cNum.inc @ V1))) @ (cNum.inc @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.inc_def,((c== @ cNum.inc) @ (^[V0]: ((((cNum.num.num_rec @ (cNum.num.Bit0 @ cNum.num.One)) @ (^[V1]: (^[V2]: (cNum.num.Bit1 @ V1)))) @ (^[V1]: (^[V2]: (cNum.num.Bit0 @ V2)))) @ V0))))
(TNum.mult_1s_4,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))) @ (cGroups.uminus_class.uminus @ V0)))))
(TNum.mult_1s_3,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)) @ (cGroups.uminus_class.uminus @ V0)))))
(TNum.mult_1s_2,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ cNum.num.One))) @ V0))))
(TNum.mult_1s_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ cNum.num.One)) @ V0)) @ V0))))
(TNum.pow_def,((c== @ cNum.pow) @ (^[V0]: (^[V1]: (((((cNum.num.num_rec @ (^[V2]: V2)) @ (^[V2]: (^[V3]: (^[V4]: (cNum.sqr @ (V3 @ V4)))))) @ (^[V2]: (^[V3]: (^[V4]: ((cNum.times_num_inst.times_num @ (cNum.sqr @ (V3 @ V4))) @ V4))))) @ V1) @ V0)))))
(TNum.sqr_def,((c== @ cNum.sqr) @ (^[V0]: ((((cNum.num.num_rec @ cNum.num.One) @ (^[V1]: (^[V2]: (cNum.num.Bit0 @ (cNum.num.Bit0 @ V2))))) @ (^[V1]: (^[V2]: (cNum.num.Bit1 @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V2) @ V1)))))) @ V0))))
(TPure.asm_rl,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TPure.cut_rl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TSMT.pat_def,(call @ (^[V0]: ((cHOL.eq @ (cSMT.pat @ V0)) @ cSMT.pattern.Pattern))))
(TSet.Bex_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))))))))
(TSet.Diff_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.minus_class.minus @ V0) @ V2))))))))))
(TSet.Diff_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TSet.Int_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.Int_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.Pow_def,(call @ (^[V0]: ((cHOL.eq @ (cSet.Pow @ V0)) @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet.Pow_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cSet.Pow @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet.Pow_top,(call @ (^[V0]: ((cSet.member @ V0) @ (cSet.Pow @ V0)))))
(TSet.Un_Diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cGroups.minus_class.minus @ V0) @ V2)) @ ((cGroups.minus_class.minus @ V1) @ V2))))))))))
(TSet.Un_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V3)))))))))))))
(TSet.ball_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cHOL.conj @ ((cSet.Ball @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Ball @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.ex_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(TSet.in_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.implies @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.insertE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V3)) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V2)) @ V3)) @ V3))))))))))))
(TSet.mono_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (V0 @ V1)) @ (V0 @ V2))) @ (V0 @ ((cLattices.sup_class.sup @ V1) @ V2)))))))))))
(TSet.set_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet.subsetD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.subsetI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet.vimageD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cSet.vimage @ V1) @ V2))) @ ((cSet.member @ (V1 @ V0)) @ V2)))))))))
(TSet.vimageE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cSet.vimage @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (V1 @ V0)) @ V4)) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ V3))))) @ V3)))))))))))
(TSet.vimageI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((cSet.member @ V1) @ ((cSet.vimage @ V0) @ V3)))))))))))))
(TATP.fAll_def,(call @ (^[V0]: ((cHOL.eq @ (cATP.fAll @ V0)) @ (cHOL.All @ V0)))))
(TATP.fAll_law,(call @ (^[V0]: ((cHOL.eq @ (cATP.fNot @ (cATP.fAll @ V0))) @ (cATP.fEx @ (cATP.fComp @ V0))))))
(TATP.fNot_def,(call @ (^[V0]: ((cHOL.eq @ (cATP.fNot @ V0)) @ (cHOL.Not @ V0)))))
(TATP.fNot_law,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cATP.fNot @ V0)) @ V0)))))
(TEnum.mlex_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cWellfounded.mlex_prod @ V0) @ V1)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V2)) @ (V0 @ V3))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ (V0 @ V2)) @ (V0 @ V3))) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)))))))))))))
(TFun.INF_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ ((cFun.comp @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cSet.image @ V2) @ V0)) @ V1)))))))))
(TFun.SUP_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ ((cFun.comp @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet.image @ V2) @ V0)) @ V1)))))))))
(TFun.bij_comp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((c==> @ (((cFun.bij_betw @ V1) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ (((cFun.bij_betw @ ((cFun.comp @ V1) @ V0)) @ cOrderings.top_class.top) @ cOrderings.top_class.top))))))))
(TFun.comp_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ (^[V2]: (V0 @ (V1 @ V2)))))))))
(TFun.fcomp_id,(call @ (^[V0]: ((cHOL.eq @ ((cFun.fcomp @ V0) @ cFun.id)) @ V0))))
(TFun.id_apply,(call @ (^[V0]: ((cHOL.eq @ (cFun.id @ V0)) @ V0))))
(TFun.id_fcomp,(call @ (^[V0]: ((cHOL.eq @ ((cFun.fcomp @ cFun.id) @ V0)) @ V0))))
(TFun.image_id,((cHOL.eq @ (cSet.image @ cFun.id)) @ cFun.id))
(TFun.inj_comp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cFun.inj_on @ V1) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ ((cFun.comp @ V0) @ V1)) @ cOrderings.top_class.top))))))))
(TFun.set.comp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (cSet.vimage @ V0)) @ (cSet.vimage @ V1))) @ (cSet.vimage @ ((cFun.comp @ V1) @ V0))))))))
(TFun.surj_def,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (V0 @ V2))))))))))
(TFun.swap_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.swap @ V0) @ V1) @ V2)) @ (((cFun.fun_upd @ (((cFun.fun_upd @ V2) @ V0) @ (V2 @ V1))) @ V1) @ (V2 @ V0))))))))))
(TGroups.Let_0,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.Let @ cGroups.zero_class.zero) @ V0)) @ (V0 @ cGroups.zero_class.zero)))))
(TGroups.Let_1,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.Let @ cGroups.one_class.one) @ V0)) @ (V0 @ cGroups.one_class.one)))))
(THOL.Eq_TrueI,(call @ (^[V0]: ((c==> @ V0) @ ((c== @ V0) @ cHOL.True)))))
(THOL.True_def,((c== @ cHOL.True) @ ((cHOL.eq @ (^[V0]: V0)) @ (^[V0]: V0))))
(THOL.all_comm,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(THOL.all_dupE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (V0 @ V3)))) @ ((c==> @ ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V3]: (V0 @ V3)))) @ V2))) @ V2)))))))))
(THOL.alt_ex1E,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ (V0 @ V3)) @ (V0 @ V4))) @ ((cHOL.eq @ V3) @ V4))))))) @ V1))))) @ V1)))))))
(THOL.arg_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (V2 @ V0)) @ (V2 @ V1))))))))))
(THOL.eq_False,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(THOL.eq_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cHOL.eq @ V1) @ V2))))))))))
(THOL.eq_cong2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c== @ ((c== @ V2) @ V0)) @ ((c== @ V2) @ V1))))))))))
(THOL.ex_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.implies @ V0) @ (V1 @ V2))))) @ ((cHOL.implies @ V0) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(THOL.ex_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ V1)))) @ ((cHOL.implies @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(THOL.ex_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.disj @ V0) @ (V1 @ V2))))) @ ((cHOL.disj @ V0) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(THOL.ex_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(THOL.ex_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ V0) @ (V1 @ V2))))) @ ((cHOL.conj @ V0) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(THOL.ex_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ V1)))) @ ((cHOL.conj @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(THOL.fun_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))))))))
(THOL.if_False,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cHOL.If @ cHOL.False) @ V0) @ V1)) @ V1))))))
(THOL.if_not_P,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ V0)) @ ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ V2)))))))))
(THOL.iff_allI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.eq @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(THOL.imp_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.implies @ V0) @ V2)) @ ((cHOL.implies @ V1) @ V3)))))))))))))
(THOL.imp_elim,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V2)) @ V0)) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(THOL.rev_notE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((c==> @ (cHOL.Not @ V1)) @ (cHOL.Not @ V0))) @ V1)))))))
(THOL.split_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cHOL.If @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ V1) @ (V0 @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ (V0 @ V3)))))))))))))
(TInt.dup_code_3,(call @ (^[V0]: ((cHOL.eq @ (cInt.dup @ (cInt.Neg @ V0))) @ (cInt.Neg @ (cNum.num.Bit0 @ V0))))))
(TInt.dup_code_2,(call @ (^[V0]: ((cHOL.eq @ (cInt.dup @ (cInt.Pos @ V0))) @ (cInt.Pos @ (cNum.num.Bit0 @ V0))))))
(TInt.dup_code_1,((cHOL.eq @ (cInt.dup @ cInt.zero_int_inst.zero_int)) @ cInt.zero_int_inst.zero_int))
(TInt.int_mult,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TInt.nat_0_le,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cInt.nat @ V0))) @ V0)))))
(TInt.nat_code_3,(call @ (^[V0]: ((cHOL.eq @ (cInt.nat @ (cInt.Pos @ V0))) @ (cNum.nat_of_num @ V0)))))
(TInt.nat_code_2,((cHOL.eq @ (cInt.nat @ cInt.zero_int_inst.zero_int)) @ cNat.zero_nat_inst.zero_nat))
(TInt.nat_code_1,(call @ (^[V0]: ((cHOL.eq @ (cInt.nat @ (cInt.Neg @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TInt.nat_le_0,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ (cInt.nat @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TInt.nat_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))))))))
(TInt.sub_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cInt.minus_int_inst.minus_int @ (cInt.dup @ ((cInt.sub @ V0) @ V1))) @ cInt.one_int_inst.one_int)))))))
(TInt.sub_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cInt.plus_int_inst.plus_int @ (cInt.dup @ ((cInt.sub @ V0) @ V1))) @ cInt.one_int_inst.one_int)))))))
(TInt.sub_code_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cInt.dup @ ((cInt.sub @ V0) @ V1))))))))
(TInt.sub_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cInt.dup @ ((cInt.sub @ V0) @ V1))))))))
(TInt.sub_code_5,(call @ (^[V0]: ((cHOL.eq @ ((cInt.sub @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cInt.Neg @ (cNum.num.Bit0 @ V0))))))
(TInt.sub_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cInt.sub @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cInt.Neg @ (cNum.BitM @ V0))))))
(TInt.sub_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cInt.sub @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cInt.Pos @ (cNum.num.Bit0 @ V0))))))
(TInt.sub_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cInt.sub @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cInt.Pos @ (cNum.BitM @ V0))))))
(TInt.sub_code_1,((cHOL.eq @ ((cInt.sub @ cNum.num.One) @ cNum.num.One)) @ cInt.zero_int_inst.zero_int))
(TInt.zabs_def,(call @ (^[V0]: ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ (cInt.uminus_int_inst.uminus_int @ V0)) @ V0)))))
(TInt.zadd_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ (cNat.semiring_1_class.of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TInt.zdvd1_eq,(call @ (^[V0]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ cInt.one_int_inst.one_int)) @ ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ V0)) @ cInt.one_int_inst.one_int)))))
(TInt.zdvd_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TInt.zsgn_def,(call @ (^[V0]: ((cHOL.eq @ (cInt.sgn_int_inst.sgn_int @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ cInt.zero_int_inst.zero_int) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ cInt.one_int_inst.one_int) @ (cInt.uminus_int_inst.uminus_int @ cInt.one_int_inst.one_int)))))))
(TList.Bex_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ (cList.set @ V0)) @ V1)) @ ((cList.list_ex @ V1) @ V0)))))))
(TList.Pow_set_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Pow @ (cList.set @ ((cList.list.Cons @ V0) @ V1)))) @ ((cHOL.Let @ (cSet.Pow @ (cList.set @ V1))) @ (^[V2]: ((cLattices.sup_class.sup @ V2) @ ((cSet.image @ (cSet.insert @ V0)) @ V2))))))))))
(TList.Pow_set_1,((cHOL.eq @ (cSet.Pow @ (cList.set @ cList.list.Nil))) @ ((cSet.insert @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot)))
(TList.drop_tl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.drop @ V0) @ (cList.tl @ V1))) @ (cList.tl @ ((cList.drop @ V0) @ V1))))))))
(TList.fold_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cList.set @ V0))) @ ((cHOL.eq @ (V1 @ V2)) @ cFun.id))))) @ ((cHOL.eq @ ((cList.fold @ V1) @ V0)) @ cFun.id)))))))
(TList.inj_map,(call @ (^[V0]: ((cHOL.eq @ ((cFun.inj_on @ (cList.map @ V0)) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)))))
(TList.last_tl,(call @ (^[V0]: ((c==> @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cHOL.Not @ ((cHOL.eq @ (cList.tl @ V0)) @ cList.list.Nil)))) @ ((cHOL.eq @ (cList.last @ (cList.tl @ V0))) @ (cList.last @ V0))))))
(TList.lex_def,(call @ (^[V0]: ((cHOL.eq @ (cList.lex @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: ((cList.lexn @ V0) @ V1)))))))
(TList.listspE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cList.listsp @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((c==> @ ((c==> @ (V0 @ V1)) @ ((c==> @ ((cList.listsp @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TList.map_def,((c== @ cList.map) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((cList.list.Cons @ (V5 @ V2)) @ (V4 @ V5))))))) @ V1) @ V0)))))
(TList.map_ext,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.implies @ ((cSet.member @ V3) @ (cList.set @ V0))) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cHOL.eq @ ((cList.map @ V1) @ V0)) @ ((cList.map @ V2) @ V0))))))))))
(TList.map_idI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cList.set @ V0))) @ ((cHOL.eq @ (V1 @ V2)) @ V2))))) @ ((cHOL.eq @ ((cList.map @ V1) @ V0)) @ V0)))))))
(TList.map_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TList.map_nth,(call @ (^[V0]: ((cHOL.eq @ ((cList.map @ (^[V1]: ((cList.nth @ V0) @ V1))) @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V0)))) @ V0))))
(TList.nth_def,((c== @ cList.nth) @ (^[V0]: (((cList.list.list_rec @ cHOL.undefined) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: (((cNat.nat.nat_case @ V1) @ (^[V5]: (V3 @ V5))) @ V4)))))) @ V0))))
(TList.nth_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.nth @ ((cList.map @ V2) @ V1)) @ V0)) @ (V2 @ ((cList.nth @ V1) @ V0)))))))))))
(TList.nth_mem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cSet.member @ ((cList.nth @ V1) @ V0)) @ (cList.set @ V1))))))))
(TList.nth_upt,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ ((cList.nth @ ((cList.upt @ V0) @ V2)) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))))
(TList.nth_zip,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V2))) @ ((cHOL.eq @ ((cList.nth @ ((cList.zip @ V1) @ V2)) @ V0)) @ ((cProduct_Type.Pair @ ((cList.nth @ V1) @ V0)) @ ((cList.nth @ V2) @ V0))))))))))))
(TList.rev_def,((c== @ cList.rev) @ (^[V0]: (((cList.list.list_rec @ cList.list.Nil) @ (^[V1]: (^[V2]: (^[V3]: ((cList.append @ V3) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))) @ V0))))
(TList.rev_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rev @ ((cList.map @ V0) @ V1))) @ ((cList.map @ V0) @ (cList.rev @ V1))))))))
(TList.rev_nth,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.nth @ (cList.rev @ V1)) @ V0)) @ ((cList.nth @ V1) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V1)) @ (cNat.Suc @ V0))))))))))
(TList.rotate0,((cHOL.eq @ (cList.rotate @ cNat.zero_nat_inst.zero_nat)) @ cFun.id))
(TList.set_def,((c== @ cList.set) @ (^[V0]: (((cList.list.list_rec @ cOrderings.bot_class.bot) @ (^[V1]: (^[V2]: (^[V3]: ((cSet.insert @ V1) @ V3))))) @ V0))))
(TList.set_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.map @ V0) @ V1))) @ ((cSet.image @ V0) @ (cList.set @ V1))))))))
(TList.set_rev,(call @ (^[V0]: ((cHOL.eq @ (cList.set @ (cList.rev @ V0))) @ (cList.set @ V0)))))
(TList.set_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.upt @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)))))))
(TList.set_zip,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.zip @ V0) @ V1))) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ ((cList.nth @ V0) @ V3)) @ ((cList.nth @ V1) @ V3)))) @ ((cNat.ord_nat_inst.less_nat @ V3) @ ((cOrderings.ord_class.min @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))))))))
(TList.take_tl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.take @ V0) @ (cList.tl @ V1))) @ (cList.tl @ ((cList.take @ (cNat.Suc @ V0)) @ V1))))))))
(TList.tl_drop,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.tl @ ((cList.drop @ V0) @ V1))) @ ((cList.drop @ V0) @ (cList.tl @ V1))))))))
(TList.tl_take,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.tl @ ((cList.take @ V0) @ V1))) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ (cList.tl @ V1))))))))
(TList.upt_def,((c== @ cList.upt) @ (^[V0]: (^[V1]: ((((cNat.nat.nat_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (((cHOL.If @ ((cNat.ord_nat_inst.less_eq_nat @ V4) @ V2)) @ ((cList.append @ (V3 @ V4)) @ ((cList.list.Cons @ V2) @ cList.list.Nil))) @ cList.list.Nil))))) @ V1) @ V0)))))
(TList.upt_rec,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upt @ V0) @ V1)) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cList.list.Cons @ V0) @ ((cList.upt @ (cNat.Suc @ V0)) @ V1))) @ cList.list.Nil)))))))
(TList.wf_lexn,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ ((cList.lexn @ V0) @ V1))))))))
(TList.zip_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.zip @ cList.list.Nil) @ V0)) @ cList.list.Nil))))
(TList.zip_def,((c== @ cList.zip) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ ((cProduct_Type.Pair @ V6) @ V2)) @ (V4 @ V7))))) @ V5)))))) @ V1) @ V0)))))
(TList.zip_rev,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.zip @ (cList.rev @ V0)) @ (cList.rev @ V1))) @ (cList.rev @ ((cList.zip @ V0) @ V1)))))))))
(TNat.Suc_le_D,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cNat.Suc @ V2))))))))))
(TNat.Suc_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))))))))
(TNat.Suc_pred,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ (cNat.Suc @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))) @ V0)))))
(TNat.add_gr_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1))))))))
(TNat.add_is_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TNat.add_is_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TNat.add_leD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2)))))))))
(TNat.add_leD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)))))))))
(TNat.le_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat.le_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.le_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2))))))))))
(TNat.less_one,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.max_Suc1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNat.Suc @ V0)) @ V1)) @ (((cNat.nat.nat_case @ (cNat.Suc @ V0)) @ (^[V2]: (cNat.Suc @ ((cOrderings.ord_class.max @ V0) @ V2)))) @ V1)))))))
(TNat.max_Suc2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ (cNat.Suc @ V1))) @ (((cNat.nat.nat_case @ (cNat.Suc @ V1)) @ (^[V2]: (cNat.Suc @ ((cOrderings.ord_class.max @ V2) @ V1)))) @ V0)))))))
(TNat.min_Suc1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNat.Suc @ V0)) @ V1)) @ (((cNat.nat.nat_case @ cNat.zero_nat_inst.zero_nat) @ (^[V2]: (cNat.Suc @ ((cOrderings.ord_class.min @ V0) @ V2)))) @ V1)))))))
(TNat.min_Suc2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ (cNat.Suc @ V1))) @ (((cNat.nat.nat_case @ cNat.zero_nat_inst.zero_nat) @ (^[V2]: (cNat.Suc @ ((cOrderings.ord_class.min @ V2) @ V1)))) @ V0)))))))
(TNat.min_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ ((cOrderings.ord_class.min @ V0) @ V2)) @ V1)))))))))
(TNat.mono_Suc,(cOrderings.order_class.mono @ cNat.Suc))
(TNat.nat.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ (cNat.Suc @ V2))) @ ((V1 @ V2) @ (((cNat.nat.nat_rec @ V0) @ V1) @ V2))))))))))
(TNat.nat.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))
(TNat.nat.size_4,(call @ (^[V0]: ((cHOL.eq @ (cNat.nat.size_nat_inst.size_nat @ (cNat.Suc @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.nat.size_nat_inst.size_nat @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TNat.nat.size_3,((cHOL.eq @ (cNat.nat.size_nat_inst.size_nat @ cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat))
(TNat.nat.size_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.nat.nat_size @ (cNat.Suc @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.nat.nat_size @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TNat.nat.size_1,((cHOL.eq @ (cNat.nat.nat_size @ cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat))
(TNum.BitM_def,((c== @ cNum.BitM) @ (^[V0]: ((((cNum.num.num_rec @ cNum.num.One) @ (^[V1]: (^[V2]: (cNum.num.Bit1 @ V2)))) @ (^[V1]: (^[V2]: (cNum.num.Bit1 @ (cNum.num.Bit0 @ V1))))) @ V0))))
(TNum.mult_inc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ V0) @ (cNum.inc @ V1))) @ ((cNum.plus_num_inst.plus_num @ ((cNum.times_num_inst.times_num @ V0) @ V1)) @ V0)))))))
(TNum.num.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ (cNum.num.Bit1 @ V3))) @ ((V2 @ V3) @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ V3))))))))))))
(TNum.num.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ (cNum.num.Bit0 @ V3))) @ ((V1 @ V3) @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ V3))))))))))))
(TNum.num.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ cNum.num.One)) @ V0))))))))
(TNum.num.size_6,(call @ (^[V0]: ((cHOL.eq @ (cNum.num.size_num_inst.size_num @ (cNum.num.Bit1 @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.num.size_num_inst.size_num @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TNum.num.size_5,(call @ (^[V0]: ((cHOL.eq @ (cNum.num.size_num_inst.size_num @ (cNum.num.Bit0 @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.num.size_num_inst.size_num @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TNum.num.size_4,((cHOL.eq @ (cNum.num.size_num_inst.size_num @ cNum.num.One)) @ cNat.zero_nat_inst.zero_nat))
(TNum.num.size_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.num.num_size @ (cNum.num.Bit1 @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.num.num_size @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TNum.num.size_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.num.num_size @ (cNum.num.Bit0 @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.num.num_size @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TNum.num.size_1,((cHOL.eq @ (cNum.num.num_size @ cNum.num.One)) @ cNat.zero_nat_inst.zero_nat))
(TNum.numerals_2,((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNat.Suc @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))
(TNum.numerals_1,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ cNat.one_nat_inst.one_nat))
(TOption.ospec,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ (cOption.set @ V0)) @ (^[V3]: (V1 @ V3)))) @ ((c==> @ ((cHOL.eq @ V0) @ (cOption.option.Some @ V2))) @ (V1 @ V2))))))))))
(TPure.meta_mp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TPure.thin_rl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ V1) @ V1)))))))
(TRandom.range,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ (cProduct_Type.fst @ ((cRandom.range @ V0) @ V1))) @ V0)))))))
(TRelation.IdE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cRelation.Id)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V2))) @ V1)))) @ V1)))))))
(TRelation.IdI,(call @ (^[V0]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V0)) @ cRelation.Id))))
(TSet.Ball_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))))))))
(TSet.CollectD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V2]: (V1 @ V2))))) @ (V1 @ V0)))))))
(TSet.CollectE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V3]: (V1 @ V3))))) @ ((c==> @ ((c==> @ (V1 @ V0)) @ V2)) @ V2)))))))))
(TSet.CollectI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((cSet.member @ V1) @ (cSet.Collect @ (^[V2]: (V0 @ V2))))))))))
(TSet.Compl_Un,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TSet.Compl_eq,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cSet.Collect @ (^[V1]: (cHOL.Not @ ((cSet.member @ V1) @ V0))))))))
(TSet.Diff_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.minus_class.minus @ V0) @ V2))))))))))
(TSet.Diff_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V1)) @ (cHOL.Not @ ((cSet.member @ V0) @ V2)))))))))))
(TSet.Int_Diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))))))))))
(TSet.Int_UNIV,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.top_class.top)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ V1) @ cOrderings.top_class.top))))))))
(TSet.Int_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V3)))))))))))))
(TSet.Pow_UNIV,((cHOL.eq @ (cSet.Pow @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(TSet.Pow_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cSet.Pow @ V0)) @ (cSet.Pow @ V1))))))))
(TSet.UNIV_def,((cHOL.eq @ cOrderings.top_class.top) @ (cSet.Collect @ (^[V0]: cHOL.True))))
(TSet.Un_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TSet.Un_empty,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))))))
(TSet.Un_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V2)) @ V1))))))))))
(TSet.all_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.implies @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(TSet.bex_UNIV,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Bex @ cOrderings.top_class.top) @ V0)) @ (cHOL.Ex @ V0)))))
(TSet.bex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cSet.Bex @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TSet.bex_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V2]: V1))) @ ((cHOL.conj @ (cHOL.Ex @ (^[V2]: ((cSet.member @ V2) @ V0)))) @ V1)))))))
(TSet.bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.bind @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ ((cSet.image @ V1) @ V0)) @ (^[V3]: ((cSet.member @ V2) @ V3)))))))))))
(TSet.equals0D,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cSet.member @ V1) @ V0))))))))
(TSet.equals0I,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((c==> @ ((cSet.member @ V1) @ V0)) @ cHOL.False)))) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TSet.image_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2))))))))))
(TSet.imp_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V2) @ V3)) @ ((cHOL.implies @ ((cHOL.implies @ V1) @ V2)) @ ((cHOL.implies @ V0) @ V3)))))))))))))
(TSet.imp_refl,(call @ (^[V0]: ((cHOL.implies @ V0) @ V0))))
(TSet.insertCI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ V0) @ V2))) @ ((cSet.member @ V0) @ ((cSet.insert @ V2) @ V1))))))))))
(TSet.insertI1,(call @ (^[V0]: (call @ (^[V1]: ((cSet.member @ V0) @ ((cSet.insert @ V0) @ V1)))))))
(TSet.insertI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ ((cSet.insert @ V2) @ V1))))))))))
(TSet.mono_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ (V0 @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TSet.not_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ (cHOL.Not @ V0))))))))
(TSet.psubsetD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.psubsetE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V1) @ V0))) @ V2))) @ V2)))))))))
(TSet.psubsetI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TSet.rev_bexI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ (V2 @ V0)) @ ((cSet.Bex @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.subsetCE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V0))) @ V3)) @ ((c==> @ ((c==> @ ((cSet.member @ V2) @ V1)) @ V3)) @ V3))))))))))))
(TSet.vimageI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ (V0 @ V1)) @ V2)) @ ((cSet.member @ V1) @ ((cSet.vimage @ V0) @ V2))))))))))
(TATP.fComp_def,(call @ (^[V0]: ((cHOL.eq @ (cATP.fComp @ V0)) @ (^[V1]: (cHOL.Not @ (V0 @ V1)))))))
(TATP.fComp_law,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fComp @ V0) @ V1)) @ (cHOL.Not @ (V0 @ V1))))))))
(TATP.fEx_table_2,(call @ (^[V0]: ((cHOL.disj @ (cHOL.Ex @ V0)) @ ((cHOL.eq @ (cATP.fEx @ V0)) @ cATP.fFalse)))))
(TATP.fEx_table_1,(call @ (^[V0]: ((cHOL.disj @ (cHOL.All @ (cATP.fComp @ V0))) @ ((cHOL.eq @ (cATP.fEx @ V0)) @ cATP.fTrue)))))
(TATP.fTrue_def,((cHOL.eq @ cATP.fTrue) @ cHOL.True))
(TATP.fconj_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fconj @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V1)))))))
(TATP.fdisj_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fdisj @ V0) @ V1)) @ ((cHOL.disj @ V0) @ V1)))))))
(TDivides.div_1,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ V0))))
(TDivides.mod_1,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ cNat.zero_nat_inst.zero_nat))))
(TEnum.all_code,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ (cEnum.enum_class.enum_all @ V0)))))
(TFun.comp_surj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ ((cSet.image @ V1) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ ((cFun.comp @ V1) @ V0)) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))))))))
(TFun.comp_swap,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cFun.comp @ V0) @ (((cFun.swap @ V1) @ V2) @ V3))) @ (((cFun.swap @ V1) @ V2) @ ((cFun.comp @ V0) @ V3))))))))))))
(TFun.fcomp_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.fcomp @ V0) @ V1)) @ (^[V2]: (V1 @ (V0 @ V2)))))))))
(TFun.image_INT,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V5]: ((cOrderings.ord_class.less_eq @ (V3 @ V5)) @ V1)))) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ V3))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ (^[V5]: ((cSet.image @ V0) @ (V3 @ V5)))))))))))))))))))
(TFun.image_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2)))))))))))
(TFun.inj_on_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.inj_on @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cHOL.conj @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.conj @ ((cFun.inj_on @ V0) @ V2)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet.image @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cSet.image @ V0) @ ((cGroups.minus_class.minus @ V2) @ V1)))) @ cOrderings.bot_class.bot)))))))))))
(TFun.inj_on_id,(call @ (^[V0]: ((cFun.inj_on @ cFun.id) @ V0))))
(TFun.o_eq_dest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ ((cFun.comp @ V2) @ V3))) @ ((cHOL.eq @ (V0 @ (V1 @ V4))) @ (V2 @ (V3 @ V4)))))))))))))))
(TFun.o_eq_elim,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ ((cFun.comp @ V2) @ V3))) @ ((c==> @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ (V0 @ (V1 @ V5))) @ (V2 @ (V3 @ V5)))))) @ V4)) @ V4)))))))))))))
(TFun.swap_self,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cFun.swap @ V0) @ V0) @ V1)) @ V1))))))
(TFun.vimage_id,((cHOL.eq @ (cSet.vimage @ cFun.id)) @ cFun.id))
(TGroups.add_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TGroups.add_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TGroups.add_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(THOL.Eq_FalseI,(call @ (^[V0]: ((c==> @ (cHOL.Not @ V0)) @ ((c== @ V0) @ cHOL.False)))))
(THOL.False_def,((c== @ cHOL.False) @ (cHOL.All @ (^[V0]: V0))))
(THOL.all_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ V0) @ (V1 @ V2))))) @ ((cHOL.implies @ V0) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(THOL.all_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ V1)))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(THOL.all_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.disj @ V0) @ (V1 @ V2))))) @ ((cHOL.disj @ V0) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(THOL.all_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ V1)))) @ ((cHOL.disj @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(THOL.all_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.conj @ V0) @ (V1 @ V2))))) @ ((cHOL.conj @ V0) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(THOL.all_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ V1)))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(THOL.arg_cong2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((cHOL.eq @ ((V4 @ V0) @ V2)) @ ((V4 @ V1) @ V3)))))))))))))))
(THOL.bool.size_4,((cHOL.eq @ (cHOL.bool.size_bool_inst.size_bool @ cHOL.False)) @ cNat.zero_nat_inst.zero_nat))
(THOL.bool.size_3,((cHOL.eq @ (cHOL.bool.size_bool_inst.size_bool @ cHOL.True)) @ cNat.zero_nat_inst.zero_nat))
(THOL.bool.size_2,((cHOL.eq @ (cHOL.bool.bool_size @ cHOL.False)) @ cNat.zero_nat_inst.zero_nat))
(THOL.bool.size_1,((cHOL.eq @ (cHOL.bool.bool_size @ cHOL.True)) @ cNat.zero_nat_inst.zero_nat))
(THOL.choice_eq,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (cHOL.Ex1 @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cHOL.Ex1 @ (^[V1]: (cHOL.All @ (^[V2]: ((V0 @ V2) @ (V1 @ V2))))))))))
(THOL.classical,(call @ (^[V0]: ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V0)) @ V0))))
(THOL.conj_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V3)))))))))))))
(THOL.conjunct1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ V0) @ V1)) @ V0))))))
(THOL.conjunct2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ V0) @ V1)) @ V1))))))
(THOL.disj_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V1)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.disj @ V0) @ V2)) @ ((cHOL.disj @ V1) @ V3)))))))))))))
(THOL.disj_not1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(THOL.disj_not2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ (cHOL.Not @ V1))) @ ((cHOL.implies @ V1) @ V0)))))))
(THOL.if_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V1)) @ V1))))))
(THOL.if_splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cHOL.If @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ V1) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.conj @ (cHOL.Not @ V1)) @ (cHOL.Not @ (V0 @ V3)))))))))))))))
(THOL.if_splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cHOL.If @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ V1) @ (V0 @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ (V0 @ V3)))))))))))))
(THOL.imp_conjL,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.implies @ ((cHOL.conj @ V0) @ V1)) @ V2)) @ ((cHOL.implies @ V0) @ ((cHOL.implies @ V1) @ V2))))))))))
(THOL.imp_conjR,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.implies @ V0) @ ((cHOL.conj @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V2))))))))))
(THOL.imp_disj1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ ((cHOL.implies @ V0) @ V1)) @ V2)) @ ((cHOL.implies @ V0) @ ((cHOL.disj @ V1) @ V2))))))))))
(THOL.imp_disj2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.implies @ V1) @ V2))) @ ((cHOL.implies @ V1) @ ((cHOL.disj @ V0) @ V2))))))))))
(THOL.imp_disjL,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.implies @ ((cHOL.disj @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ V2)) @ ((cHOL.implies @ V1) @ V2))))))))))
(THOL.nnf_simps_6,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(THOL.nnf_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ (cHOL.Not @ V1))) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ V1))))))))
(THOL.nnf_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1)))))))))
(THOL.nnf_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)))))))
(THOL.nnf_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(THOL.nnf_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(THOL.notFalseE,(call @ (^[V0]: ((c==> @ (cHOL.Not @ cHOL.False)) @ ((c==> @ V0) @ V0)))))
(THOL.rev_iffD1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V1)))))))
(THOL.rev_iffD2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((cHOL.eq @ V1) @ V0)) @ V1)))))))
(THOL.simp_thms_42,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cHOL.eq @ V0) @ V2)) @ (V1 @ V2))))) @ (V1 @ V0)))))))
(THOL.simp_thms_41,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cHOL.eq @ V2) @ V0)) @ (V1 @ V2))))) @ (V1 @ V0)))))))
(THOL.simp_thms_40,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ (V1 @ V2))))) @ (V1 @ V0)))))))
(THOL.simp_thms_39,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V0)) @ (V1 @ V2))))) @ (V1 @ V0)))))))
(THOL.simp_thms_38,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ V1))))))
(THOL.simp_thms_37,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V1) @ V0))))))
(THOL.simp_thms_36,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: V0))) @ V0))))
(THOL.simp_thms_35,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: V0))) @ V0))))
(THOL.simp_thms_34,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.disj @ V0) @ V1)))))))
(THOL.simp_thms_33,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V0)) @ V0))))
(THOL.simp_thms_32,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ cHOL.False) @ V0)) @ V0))))
(THOL.simp_thms_31,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ cHOL.False)) @ V0))))
(THOL.simp_thms_30,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ cHOL.True) @ V0)) @ cHOL.True))))
(THOL.simp_thms_29,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ cHOL.True)) @ cHOL.True))))
(THOL.simp_thms_28,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ (cHOL.Not @ V0)) @ V0)) @ cHOL.False))))
(THOL.simp_thms_27,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ (cHOL.Not @ V0))) @ cHOL.False))))
(THOL.simp_thms_26,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.conj @ V0) @ V1)))))))
(THOL.simp_thms_25,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V0)) @ V0))))
(THOL.simp_thms_24,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ cHOL.False) @ V0)) @ cHOL.False))))
(THOL.simp_thms_23,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ cHOL.False)) @ cHOL.False))))
(THOL.simp_thms_22,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ cHOL.True) @ V0)) @ V0))))
(THOL.simp_thms_21,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ cHOL.True)) @ V0))))
(THOL.simp_thms_20,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ (cHOL.Not @ V0))) @ (cHOL.Not @ V0)))))
(THOL.simp_thms_19,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(THOL.simp_thms_18,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ V0)) @ cHOL.True))))
(THOL.simp_thms_17,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ cHOL.True)) @ cHOL.True))))
(THOL.simp_thms_16,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ cHOL.False) @ V0)) @ cHOL.True))))
(THOL.simp_thms_15,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ cHOL.True) @ V0)) @ V0))))
(THOL.simp_thms_14,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(THOL.simp_thms_13,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cHOL.False) @ V0)) @ (cHOL.Not @ V0)))))
(THOL.simp_thms_12,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.True)) @ V0))))
(THOL.simp_thms_11,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cHOL.True) @ V0)) @ V0))))
(THOL.simp_thms_10,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ V0) @ (cHOL.Not @ V0))))))
(THOL.simp_thms_9,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cHOL.Not @ V0)) @ V0)))))
(THOL.simp_thms_8,((cHOL.eq @ (cHOL.Not @ cHOL.False)) @ cHOL.True))
(THOL.simp_thms_7,((cHOL.eq @ (cHOL.Not @ cHOL.True)) @ cHOL.False))
(THOL.simp_thms_6,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V0)) @ cHOL.True))))
(THOL.simp_thms_5,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V0)) @ cHOL.True))))
(THOL.simp_thms_4,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ (cHOL.Not @ V0))) @ cHOL.True))))
(THOL.simp_thms_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ V0) @ (cHOL.Not @ V1))))))))
(THOL.simp_thms_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(THOL.simp_thms_1,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(THOL.thin_refl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V0)) @ ((c==> @ V1) @ V1)))))))
(THOL.trans_sym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V1)) @ ((cHOL.eq @ V0) @ V2))))))))))
(TInt.abs_split,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (V0 @ (cGroups.abs_class.abs @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ (V0 @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ (V0 @ (cGroups.uminus_class.uminus @ V1))))))))))
(TInt.int_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V2))) @ V1)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V2))))) @ V1)))) @ V1)))))))
(TInt.int_power,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ (cNat.semiring_1_class.of_nat @ V0)) @ V1)))))))
(TInt.nat_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cInt.nat @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)))))
(TInt.nat_arith,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TInt.split_nat,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (V0 @ (cInt.nat @ V1))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cHOL.eq @ V1) @ (cNat.semiring_1_class.of_nat @ V2))) @ (V0 @ V2))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ (V0 @ cNat.zero_nat_inst.zero_nat)))))))))
(TInt.zdiff_int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ (cNat.semiring_1_class.of_nat @ V1)) @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))))))))
(TInt.zless_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TInt.zmult_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ (cNat.semiring_1_class.of_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))))))))
(TLifting.eq_OO,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcompp @ cHOL.eq) @ V0)) @ V0))))
(TList.Ball_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ (cList.set @ V0)) @ V1)) @ ((cList.list_all @ V1) @ V0)))))))
(TList.bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.bind @ V0) @ V1)) @ (cList.concat @ ((cList.map @ V1) @ V0))))))))
(TList.card_set,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ (cList.set @ V0))) @ (cNat.size_class.size @ (cList.remdups @ V0))))))
(TList.drop_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.drop @ (cNat.Suc @ V0)) @ V1)) @ ((cList.drop @ V0) @ (cList.tl @ V1))))))))
(TList.drop_all,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ V1)) @ ((cHOL.eq @ ((cList.drop @ V1) @ V0)) @ cList.list.Nil)))))))
(TList.drop_def,((c== @ cList.drop) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cNat.nat.nat_case @ ((cList.list.Cons @ V2) @ V3)) @ (^[V6]: (V4 @ V6))) @ V5)))))) @ V1) @ V0)))))
(TList.drop_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ V1) @ ((cList.drop @ V0) @ V2))))))))))
(TList.drop_upt,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.upt @ V1) @ V2))) @ ((cList.upt @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V0)) @ V2)))))))))
(TList.drop_zip,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.zip @ V1) @ V2))) @ ((cList.zip @ ((cList.drop @ V0) @ V1)) @ ((cList.drop @ V0) @ V2))))))))))
(TList.find_def,((c== @ cList.find) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cOption.option.None)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ (V5 @ V2)) @ (cOption.option.Some @ V2)) @ (V4 @ V5))))))) @ V1) @ V0)))))
(TList.fold_def,((c== @ cList.fold) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cFun.id)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((cFun.comp @ (V4 @ V5)) @ (V5 @ V2))))))) @ V1) @ V0)))))
(TList.fold_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.fold @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.fold @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TList.fold_rev,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V2) @ (cList.set @ V0))) @ ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V3)) @ (V1 @ V2))) @ ((cFun.comp @ (V1 @ V2)) @ (V1 @ V3)))))))))) @ ((cHOL.eq @ ((cList.fold @ V1) @ (cList.rev @ V0))) @ ((cList.fold @ V1) @ V0))))))))
(TList.hd.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.hd @ ((cList.list.Cons @ V0) @ V1))) @ V0))))))
(TList.inj_mapD,(call @ (^[V0]: ((c==> @ ((cFun.inj_on @ (cList.map @ V0)) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)))))
(TList.inj_mapI,(call @ (^[V0]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ (cList.map @ V0)) @ cOrderings.top_class.top)))))
(TList.last_def,((c== @ cList.last) @ (^[V0]: (((cList.list.list_rec @ cHOL.undefined) @ (^[V1]: (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ V1) @ V3))))) @ V0))))
(TList.last_map,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.last @ ((cList.map @ V1) @ V0))) @ (V1 @ (cList.last @ V0)))))))))
(TList.last_rev,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.last @ (cList.rev @ V0))) @ (cList.hd @ V0))))))
(TList.last_upt,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ (cList.last @ ((cList.upt @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ cNat.one_nat_inst.one_nat))))))))
(TList.lex_conv,(call @ (^[V0]: ((cHOL.eq @ (cList.lex @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V3) @ ((cList.list.Cons @ V4) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.append @ V3) @ ((cList.list.Cons @ V5) @ V7)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V0))))))))))))))))))))))
(TList.lexn_def,((c== @ cList.lexn) @ (^[V0]: (^[V1]: ((((cNat.nat.nat_rec @ (^[V2]: cOrderings.bot_class.bot)) @ (^[V2]: (^[V3]: (^[V4]: ((cLattices.inf_class.inf @ ((cSet.image @ ((cProduct_Type.map_pair @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cList.list.Cons @ V5) @ V6))))) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cList.list.Cons @ V5) @ V6)))))) @ ((cWellfounded.lex_prod @ V4) @ (V3 @ V4)))) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V5)) @ (cNat.Suc @ V2))) @ ((cHOL.eq @ (cNat.size_class.size @ V6)) @ (cNat.Suc @ V2)))))))))))) @ V1) @ V0)))))
(TList.map.comp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (cList.map @ V0)) @ (cList.map @ V1))) @ (cList.map @ ((cFun.comp @ V0) @ V1))))))))
(TList.map_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V1))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cList.map @ V2) @ V0)) @ ((cList.map @ V3) @ V1)))))))))))))
(TList.maps_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.maps @ V0) @ V1)) @ (cList.concat @ ((cList.map @ V0) @ V1))))))))
(TList.nth_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ (cNat.size_class.size @ V2))) @ ((cHOL.eq @ ((cList.nth @ ((cList.drop @ V0) @ V2)) @ V1)) @ ((cList.nth @ V2) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)))))))))))
(TList.nth_take,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cList.nth @ ((cList.take @ V1) @ V2)) @ V0)) @ ((cList.nth @ V2) @ V0))))))))))
(TList.null_def,(call @ (^[V0]: ((cHOL.eq @ (cList.null @ V0)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.null_rec_2,((cHOL.eq @ (cList.null @ cList.list.Nil)) @ cHOL.True))
(TList.null_rec_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.null @ ((cList.list.Cons @ V0) @ V1))) @ cHOL.False))))))
(TList.rev_drop,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rev @ ((cList.drop @ V0) @ V1))) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V1)) @ V0)) @ (cList.rev @ V1))))))))
(TList.rev_swap,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cList.rev @ V0)) @ V1)) @ ((cHOL.eq @ V0) @ (cList.rev @ V1))))))))
(TList.rev_take,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rev @ ((cList.take @ V0) @ V1))) @ ((cList.drop @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V1)) @ V0)) @ (cList.rev @ V1))))))))
(TList.set_upto,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.upto @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)))))))
(TList.take_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ ((cList.take @ (cNat.Suc @ V1)) @ V0)) @ ((cList.list.Cons @ (cList.hd @ V0)) @ ((cList.take @ V1) @ (cList.tl @ V0))))))))))
(TList.take_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cList.append @ ((cList.take @ V0) @ V2)) @ ((cList.take @ V1) @ ((cList.drop @ V0) @ V2)))))))))))
(TList.take_all,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ V1)) @ ((cHOL.eq @ ((cList.take @ V1) @ V0)) @ V0)))))))
(TList.take_def,((c== @ cList.take) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cNat.nat.nat_case @ cList.list.Nil) @ (^[V6]: ((cList.list.Cons @ V2) @ (V4 @ V6)))) @ V5)))))) @ V1) @ V0)))))
(TList.take_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ V1) @ ((cList.take @ V0) @ V2))))))))))
(TList.take_upt,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ ((cList.take @ V1) @ ((cList.upt @ V0) @ V2))) @ ((cList.upt @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)))))))))))
(TList.take_zip,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.zip @ V1) @ V2))) @ ((cList.zip @ ((cList.take @ V0) @ V1)) @ ((cList.take @ V0) @ V2))))))))))
(TList.tl.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.tl @ ((cList.list.Cons @ V0) @ V1))) @ V1))))))
(TList.tl.simps_1,((cHOL.eq @ (cList.tl @ cList.list.Nil)) @ cList.list.Nil))
(TList.upto_def,((c== @ cList.upto) @ (^[V0]: (^[V1]: (cList.upto_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TList.zip_map1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ ((cList.map @ V0) @ V1)) @ V2)) @ ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cProduct_Type.Pair @ (V0 @ V3)) @ V4))))) @ ((cList.zip @ V1) @ V2))))))))))
(TList.zip_map2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cProduct_Type.Pair @ V3) @ (V1 @ V4)))))) @ ((cList.zip @ V0) @ V2))))))))))
(TList.zip_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.set @ ((cList.zip @ V2) @ V2)))) @ ((cHOL.conj @ ((cSet.member @ V0) @ (cList.set @ V2))) @ ((cHOL.eq @ V0) @ V1))))))))))
(TMap.dom_const,(call @ (^[V0]: ((cHOL.eq @ (cMap.dom @ (^[V1]: (cOption.option.Some @ (V0 @ V1))))) @ cOrderings.top_class.top))))
(TMap.dom_empty,((cHOL.eq @ (cMap.dom @ (^[V0]: cOption.option.None))) @ cOrderings.bot_class.bot))
(TMap.dom_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ cOption.option.None)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ (cMap.dom @ V0)) @ ((cSet.insert @ V1) @ V2))) @ ((cGroups.minus_class.minus @ (cMap.dom @ V0)) @ V2))))))))))
(TMap.ran_empty,((cHOL.eq @ (cMap.ran @ (^[V0]: cOption.option.None))) @ cOrderings.bot_class.bot))
(TMeson.not_exD,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cHOL.Ex @ (^[V1]: (V0 @ V1))))) @ (cHOL.All @ (^[V1]: (cHOL.Not @ (V0 @ V1))))))))
(TNat.Least_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.Not @ (V0 @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ (cOrderings.ord_class.Least @ (^[V2]: (V0 @ V2)))) @ (cNat.Suc @ (cOrderings.ord_class.Least @ (^[V2]: (V0 @ (cNat.Suc @ V2)))))))))))))
(TNat.Nat.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat.Nat @ V0)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cNat.Zero_Rep)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.Suc_Rep @ V2))) @ ((c==> @ (cNat.Nat @ V2)) @ V1))))) @ V1))))))))
(TNat.Nat.simps,(call @ (^[V0]: ((cHOL.eq @ (cNat.Nat @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.Zero_Rep)) @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cHOL.eq @ V0) @ (cNat.Suc_Rep @ V1))) @ (cNat.Nat @ V1)))))))))
(TNat.Suc_le_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat.Suc_lessD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat.Suc_lessE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ (cNat.Suc @ V3))) @ V2))))) @ V2)))))))))
(TNat.Suc_lessI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ (cNat.Suc @ V0)) @ V1))) @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ V1))))))))
(TNat.Suc_pred',(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ V0) @ (cNat.Suc @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)))))))
(TNat.add_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V1) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V1)))))))))
(TNat.diff_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V1))))))))
(TNat.dvd.monoD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.order.mono @ cRings.dvd_class.dvd) @ V0)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat.dvd.monoE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.order.mono @ cRings.dvd_class.dvd) @ V0)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2))) @ V3)) @ V3))))))))))))
(TNat.dvd.monoI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2)))))))) @ ((cOrderings.order.mono @ cRings.dvd_class.dvd) @ V0)))))
(TNat.dvd_diffD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))))))
(TNat.dvd_plusE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ V3)) @ V3))))))))))))
(TNat.eq_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.le_Suc_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.Suc @ V1))) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ V0) @ (cNat.Suc @ V1)))))))))
(TNat.le_square,(call @ (^[V0]: ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V0) @ V0)))))
(TNat.less_Suc0,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.less_SucE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V2)) @ V2))))))))))
(TNat.less_SucI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))))))))
(TNat.mult_is_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TNat.nat.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ (cNat.Suc @ V2))) @ (V1 @ V2)))))))))
(TNat.nat.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))
(TNat.nat.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ (cNat.Suc @ V2))) @ ((V1 @ V2) @ (((cNat.nat.nat_rec @ V0) @ V1) @ V2))))))))))
(TNat.nat.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))
(TNat.nat.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ (cNat.Suc @ V2))) @ (V1 @ V2)))))))))
(TNat.nat.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))
(TNat.nat.simps_3,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNat.Suc @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.nat.simps_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V0))))))
(TNat.nat.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.nat.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cNat.nat.nat_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cNat.zero_nat_inst.zero_nat)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cNat.Suc @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TNat.nat_rec_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))
(TNat.neq0_conv,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)))))
(TNat.not_less0,(call @ (^[V0]: (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.of_nat_id,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ V0))))
(TNum.inc.simps_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.inc @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit0 @ (cNum.inc @ V0))))))
(TNum.inc.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.inc @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit1 @ V0)))))
(TNum.inc.simps_1,((cHOL.eq @ (cNum.inc @ cNum.num.One)) @ (cNum.num.Bit0 @ cNum.num.One)))
(TNum.num.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_case @ V0) @ V1) @ V2) @ (cNum.num.Bit1 @ V3))) @ (V2 @ V3)))))))))))
(TNum.num.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_case @ V0) @ V1) @ V2) @ (cNum.num.Bit0 @ V3))) @ (V1 @ V3)))))))))))
(TNum.num.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cNum.num.num_case @ V0) @ V1) @ V2) @ cNum.num.One)) @ V0))))))))
(TNum.num.simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ (cNum.num.Bit1 @ V3))) @ ((V2 @ V3) @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ V3))))))))))))
(TNum.num.simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ (cNum.num.Bit0 @ V3))) @ ((V1 @ V3) @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ V3))))))))))))
(TNum.num.simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cNum.num.num_rec @ V0) @ V1) @ V2) @ cNum.num.One)) @ V0))))))))
(TNum.num.simps_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_case @ V0) @ V1) @ V2) @ (cNum.num.Bit1 @ V3))) @ (V2 @ V3)))))))))))
(TNum.num.simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNum.num.num_case @ V0) @ V1) @ V2) @ (cNum.num.Bit0 @ V3))) @ (V1 @ V3)))))))))))
(TNum.num.simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cNum.num.num_case @ V0) @ V1) @ V2) @ cNum.num.One)) @ V0))))))))
(TNum.num.simps_8,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))))))))
(TNum.num.simps_7,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))))))))
(TNum.num.simps_6,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)))))
(TNum.num.simps_5,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit1 @ V0))))))
(TNum.num.simps_4,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)))))
(TNum.num.simps_3,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit0 @ V0))))))
(TNum.num.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cNum.num.num_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cNum.num.One)) @ (V0 @ V1))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cNum.num.Bit0 @ V5))) @ (V0 @ (V2 @ V5)))))) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cNum.num.Bit1 @ V5))) @ (V0 @ (V3 @ V5)))))))))))))))))))
(TNum.pow.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.pow @ V0) @ (cNum.num.Bit1 @ V1))) @ ((cNum.times_num_inst.times_num @ (cNum.sqr @ ((cNum.pow @ V0) @ V1))) @ V0)))))))
(TNum.pow.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.pow @ V0) @ (cNum.num.Bit0 @ V1))) @ (cNum.sqr @ ((cNum.pow @ V0) @ V1))))))))
(TNum.pow.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNum.pow @ V0) @ cNum.num.One)) @ V0))))
(TNum.rel_simps_69,(cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNum.rel_simps_68,(cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ cGroups.one_class.one)))
(TNum.rel_simps_67,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.rel_simps_66,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.rel_simps_65,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.rel_simps_64,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.rel_simps_63,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TNum.rel_simps_62,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNum.rel_simps_61,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.rel_simps_60,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))))))
(TNum.rel_simps_59,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.rel_simps_58,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cHOL.eq @ cNum.num.One) @ V0)))))
(TNum.rel_simps_57,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ cNum.num.One)))))
(TNum.rel_simps_56,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.rel_simps_55,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ cGroups.one_class.one)))
(TNum.rel_simps_54,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ cGroups.zero_class.zero)))
(TNum.rel_simps_53,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNum.rel_simps_52,((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TNum.rel_simps_51,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.rel_simps_50,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNum.rel_simps_49,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.rel_simps_48,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNum.rel_simps_47,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNum.rel_simps_46,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNum.rel_simps_45,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V1) @ V0)))))))
(TNum.rel_simps_44,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.rel_simps_43,(call @ (^[V0]: ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.rel_simps_42,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.rel_simps_41,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ V0)))))
(TNum.rel_simps_40,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.rel_simps_39,((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ cGroups.one_class.one))
(TNum.rel_simps_38,((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ cGroups.zero_class.zero))
(TNum.rel_simps_37,(cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNum.rel_simps_36,((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TNum.rel_simps_35,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.rel_simps_34,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNum.rel_simps_33,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.rel_simps_32,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNum.rel_simps_31,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNum.rel_simps_30,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNum.rel_simps_29,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V1) @ V0)))))))
(TNum.rel_simps_28,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.rel_simps_27,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.rel_simps_26,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ cNum.num.One)))))
(TNum.rel_simps_25,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.rel_simps_24,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.rel_simps_23,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.rel_simps_22,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ cHOL.False))))))
(TNum.rel_simps_21,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ cHOL.False))))))
(TNum.rel_simps_20,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.rel_simps_19,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.rel_simps_18,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.rel_simps_17,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ cHOL.False))))
(TNum.rel_simps_16,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ cHOL.False))))
(TNum.rel_simps_15,((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ cNum.num.One)) @ cHOL.True))
(TNum.rel_simps_14,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.rel_simps_13,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.rel_simps_12,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.rel_simps_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.rel_simps_10,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ cHOL.True))))
(TNum.rel_simps_9,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ cHOL.True))))
(TNum.rel_simps_8,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ V0) @ cNum.num.One)) @ cHOL.False))))
(TNum.rel_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.rel_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.rel_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.rel_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.rel_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.rel_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.rel_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ cNum.num.One) @ V0)) @ cHOL.True))))
(TNum.sqr.simps_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.sqr @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ (cNum.sqr @ V0)) @ V0)))))))
(TNum.sqr.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.sqr @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.sqr @ V0)))))))
(TNum.sqr.simps_1,((cHOL.eq @ (cNum.sqr @ cNum.num.One)) @ cNum.num.One))
(TOption.map.id,((cHOL.eq @ (cOption.map @ cFun.id)) @ cFun.id))
(TOrderings.xt1_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V0)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V5)) @ (V2 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ V3) @ (V2 @ V1))))))))))))))
(TOrderings.xt1_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V5)) @ (V1 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V0)))))))))))))
(TOrderings.xt1_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V0)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V2 @ V5)) @ (V2 @ V4)))))))) @ ((cOrderings.ord_class.less @ V3) @ (V2 @ V1))))))))))))))
(TOrderings.xt1_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V1 @ V5)) @ (V1 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V1 @ V3)) @ V0)))))))))))))
(TOrderings.xt1_12,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.xt1_11,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.xt1_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xt1_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)))))))))
(TOrderings.xt1_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xt1_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xt1_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))))))))
(TOrderings.xt1_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.xt1_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))))))))
(TOrderings.xt1_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V0))))))))))
(TOrderings.xt1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xt1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cOrderings.ord_class.less @ V2) @ V0))))))))))
(TOrderings.xt2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xt3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ V2) @ (V3 @ V1))))))))))))))
(TOrderings.xt4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xt5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V1))))))))))))))
(TOrderings.xt6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xt7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V1))))))))))))))
(TOrderings.xt8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xt9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V1))))))))))))))
(TPure.imp_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ V0) @ ((c== @ V1) @ V2))) @ ((c== @ ((c==> @ V0) @ V1)) @ ((c==> @ V0) @ V2))))))))))
(TPure.prop_def,(call @ (^[V0]: ((c== @ (cprop @ V0)) @ V0))))
(TPure.protectD,(call @ (^[V0]: ((c==> @ (cprop @ V0)) @ V0))))
(TPure.protectI,(call @ (^[V0]: ((c==> @ V0) @ (cprop @ V0)))))
(TPure.term_def,(call @ (^[V0]: ((c== @ (cPure.term @ V0)) @ (call @ (^[V1]: ((c==> @ V1) @ V1)))))))
(TRandom.select,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cSet.member @ (cProduct_Type.fst @ ((cRandom.select @ V0) @ V1))) @ (cList.set @ V0))))))))
(TRelation.symD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRelation.sym @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0))))))))))
(TRelation.symE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRelation.sym @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0)) @ V3)) @ V3))))))))))))
(TRelation.symI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0))))))) @ (cRelation.sym @ V0)))))
(TSMT.nopat_def,(call @ (^[V0]: ((cHOL.eq @ (cSMT.nopat @ V0)) @ cSMT.pattern.Pattern))))
(TSMT.z3div_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSMT.z3div @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ (cInt.uminus_int_inst.uminus_int @ ((cDivides.div_int_inst.div_int @ V0) @ (cInt.uminus_int_inst.uminus_int @ V1))))))))))
(TSMT.z3mod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSMT.z3mod @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ ((cDivides.div_int_inst.mod_int @ V0) @ (cInt.uminus_int_inst.uminus_int @ V1)))))))))
(TSet.Compl_Int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TSet.Compl_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cHOL.Not @ ((cSet.member @ V0) @ V1))))))))
(TSet.Diff_Int2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V2) @ V1))) @ ((cGroups.minus_class.minus @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)))))))))
(TSet.Diff_UNIV,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cOrderings.top_class.top)) @ cOrderings.bot_class.bot))))
(TSet.Diff_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V3)) @ ((cGroups.minus_class.minus @ V1) @ V2)))))))))))))
(TSet.Diff_triv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V0)))))))
(TSet.Int_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TSet.Pow_Compl,(call @ (^[V0]: ((cHOL.eq @ (cSet.Pow @ (cGroups.uminus_class.uminus @ V0))) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cGroups.uminus_class.uminus @ V2))) @ ((cSet.member @ V0) @ (cSet.Pow @ V2)))))))))))
(TSet.Pow_empty,((cHOL.eq @ (cSet.Pow @ cOrderings.bot_class.bot)) @ ((cSet.insert @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot)))
(TSet.UNIV_bool,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cHOL.False) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))))
(TSet.UNIV_eq_I,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((cSet.member @ V1) @ V0)))) @ ((cHOL.eq @ cOrderings.top_class.top) @ V0)))))
(TSet.Un_absorb,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V0)) @ V0))))
(TSet.Un_upper1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TSet.Un_upper2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TSet.ball_UNIV,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Ball @ cOrderings.top_class.top) @ V0)) @ (cHOL.All @ V0)))))
(TSet.ball_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cSet.Ball @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TSet.ball_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V2]: V1))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V2]: ((cSet.member @ V2) @ V0)))) @ V1)))))))
(TSet.bex_empty,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Bex @ cOrderings.bot_class.bot) @ V0)) @ cHOL.False))))
(TSet.bex_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cSet.Bex @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: (cHOL.Not @ (V1 @ V2))))))))))
(TSet.bex_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ ((cSet.image @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Bex @ V1) @ (^[V3]: (V2 @ (V0 @ V3))))))))))))
(TSet.bex_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ (cSet.Collect @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TSet.bex_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ ((cSet.insert @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cHOL.disj @ (V2 @ V0)) @ ((cSet.Bex @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.bex_simps_4,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Bex @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1)))) @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))))))
(TSet.bex_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Bex @ cOrderings.bot_class.bot) @ (^[V1]: (V0 @ V1)))) @ cHOL.False))))
(TSet.bex_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V3]: ((cHOL.conj @ V1) @ (V2 @ V3))))) @ ((cHOL.conj @ V1) @ ((cSet.Bex @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.bex_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V3]: ((cHOL.conj @ (V1 @ V3)) @ V2)))) @ ((cHOL.conj @ ((cSet.Bex @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TSet.bind_bind,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.bind @ ((cSet.bind @ V0) @ V1)) @ V2)) @ ((cSet.bind @ V0) @ (^[V3]: ((cSet.bind @ (V1 @ V3)) @ V2)))))))))))
(TSet.conj_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V2) @ V3)) @ ((cHOL.implies @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V3)))))))))))))
(TSet.disj_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V2) @ V3)) @ ((cHOL.implies @ ((cHOL.disj @ V0) @ V2)) @ ((cHOL.disj @ V1) @ V3)))))))))))))
(TSet.empty_def,((cHOL.eq @ cOrderings.bot_class.bot) @ (cSet.Collect @ (^[V0]: cHOL.False))))
(TSet.empty_iff,(call @ (^[V0]: ((cHOL.eq @ ((cSet.member @ V0) @ cOrderings.bot_class.bot)) @ cHOL.False))))
(TSet.equalityE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ V2))) @ V2)))))))))
(TSet.equalityI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TSet.image_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V1) @ (^[V3]: ((cHOL.eq @ V2) @ (V0 @ V3))))))))))))
(TSet.image_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((cSet.member @ V0) @ ((cSet.image @ V1) @ V3)))))))))))))
(TSet.image_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.image @ V1) @ V2))) @ ((cSet.Bex @ V2) @ (^[V3]: ((cHOL.eq @ V0) @ (V1 @ V3))))))))))))
(TSet.range_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((cSet.member @ V0) @ ((cSet.image @ V1) @ cOrderings.top_class.top))))))))))
(TSet.split_ifs_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ V0) @ (((cHOL.If @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ V1) @ ((cSet.member @ V0) @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ ((cSet.member @ V0) @ V3)))))))))))))
(TSet.split_ifs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ (((cHOL.If @ V0) @ V1) @ V2)) @ V3)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ ((cSet.member @ V1) @ V3))) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ ((cSet.member @ V2) @ V3)))))))))))))
(TSet.split_ifs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ V0) @ (((cHOL.If @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ V1) @ ((cHOL.eq @ V0) @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ ((cHOL.eq @ V0) @ V3)))))))))))))
(TSet.split_ifs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ V3)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TSet.split_ifs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ V2))))))))))
(TSet.subset_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.member @ V2) @ V1)))))))))
(TSet.vimage_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cSet.vimage @ V0) @ V1)) @ ((cSet.vimage @ V0) @ V2))))))))))
(TSet.vimage_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.vimage @ V1) @ V2))) @ ((cSet.member @ (V1 @ V0)) @ V2)))))))))
(TSet.vimage_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.vimage @ (^[V4]: (((cHOL.If @ ((cSet.member @ V4) @ V0)) @ V1) @ V2))) @ V3)) @ (((cHOL.If @ ((cSet.member @ V1) @ V3)) @ (((cHOL.If @ ((cSet.member @ V2) @ V3)) @ cOrderings.top_class.top) @ V0)) @ (((cHOL.If @ ((cSet.member @ V2) @ V3)) @ (cGroups.uminus_class.uminus @ V0)) @ cOrderings.bot_class.bot))))))))))))
(TSum_Type.InlI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ (cSum_Type.Inl @ V0)) @ ((cSum_Type.Plus @ V1) @ V2))))))))))
(TSum_Type.InrI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ (cSum_Type.Inr @ V0)) @ ((cSum_Type.Plus @ V2) @ V1))))))))))
(TSum_Type.sumE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Inl @ V2))) @ V1)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Inr @ V2))) @ V1)))) @ V1)))))))
(TATP.fAll_table_2,(call @ (^[V0]: ((cHOL.disj @ (cHOL.All @ V0)) @ ((cHOL.eq @ (cATP.fAll @ V0)) @ cATP.fFalse)))))
(TATP.fAll_table_1,(call @ (^[V0]: ((cHOL.disj @ (cHOL.Ex @ (cATP.fComp @ V0))) @ ((cHOL.eq @ (cATP.fAll @ V0)) @ cATP.fTrue)))))
(TATP.fFalse_def,((cHOL.eq @ cATP.fFalse) @ cHOL.False))
(TATP.fNot_table_2,((cHOL.eq @ (cATP.fNot @ cATP.fTrue)) @ cATP.fFalse))
(TATP.fNot_table_1,((cHOL.eq @ (cATP.fNot @ cATP.fFalse)) @ cATP.fTrue))
(TATP.fconj_laws_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cATP.fNot @ ((cATP.fconj @ V0) @ V1))) @ ((cATP.fdisj @ (cATP.fNot @ V0)) @ (cATP.fNot @ V1))))))))
(TATP.fconj_laws_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fconj @ V0) @ V1)) @ ((cATP.fconj @ V1) @ V0)))))))
(TATP.fconj_laws_1,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fconj @ V0) @ V0)) @ V0))))
(TATP.fdisj_laws_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cATP.fNot @ ((cATP.fdisj @ V0) @ V1))) @ ((cATP.fconj @ (cATP.fNot @ V0)) @ (cATP.fNot @ V1))))))))
(TATP.fdisj_laws_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fdisj @ V0) @ V1)) @ ((cATP.fdisj @ V1) @ V0)))))))
(TATP.fdisj_laws_1,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fdisj @ V0) @ V0)) @ V0))))
(TATP.fequal_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fequal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.Split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDatatype.Split @ V0) @ ((cDatatype.Scons @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TDatatype.dsumE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cDatatype.dsum @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (cDatatype.In0 @ V4)) @ (cDatatype.In0 @ V5)))) @ V3))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (cDatatype.In1 @ V4)) @ (cDatatype.In1 @ V5)))) @ V3))))))) @ V3))))))))))))
(TDatatype.usumE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cDatatype.usum @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ (cDatatype.In0 @ V4))) @ V3))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((c==> @ ((cHOL.eq @ V0) @ (cDatatype.In1 @ V4))) @ V3))))) @ V3))))))))))))
(TDivides.add_0s_2,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TDivides.add_0s_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TDivides.div_if,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V1) @ V0)) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V1) @ V0)) @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ ((cDivides.div_nat_inst.div_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V0))))))))))
(TDivides.mod_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ V0) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V1))))))))
(TEnum.order_fun_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cEnum.enum_class.enum_ex @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))))))))))
(TEnum.order_fun_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cEnum.enum_class.enum_all @ (^[V2]: ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TFun.bij_is_inj,(call @ (^[V0]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)))))
(TFun.comp_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.comp @ V0) @ V1) @ V2)) @ (V0 @ (V1 @ V2))))))))))
(TFun.comp_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cFun.comp @ V0) @ ((cFun.comp @ V1) @ V2))))))))))
(TFun.image_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cSet.image @ V0) @ ((cSet.image @ V1) @ V2))))))))))
(TFun.inj_on_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.disj @ ((cFun.inj_on @ V0) @ V1)) @ ((cFun.inj_on @ V0) @ V2))) @ ((cFun.inj_on @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TFun.inj_on_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.inj_on @ V0) @ V1)) @ ((cSet.Ball @ V1) @ (^[V2]: ((cSet.Ball @ V1) @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ (V0 @ V2)) @ (V0 @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TFun.inj_on_id2,(call @ (^[V0]: ((cFun.inj_on @ (^[V1]: V1)) @ V0))))
(TFun.inj_on_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V2)) @ (V0 @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))))
(TFun.map_fun.id,((cHOL.eq @ ((cFun.map_fun @ cFun.id) @ cFun.id)) @ cFun.id))
(TGroups.mult_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TGroups.mult_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TGroups.mult_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(THOL.Let_folded,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c== @ (V0 @ V1)) @ (V2 @ V1))) @ ((c== @ ((cHOL.Let @ V1) @ V0)) @ ((cHOL.Let @ V1) @ V2))))))))))
(THOL.Let_unfold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c== @ (V0 @ V1)) @ V2)) @ ((c== @ ((cHOL.Let @ V1) @ V0)) @ V2)))))))))
(THOL.Not_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(THOL.all_not_ex,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ (cHOL.Not @ (cHOL.Ex @ (^[V1]: (cHOL.Not @ (V0 @ V1)))))))))
(THOL.atomize_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c== @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(THOL.back_subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ (V0 @ V2))))))))))
(THOL.box_equals,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(THOL.case_split,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V1)) @ V1)))))))
(THOL.cases_simp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ V1))) @ V1))))))
(THOL.conj_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ ((cHOL.conj @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V1) @ V2))))))))))
(THOL.conj_comms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V1) @ V2))) @ ((cHOL.conj @ V1) @ ((cHOL.conj @ V0) @ V2))))))))))
(THOL.conj_comms_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V1) @ V0)))))))
(THOL.disj_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ ((cHOL.disj @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V1) @ V2))))))))))
(THOL.disj_comms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.disj @ V1) @ ((cHOL.disj @ V0) @ V2))))))))))
(THOL.disj_comms_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ V1) @ V0)))))))
(THOL.eq_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ V0)))))))
(THOL.forw_subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (V2 @ V1)) @ (V2 @ V0))))))))))
(THOL.fun_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))))))))
(THOL.if_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cHOL.If @ V1) @ V2) @ V3))) @ (((cHOL.If @ V1) @ (V0 @ V2)) @ (V0 @ V3))))))))))))
(TInt.abs_int_eq,(call @ (^[V0]: ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TInt.cr_int_def,((c== @ cInt.cr_int) @ (^[V0]: (^[V1]: ((cHOL.eq @ (cInt.Abs_Integ @ V0)) @ V1)))))
(TInt.int_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (cInt.nat @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1))))))))
(TInt.int_equivp,(cEquiv_Relations.equivp @ cInt.intrel))
(TInt.int_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V3)) @ ((c==> @ (V0 @ V3)) @ (V0 @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int))))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V1)) @ ((c==> @ (V0 @ V3)) @ (V0 @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))))))) @ (V0 @ V2)))))))))))
(TInt.int_int_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TInt.int_nat_eq,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cInt.nat @ V0))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ V0) @ cInt.zero_int_inst.zero_int)))))
(TInt.int_setsum,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cNat.semiring_1_class.of_nat @ (V0 @ V2)))) @ V1)))))))
(TInt.intrel_def,((cHOL.eq @ cInt.intrel) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TInt.intrel_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cInt.intrel @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))))
(TInt.le_nat_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ (cInt.nat @ V0))) @ ((cInt.ord_int_inst.less_eq_int @ (cNat.semiring_1_class.of_nat @ V1)) @ V0))))))))
(TInt.nat.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cInt.nat @ (cInt.Abs_Integ @ V0))) @ ((cProduct_Type.prod.prod_case @ cNat.minus_nat_inst.minus_nat) @ V0)))))
(TInt.nat.rep_eq,(call @ (^[V0]: ((c== @ (cInt.nat @ V0)) @ ((cProduct_Type.prod.prod_case @ cNat.minus_nat_inst.minus_nat) @ (cInt.Rep_Integ @ V0))))))
(TInt.nat_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cInt.nat @ V0)) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TInt.nat_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cInt.nat @ V0)) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TInt.zpower_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cNat.semiring_1_class.of_nat @ V0)) @ V1)) @ (cNat.semiring_1_class.of_nat @ ((cPower.power_class.power @ V0) @ V1))))))))
(TLattices.inf1E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLattices.inf_class.inf @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ (V0 @ V2)) @ ((c==> @ (V1 @ V2)) @ V3))) @ V3)))))))))))
(TLattices.inf1I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (V2 @ V1)) @ (((cLattices.inf_class.inf @ V0) @ V2) @ V1))))))))))
(TLattices.inf2E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLattices.inf_class.inf @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V1 @ V2) @ V3)) @ V4))) @ V4)))))))))))))
(TLattices.inf2I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V3 @ V1) @ V2)) @ ((((cLattices.inf_class.inf @ V0) @ V3) @ V1) @ V2))))))))))))
(TLattices.sup1E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLattices.sup_class.sup @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ (V0 @ V2)) @ V3)) @ ((c==> @ ((c==> @ (V1 @ V2)) @ V3)) @ V3))))))))))))
(TLattices.sup2E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLattices.sup_class.sup @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((V0 @ V2) @ V3)) @ V4)) @ ((c==> @ ((c==> @ ((V1 @ V2) @ V3)) @ V4)) @ V4))))))))))))))
(TList.Id_on_set,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Id_on @ (cList.set @ V0))) @ (cList.set @ ((cList.map @ (^[V1]: ((cProduct_Type.Pair @ V1) @ V1))) @ V0))))))
(TList.compl_set,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cList.set @ V0))) @ (cList.coset @ V0)))))
(TList.coset_def,(call @ (^[V0]: ((cHOL.eq @ (cList.coset @ V0)) @ (cGroups.uminus_class.uminus @ (cList.set @ V0))))))
(TList.drop_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.drop @ V1) @ V2))) @ ((cList.drop @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)))))))))
(TList.drop_take,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.take @ V1) @ V2))) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ ((cList.drop @ V0) @ V2))))))))))
(TList.empty_set,((cHOL.eq @ cOrderings.bot_class.bot) @ (cList.set @ cList.list.Nil)))
(TList.find_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V1))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cList.find @ V2) @ V0)) @ ((cList.find @ V3) @ V1)))))))))))))
(TList.fold_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ (cList.set @ V2))) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ (((cList.fold @ V4) @ V2) @ V0)) @ (((cList.fold @ V5) @ V3) @ V1))))))))))))))))))
(TList.foldl_def,((c== @ cList.foldl) @ (^[V0]: (^[V1]: (^[V2]: (((((cList.list.list_rec @ (^[V3]: (^[V4]: V4))) @ (^[V3]: (^[V4]: (^[V5]: (^[V6]: (^[V7]: ((V5 @ V6) @ ((V6 @ V7) @ V3)))))))) @ V2) @ V0) @ V1))))))
(TList.foldl_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ ((cList.map @ V2) @ V3))) @ (((cList.foldl @ (^[V4]: (^[V5]: ((V0 @ V4) @ (V2 @ V5))))) @ V1) @ V3)))))))))))
(TList.foldr_def,((c== @ cList.foldr) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cFun.id)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((cFun.comp @ (V5 @ V2)) @ (V4 @ V5))))))) @ V1) @ V0)))))
(TList.foldr_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.foldr @ V0) @ ((cList.map @ V1) @ V2)) @ V3)) @ (((cList.foldr @ ((cFun.comp @ V0) @ V1)) @ V2) @ V3)))))))))))
(TList.hd_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.hd @ ((cList.append @ V0) @ V1))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cList.hd @ V1)) @ (cList.hd @ V0))))))))
(TList.hd_in_set,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cSet.member @ (cList.hd @ V0)) @ (cList.set @ V0))))))
(TList.image_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ V0) @ (cList.set @ V1))) @ (cList.set @ ((cList.map @ V0) @ V1))))))))
(TList.in_listsD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.lists @ V1))) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cSet.member @ V2) @ V1)))))))))
(TList.in_listsI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cSet.member @ V2) @ V1)))) @ ((cSet.member @ V0) @ (cList.lists @ V1))))))))
(TList.last_drop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (cList.last @ ((cList.drop @ V0) @ V1))) @ (cList.last @ V1))))))))
(TList.last_snoc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.last @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))) @ V1))))))
(TList.length_tl,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.tl @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat)))))
(TList.lexn_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.lexn @ V0) @ V1)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V3)) @ V1)) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.append @ V4) @ ((cList.list.Cons @ V5) @ V7)))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.append @ V4) @ ((cList.list.Cons @ V6) @ V8)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V0)))))))))))))))))))))))))
(TList.list.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list.list_rec @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ (((V1 @ V2) @ V3) @ (((cList.list.list_rec @ V0) @ V1) @ V3))))))))))))
(TList.list.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list.list_rec @ V0) @ V1) @ cList.list.Nil)) @ V0))))))
(TList.list.size_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.list.Cons @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TList.list.size_3,((cHOL.eq @ (cNat.size_class.size @ cList.list.Nil)) @ cNat.zero_nat_inst.zero_nat))
(TList.list.size_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list.list_size @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ ((cList.list.list_size @ V0) @ V2))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TList.list.size_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.list.list_size @ V0) @ cList.list.Nil)) @ cNat.zero_nat_inst.zero_nat))))
(TList.listrel1E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel1 @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ ((cHOL.eq @ V0) @ ((cList.append @ V6) @ ((cList.list.Cons @ V4) @ V7)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.append @ V6) @ ((cList.list.Cons @ V5) @ V7)))) @ V3)))))))))))) @ V3)))))))))))
(TList.listrel1I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cHOL.eq @ V3) @ ((cList.append @ V4) @ ((cList.list.Cons @ V0) @ V5)))) @ ((c==> @ ((cHOL.eq @ V6) @ ((cList.append @ V4) @ ((cList.list.Cons @ V1) @ V5)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V6)) @ (cList.listrel1 @ V2))))))))))))))))))))
(TList.lists.Nil,(call @ (^[V0]: ((cSet.member @ cList.list.Nil) @ (cList.lists @ V0)))))
(TList.lists_def,((c== @ cList.lists) @ (^[V0]: (cSet.Collect @ (^[V1]: ((cList.listsp @ (^[V2]: ((cSet.member @ V2) @ V0))) @ V1))))))
(TList.map.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.list.Cons @ (V0 @ V1)) @ ((cList.map @ V0) @ V2))))))))))
(TList.map.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.map @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.map_ident,((cHOL.eq @ (cList.map @ (^[V0]: V0))) @ (^[V0]: V0)))
(TList.nth.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ (((cNat.nat.nat_case @ V0) @ (^[V3]: ((cList.nth @ V1) @ V3))) @ V2)))))))))
(TList.nth_Cons',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ V0) @ ((cList.nth @ V1) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ cNat.one_nat_inst.one_nat)))))))))))
(TList.nth_drop',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.list.Cons @ ((cList.nth @ V1) @ V0)) @ ((cList.drop @ (cNat.Suc @ V0)) @ V1))) @ ((cList.drop @ V0) @ V1))))))))
(TList.rev.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rev @ ((cList.list.Cons @ V0) @ V1))) @ ((cList.append @ (cList.rev @ V1)) @ ((cList.list.Cons @ V0) @ cList.list.Nil))))))))
(TList.rev.simps_1,((cHOL.eq @ (cList.rev @ cList.list.Nil)) @ cList.list.Nil))
(TList.rev_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V1)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ cList.list.Nil)))) @ V1)))))) @ V1)))))))
(TList.rotate_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.size_class.size @ V1))) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ ((cList.rotate @ V0) @ V1)) @ V1)))))))
(TList.set.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.list.Cons @ V0) @ V1))) @ ((cSet.insert @ V0) @ (cList.set @ V1))))))))
(TList.set.simps_1,((cHOL.eq @ (cList.set @ cList.list.Nil)) @ cOrderings.bot_class.bot))
(TList.set_ConsD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ ((cList.list.Cons @ V1) @ V2)))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cSet.member @ V0) @ (cList.set @ V2)))))))))))
(TList.set_empty,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.set @ V0)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.take_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.drop @ V1) @ V2))) @ ((cList.drop @ V1) @ ((cList.take @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2))))))))))
(TList.take_take,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.take @ V1) @ V2))) @ ((cList.take @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)))))))))
(TList.those_def,((c== @ cList.those) @ (^[V0]: (((cList.list.list_rec @ (cOption.option.Some @ cList.list.Nil)) @ (^[V1]: (^[V2]: (^[V3]: (((cOption.option.option_case @ cOption.option.None) @ (^[V4]: ((cOption.map @ (cList.list.Cons @ V4)) @ V3))) @ V1))))) @ V0))))
(TList.tl_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.tl @ ((cList.append @ V0) @ V1))) @ (((cList.list.list_case @ (cList.tl @ V1)) @ (^[V2]: (^[V3]: ((cList.append @ V3) @ V1)))) @ V0)))))))
(TList.upt.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upt @ V0) @ (cNat.Suc @ V1))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cList.append @ ((cList.upt @ V0) @ V1)) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ cList.list.Nil)))))))
(TList.upt.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.upt @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cList.list.Nil))))
(TList.upt.upt_0,(call @ (^[V0]: ((cHOL.eq @ ((cList.upt @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cList.list.Nil))))
(TList.upto_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto @ V0) @ V1)) @ (((cList.upto_aux @ V0) @ V1) @ cList.list.Nil)))))))
(TList.upto_rec1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cHOL.eq @ ((cList.upto @ V0) @ V1)) @ ((cList.list.Cons @ V0) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)))))))))
(TList.upto_rec2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cHOL.eq @ ((cList.upto @ V0) @ V1)) @ ((cList.append @ ((cList.upto @ V0) @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))))))
(TList.wf_lenlex,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ (cList.lenlex @ V0))))))
(TList.zip.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ ((cProduct_Type.Pair @ V3) @ V1)) @ ((cList.zip @ V4) @ V2))))) @ V0)))))))))
(TList.zip.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.zip @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.zip_Cons1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ (((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ V3)) @ ((cList.zip @ V1) @ V4))))) @ V2)))))))))
(TMap.insert_dom,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (cOption.option.Some @ V2))) @ ((cHOL.eq @ ((cSet.insert @ V1) @ (cMap.dom @ V0))) @ (cMap.dom @ V0))))))))))
(TMap.map_le_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMap.map_le @ V0) @ V1)) @ ((cSet.Ball @ (cMap.dom @ V0)) @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TMap.map_le_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cMap.map_le @ V0) @ V1)) @ ((cMap.map_le @ (((cFun.fun_upd @ V0) @ V2) @ V3)) @ (((cFun.fun_upd @ V1) @ V2) @ V3))))))))))))
(TMap.map_of_def,((c== @ cMap.map_of) @ (^[V0]: (((cList.list.list_rec @ (^[V1]: cOption.option.None)) @ (^[V1]: (^[V2]: (^[V3]: (((cFun.fun_upd @ V3) @ (cProduct_Type.fst @ V1)) @ (cOption.option.Some @ (cProduct_Type.snd @ V1))))))) @ V0))))
(TMap.map_of_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cList.set @ ((cList.map @ cProduct_Type.fst) @ V0))) @ (cList.set @ ((cList.map @ cProduct_Type.fst) @ V1)))) @ ((c==> @ ((cSet.Ball @ (cList.set @ ((cList.map @ cProduct_Type.fst) @ V0))) @ (^[V2]: ((cHOL.eq @ ((cMap.map_of @ V0) @ V2)) @ ((cMap.map_of @ V1) @ V2))))) @ ((cHOL.eq @ (cMap.map_of @ V0)) @ (cMap.map_of @ V1)))))))))
(TMap.map_of_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.map_of @ ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ V2) @ (V0 @ V3)))))) @ V1))) @ ((cFun.comp @ (cOption.map @ V0)) @ (cMap.map_of @ V1))))))))
(TMeson.disj_exD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TMeson.not_allD,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cHOL.All @ (^[V1]: (V0 @ V1))))) @ (cHOL.Ex @ (^[V1]: (cHOL.Not @ (V0 @ V1))))))))
(TMeson.not_iffD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1)))))))))
(TMeson.not_impD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.implies @ V0) @ V1))) @ ((cHOL.conj @ V0) @ (cHOL.Not @ V1))))))))
(TMeson.not_notD,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(TNat.Least_Suc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (cHOL.Not @ (V0 @ cNat.zero_nat_inst.zero_nat))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.eq @ (V0 @ (cNat.Suc @ V4))) @ (V2 @ V4))))) @ ((cHOL.eq @ (cOrderings.ord_class.Least @ V0)) @ (cNat.Suc @ (cOrderings.ord_class.Least @ V2))))))))))))))))
(TNat.Nat.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat.Nat @ V0)) @ ((c==> @ (V1 @ cNat.Zero_Rep)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNat.Nat @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cNat.Suc_Rep @ V2))))))) @ (V1 @ V0)))))))))
(TNat.Nat.intros_2,(call @ (^[V0]: ((c==> @ (cNat.Nat @ V0)) @ (cNat.Nat @ (cNat.Suc_Rep @ V0))))))
(TNat.Nat.intros_1,(cNat.Nat @ cNat.Zero_Rep))
(TNat.Suc_diff_1,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ (cNat.Suc @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat))) @ V0)))))
(TNat.Suc_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.add_lessD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V2)))))))))
(TNat.dec_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ (V2 @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V3)) @ ((c==> @ (V2 @ V3)) @ (V2 @ (cNat.Suc @ V3))))))) @ (V2 @ V1)))))))))))
(TNat.diff_Suc_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V0)) @ cNat.one_nat_inst.one_nat)) @ V0))))
(TNat.diff_add_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TNat.dvd.eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))
(TNat.dvd_1_left,(call @ (^[V0]: ((cRings.dvd_class.dvd @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V0))))
(TNat.dvd_diffD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ V2)))))))))))
(TNat.dvd_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1))))))))
(TNat.dvd_reduce,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V0))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.funpow_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.compow @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cFun.comp @ ((cNat.compow @ V0) @ V2)) @ ((cNat.compow @ V1) @ V2))))))))))
(TNat.funpow_def,((c== @ cNat.compow) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: cFun.id)) @ (^[V1]: (^[V2]: (^[V3]: ((cFun.comp @ V3) @ (V2 @ V3)))))) @ V0))))
(TNat.inc_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ (V2 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V1)) @ ((c==> @ (V2 @ (cNat.Suc @ V3))) @ (V2 @ V3)))))) @ (V2 @ V0)))))))))))
(TNat.le_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.le_iff_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))))))))))
(TNat.less_zeroE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V1))))))
(TNat.mult_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V1)))))))))
(TNat.nat.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNat.Suc @ V2)))))) @ (V0 @ V1))))))))
(TNat.nat.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.nat.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cNat.nat.nat_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cNat.zero_nat_inst.zero_nat)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cNat.Suc @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TNat.nat.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cNat.nat.nat_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cNat.zero_nat_inst.zero_nat)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cNat.Suc @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TNat.nat_case_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))
(TNat.nat_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNat.Suc @ V2)))))) @ (V0 @ V1))))))))
(TNat.nat_mult_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ cNat.one_nat_inst.one_nat) @ V0)) @ V0))))
(TNat.one_is_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TNum.BitM.simps_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.BitM @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ V0))))))
(TNum.BitM.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.BitM @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit1 @ (cNum.BitM @ V0))))))
(TNum.BitM.simps_1,((cHOL.eq @ (cNum.BitM @ cNum.num.One)) @ cNum.num.One))
(TNum.num.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cNum.num.One)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNum.num.Bit0 @ V2)))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNum.num.Bit1 @ V2)))))) @ (V0 @ V1)))))))))
(TNum.num.inject_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.inject_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cNum.num.num_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cNum.num.One)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cNum.num.Bit0 @ V5))) @ (cHOL.Not @ (V0 @ (V2 @ V5))))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cNum.num.Bit1 @ V5))) @ (cHOL.Not @ (V0 @ (V3 @ V5)))))))))))))))))))))
(TNum.num.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cNum.num.num_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cNum.num.One)) @ (V0 @ V1))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cNum.num.Bit0 @ V5))) @ (V0 @ (V2 @ V5)))))) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cNum.num.Bit1 @ V5))) @ (V0 @ (V3 @ V5)))))))))))))))))))
(TNum.num_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V1))))))))
(TNum.num_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cNum.num.One)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNum.inc @ V2)))))) @ (V0 @ V1))))))))
(TOption.map_def,((cHOL.eq @ cOption.map) @ (^[V0]: (^[V1]: (((cOption.option.option_case @ cOption.option.None) @ (^[V2]: (cOption.option.Some @ (V0 @ V2)))) @ V1)))))
(TOption.set_def,((c== @ cOption.set) @ (^[V0]: (((cOption.option.option_rec @ cOrderings.bot_class.bot) @ (^[V1]: ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ V0))))
(TOption.the_def,((c== @ cOption.the) @ (^[V0]: (((cOption.option.option_rec @ cHOL.undefined) @ (^[V1]: V1)) @ V0))))
(TPredicate.botE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPredicate.eval @ cOrderings.bot_class.bot) @ V0)) @ V1))))))
(TPredicate.supE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPredicate.eval @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cPredicate.eval @ V0) @ V2)) @ V3)) @ ((c==> @ ((c==> @ ((cPredicate.eval @ V1) @ V2)) @ V3)) @ V3))))))))))))
(TPure.meta_allE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (V0 @ V3)))) @ ((c==> @ ((c==> @ (V0 @ V1)) @ V2)) @ V2)))))))))
(TPure.meta_impE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ V0) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(TPure.meta_spec,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ V2)))) @ (V0 @ V1)))))))
(TPure.reflexive,(call @ (^[V0]: ((c== @ V0) @ V0))))
(TPure.revcut_rl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((c==> @ V0) @ V1)) @ V1)))))))
(TPure.symmetric,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ V1)) @ ((c== @ V1) @ V0)))))))
(TQuotient.QT_ex,(call @ (^[V0]: ((c==> @ (cQuotient.Quot_True @ (cHOL.Ex @ V0))) @ (cQuotient.Quot_True @ V0)))))
(TQuotient.o_prs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ ((c==> @ (((cQuotient.Quotient3 @ V6) @ V7) @ V8)) @ ((cHOL.eq @ (((cFun.map_fun @ cFun.id) @ ((cFun.map_fun @ ((cFun.map_fun @ V1) @ cFun.id)) @ ((cFun.map_fun @ V2) @ cFun.id))) @ cFun.comp)) @ cFun.comp)))))))))))))))))))))))
(TQuotient.o_prs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ ((c==> @ (((cQuotient.Quotient3 @ V6) @ V7) @ V8)) @ ((cHOL.eq @ (((cFun.map_fun @ ((cFun.map_fun @ V4) @ V8)) @ ((cFun.map_fun @ ((cFun.map_fun @ V1) @ V5)) @ ((cFun.map_fun @ V2) @ V7))) @ cFun.comp)) @ cFun.comp)))))))))))))))))))))))
(TQuotient.o_rsp_2,(call @ (^[V0]: ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ cFun.comp) @ cFun.comp))))
(TQuotient.o_rsp_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V2) @ V0)) @ ((cTransfer.fun_rel @ V2) @ V1))) @ cFun.comp) @ cFun.comp))))))))
(TRandom.log_def,((c== @ cRandom.log) @ (^[V0]: (^[V1]: (cRandom.log_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TRelation.sympD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TRelation.sympE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((c==> @ ((V0 @ V2) @ V1)) @ V3)) @ V3))))))))))))
(TRelation.sympI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (cRelation.symp @ V0)))))
(TRings.dvd.dvdE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cRings.dvd.dvd @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V2) @ ((V0 @ V1) @ V4))) @ V3)))) @ V3)))))))))))
(TRings.dvd.dvdI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((V1 @ V2) @ V3))) @ (((cRings.dvd.dvd @ V1) @ V2) @ V0)))))))))))
(TSMT.weight_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSMT.weight @ V0) @ V1)) @ V1))))))
(TSet.Diff_Compl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TSet.Diff_empty,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cOrderings.bot_class.bot)) @ V0))))
(TSet.Diff_idemp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V1)) @ ((cGroups.minus_class.minus @ V0) @ V1)))))))
(TSet.Int_absorb,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V0)) @ V0))))
(TSet.Int_lower1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0))))))
(TSet.Int_lower2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V1))))))
(TSet.Least_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cSet.Bex @ V1) @ (^[V2]: ((cSet.Ball @ V1) @ (^[V3]: ((cOrderings.ord_class.less_eq @ V2) @ V3)))))) @ ((cHOL.eq @ (cOrderings.ord_class.Least @ (^[V2]: ((cSet.member @ V2) @ ((cSet.image @ V0) @ V1))))) @ (V0 @ (cOrderings.ord_class.Least @ (^[V2]: ((cSet.member @ V2) @ V1))))))))))))
(TSet.Pow_Int_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Pow @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cSet.Pow @ V0)) @ (cSet.Pow @ V1))))))))
(TSet.Pow_bottom,(call @ (^[V0]: ((cSet.member @ cOrderings.bot_class.bot) @ (cSet.Pow @ V0)))))
(TSet.Pow_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Pow @ ((cSet.insert @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cSet.Pow @ V1)) @ ((cSet.image @ (cSet.insert @ V0)) @ (cSet.Pow @ V1)))))))))
(TSet.Un_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V1)))))))
(TSet.Un_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ V0)) @ V1)))))))
(TSet.Un_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TSet.ball_empty,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Ball @ cOrderings.bot_class.bot) @ V0)) @ cHOL.True))))
(TSet.ball_simps_10,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cSet.Ball @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cSet.Bex @ V0) @ (^[V2]: (cHOL.Not @ (V1 @ V2))))))))))
(TSet.ball_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ ((cSet.image @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Ball @ V1) @ (^[V3]: (V2 @ (V0 @ V3))))))))))))
(TSet.ball_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ (cSet.Collect @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TSet.ball_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ ((cSet.insert @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cHOL.conj @ (V2 @ V0)) @ ((cSet.Ball @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.ball_simps_6,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Ball @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: (V0 @ V1)))))))
(TSet.ball_simps_5,(call @ (^[V0]: ((cHOL.eq @ ((cSet.Ball @ cOrderings.bot_class.bot) @ (^[V1]: (V0 @ V1)))) @ cHOL.True))))
(TSet.ball_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ V2)))) @ ((cHOL.implies @ ((cSet.Bex @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TSet.ball_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ V1) @ (V2 @ V3))))) @ ((cHOL.implies @ V1) @ ((cSet.Ball @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.ball_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.disj @ V1) @ (V2 @ V3))))) @ ((cHOL.disj @ V1) @ ((cSet.Ball @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.ball_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.disj @ (V1 @ V3)) @ V2)))) @ ((cHOL.disj @ ((cSet.Ball @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TSet.bind_const,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.bind @ V0) @ (^[V2]: V1))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ V1)))))))
(TSet.empty_Diff,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TSet.empty_bind,(call @ (^[V0]: ((cHOL.eq @ ((cSet.bind @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TSet.eq_to_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ ((cHOL.implies @ V1) @ V3)) @ ((cHOL.implies @ V0) @ V2)))))))))))))
(TSet.equalityCE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ V3))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V0))) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V1))) @ V3))) @ V3))))))))))))
(TSet.equalityD1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet.equalityD2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet.ex_bool_eq,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ ((cHOL.disj @ (V0 @ cHOL.True)) @ (V0 @ cHOL.False))))))
(TSet.ex_in_conv,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: ((cSet.member @ V1) @ V0)))) @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))))))
(TSet.filter_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.filter @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V1)) @ (V0 @ V2))))))))))
(TSet.image_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cSet.image @ V2) @ V0)) @ ((cSet.image @ V3) @ V1)))))))))))))
(TSet.image_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V2) @ V0)) @ ((cSet.image @ V2) @ V1))))))))))
(TSet.insert_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ ((cLattices.sup_class.sup @ (cSet.Collect @ (^[V2]: ((cHOL.eq @ V2) @ V0)))) @ V1)))))))
(TSet.insert_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.psubset_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TSet.remove_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.remove @ V0) @ V1)) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))))
(TSet.set_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.set_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ ((cSet.insert @ V0) @ V3))) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V3))) @ V2))))) @ V2)))))))))
(TSet.set_rev_mp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.singletonD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet.singletonE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V2)) @ V2)))))))))
(TSet.singletonI,(call @ (^[V0]: ((cSet.member @ V0) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TSet.subset_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.vimage_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cSet.vimage @ V0) @ V1)) @ ((cSet.vimage @ V0) @ V2))))))))))
(TSet.vimage_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet.vimage @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cSet.member @ (V0 @ V2)) @ V1)))))))))
(TSum_Type.PlusE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cSum_Type.Plus @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Inl @ V4))) @ V3))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Inr @ V4))) @ V3))))) @ V3))))))))))))
(TATP.fconj_table_3,((cHOL.eq @ ((cATP.fconj @ cATP.fTrue) @ cATP.fTrue)) @ cATP.fTrue))
(TATP.fconj_table_2,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fconj @ V0) @ cATP.fFalse)) @ cATP.fFalse))))
(TATP.fconj_table_1,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fconj @ cATP.fFalse) @ V0)) @ cATP.fFalse))))
(TATP.fdisj_table_3,((cHOL.eq @ ((cATP.fdisj @ cATP.fFalse) @ cATP.fFalse)) @ cATP.fFalse))
(TATP.fdisj_table_2,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fdisj @ V0) @ cATP.fTrue)) @ cATP.fTrue))))
(TATP.fdisj_table_1,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fdisj @ cATP.fTrue) @ V0)) @ cATP.fTrue))))
(TATP.fequal_laws_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.disj @ ((cHOL.eq @ ((cATP.fequal @ V0) @ V1)) @ cATP.fFalse)) @ ((cHOL.eq @ ((cATP.fequal @ (V2 @ V0)) @ (V2 @ V1))) @ cATP.fTrue)))))))))
(TATP.fequal_laws_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.disj @ ((cHOL.eq @ ((cATP.fequal @ V0) @ V1)) @ cATP.fFalse)) @ ((cHOL.disj @ ((cHOL.eq @ ((cATP.fequal @ V1) @ V2)) @ cATP.fFalse)) @ ((cHOL.eq @ ((cATP.fequal @ V0) @ V2)) @ cATP.fTrue))))))))))
(TATP.fequal_laws_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fequal @ V0) @ V1)) @ ((cATP.fequal @ V1) @ V0)))))))
(TDatatype.In0_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cDatatype.In0 @ V0)) @ (cDatatype.In0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.In1_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cDatatype.In1 @ V0)) @ (cDatatype.In1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.dprodE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cDatatype.dprod @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V6)) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V7)) @ V2)) @ ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cDatatype.Scons @ V4) @ V5)) @ ((cDatatype.Scons @ V6) @ V7)))) @ V3)))))))))))) @ V3)))))))))))
(TDatatype.dprodI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V5)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cDatatype.Scons @ V0) @ V3)) @ ((cDatatype.Scons @ V1) @ V4))) @ ((cDatatype.dprod @ V2) @ V5)))))))))))))))))
(TDatatype.uprodE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cDatatype.uprod @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((c==> @ ((cSet.member @ V5) @ V2)) @ ((c==> @ ((cHOL.eq @ V0) @ ((cDatatype.Scons @ V4) @ V5))) @ V3)))))))) @ V3)))))))))))
(TDatatype.uprodI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((cSet.member @ ((cDatatype.Scons @ V0) @ V2)) @ ((cDatatype.uprod @ V1) @ V3)))))))))))))
(TDivides.abs_div,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ ((cDivides.div_int_inst.div_int @ (cInt.abs_int_inst.abs_int @ V1)) @ (cInt.abs_int_inst.abs_int @ V0)))))))))
(TDivides.div_geq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V1) @ V0))) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V1) @ V0)) @ (cNat.Suc @ ((cDivides.div_nat_inst.div_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V0))))))))))
(TDivides.mod_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ V0)) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ (cNat.Suc @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))) @ V1)) @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)))))))))
(TDivides.mod_eqD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ ((cNat.times_nat_inst.times_nat @ V3) @ V1)))))))))))))
(TDivides.mod_geq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V1))))))))
(TEnum.max_ext_eq,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.max_ext @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.conj @ (cFinite_Set.finite @ V1)) @ ((cHOL.conj @ (cFinite_Set.finite @ V2)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ V3) @ V1)) @ ((cSet.Bex @ V2) @ (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)))))))))))))))))
(TFun.bij_betw_id,(call @ (^[V0]: (((cFun.bij_betw @ cFun.id) @ V0) @ V0))))
(TFun.bij_is_surj,(call @ (^[V0]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)))))
(TFun.comp_inj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ ((cSet.image @ V0) @ V1))) @ ((cFun.inj_on @ ((cFun.comp @ V2) @ V0)) @ V1))))))))))
(TFun.fcomp_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.fcomp @ V0) @ V1) @ V2)) @ (V1 @ (V0 @ V2))))))))))
(TFun.fcomp_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.fcomp @ ((cFun.fcomp @ V0) @ V1)) @ V2)) @ ((cFun.fcomp @ V0) @ ((cFun.fcomp @ V1) @ V2))))))))))
(TFun.fun_upd_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cFun.fun_upd @ V0) @ V1) @ V2)) @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ V1)) @ V2) @ (V0 @ V3)))))))))))
(TFun.fun_upd_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cFun.fun_upd @ (((cFun.fun_upd @ V0) @ V1) @ V2)) @ V1) @ V3)) @ (((cFun.fun_upd @ V0) @ V1) @ V3)))))))))))
(TFun.inj_on_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cHOL.eq @ ((cFun.inj_on @ V1) @ V0)) @ ((cFun.inj_on @ V2) @ V0))))))))))
(TFun.inj_on_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cFun.inj_on @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))))))))))
(TFun.map_fun_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.map_fun @ V0) @ V1) @ V2)) @ ((cFun.comp @ ((cFun.comp @ V1) @ V2)) @ V0)))))))))
(TFun.swap_triple,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V1))) @ ((cHOL.eq @ (((cFun.swap @ V0) @ V2) @ (((cFun.swap @ V2) @ V1) @ (((cFun.swap @ V0) @ V2) @ V3)))) @ (((cFun.swap @ V0) @ V1) @ V3)))))))))))))
(TFun.the_inv_f_f,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (((cFun.the_inv_into @ cOrderings.top_class.top) @ V0) @ (V0 @ V1))) @ V1)))))))
(TFun.vimage_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cSet.vimage @ V1) @ ((cSet.vimage @ V0) @ V2))))))))))
(TFunDef.let_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cHOL.Let @ V0) @ V2)) @ ((cHOL.Let @ V1) @ V3)))))))))))))
(TGroups.diff_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(THOL.atomize_all,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: (V0 @ V1)))))))
(THOL.atomize_exL,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ V1)))) @ ((c==> @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(THOL.atomize_imp,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c==> @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(THOL.atomize_not,(call @ (^[V0]: ((c== @ ((c==> @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(THOL.conj_absorb,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V0)) @ V0))))
(THOL.disj_absorb,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V0)) @ V0))))
(THOL.eq_sym_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ V0)))))))
(THOL.equal.equal,(call @ (^[V0]: ((c==> @ (cHOL.class.equal @ V0)) @ ((cHOL.eq @ V0) @ cHOL.eq)))))
(THOL.induct_conj_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((c==> @ ((cHOL.induct_conj @ V0) @ V1)) @ V2)) @ ((c==> @ V0) @ ((c==> @ V1) @ V2))))))))))
(THOL.induct_conj_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.induct_implies @ V0) @ ((cHOL.induct_conj @ V1) @ V2))) @ ((cHOL.induct_conj @ ((cHOL.induct_implies @ V0) @ V1)) @ ((cHOL.induct_implies @ V0) @ V2))))))))))
(THOL.induct_conj_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.induct_forall @ (^[V2]: ((cHOL.induct_conj @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.induct_conj @ (cHOL.induct_forall @ V0)) @ (cHOL.induct_forall @ V1))))))))
(THOL.neq_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))))))))
(TInt.Let_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.Let @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ (V1 @ (cNum.numeral_class.numeral @ V0))))))))
(TInt.add1_zle_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)) @ ((cInt.ord_int_inst.less_int @ V0) @ V1)))))))
(TInt.dvd_int_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cRings.dvd_class.dvd @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V0))) @ V1)))))))
(TInt.inf_int_def,((cHOL.eq @ cInt.inf_int_inst.inf_int) @ cOrderings.ord_class.min))
(TInt.int.Rep_int,(call @ (^[V0]: ((cSet.member @ (cInt.Rep_int @ V0)) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cInt.intrel @ V2) @ V2)) @ ((cHOL.eq @ V1) @ (cSet.Collect @ (cInt.intrel @ V2))))))))))))
(TInt.int_distrib_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ V0) @ ((cInt.minus_int_inst.minus_int @ V1) @ V2))) @ ((cInt.minus_int_inst.minus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ ((cInt.times_int_inst.times_int @ V0) @ V2))))))))))
(TInt.int_distrib_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ ((cInt.minus_int_inst.minus_int @ V0) @ V1)) @ V2)) @ ((cInt.minus_int_inst.minus_int @ ((cInt.times_int_inst.times_int @ V0) @ V2)) @ ((cInt.times_int_inst.times_int @ V1) @ V2))))))))))
(TInt.int_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ V2))) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ ((cInt.times_int_inst.times_int @ V0) @ V2))))))))))
(TInt.int_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V1)) @ V2)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V2)) @ ((cInt.times_int_inst.times_int @ V1) @ V2))))))))))
(TInt.int_dvd_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cNat.semiring_1_class.of_nat @ V0)) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V1)))))))))
(TInt.int_numeral,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TInt.int_setprod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (cNat.semiring_1_class.of_nat @ (V0 @ V2)))) @ V1)))))))
(TInt.int_zle_neg,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TInt.nat_dvd_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cInt.nat @ V0)) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cRings.dvd_class.dvd @ V0) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TInt.nat_eq_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ (cInt.nat @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ V1) @ (cNat.semiring_1_class.of_nat @ V0))) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))))))))
(TInt.nat_numeral,(call @ (^[V0]: ((cHOL.eq @ (cInt.nat @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TInt.odd_nonzero,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ V0)) @ V0)) @ cInt.zero_int_inst.zero_int)))))
(TInt.one_int.rsp,((cInt.intrel @ ((cProduct_Type.Pair @ cNat.one_nat_inst.one_nat) @ cNat.zero_nat_inst.zero_nat)) @ ((cProduct_Type.Pair @ cNat.one_nat_inst.one_nat) @ cNat.zero_nat_inst.zero_nat)))
(TInt.one_int_def,((c== @ cInt.one_int_inst.one_int) @ (cInt.Abs_Integ @ ((cProduct_Type.Pair @ cNat.one_nat_inst.one_nat) @ cNat.zero_nat_inst.zero_nat))))
(TInt.sup_int_def,((cHOL.eq @ cInt.sup_int_inst.sup_int) @ cOrderings.ord_class.max))
(TInt.zdvd_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1))))))))
(TInt.zdvd_period,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ V2) @ V3))) @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.plus_int_inst.plus_int @ V2) @ ((cInt.times_int_inst.times_int @ V4) @ V1))) @ V3)))))))))))))))
(TInt.zdvd_reduce,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ ((cInt.times_int_inst.times_int @ V0) @ V2)))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))))
(TInt.zdvd_zdiffD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.minus_int_inst.minus_int @ V1) @ V2))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V1))))))))))
(TLattices.inf1D1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.inf_class.inf @ V0) @ V1) @ V2)) @ (V0 @ V2)))))))))
(TLattices.inf1D2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.inf_class.inf @ V0) @ V1) @ V2)) @ (V1 @ V2)))))))))
(TLattices.inf2D1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.inf_class.inf @ V0) @ V1) @ V2) @ V3)) @ ((V0 @ V2) @ V3)))))))))))
(TLattices.inf2D2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.inf_class.inf @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ V2) @ V3)))))))))))
(TLattices.sup1CI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ (V0 @ V1))) @ (V2 @ V1))) @ (((cLattices.sup_class.sup @ V2) @ V0) @ V1)))))))))
(TLattices.sup1I1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ (((cLattices.sup_class.sup @ V0) @ V2) @ V1)))))))))
(TLattices.sup1I2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ (((cLattices.sup_class.sup @ V2) @ V0) @ V1)))))))))
(TLattices.sup2CI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ (cHOL.Not @ ((V0 @ V1) @ V2))) @ ((V3 @ V1) @ V2))) @ ((((cLattices.sup_class.sup @ V3) @ V0) @ V1) @ V2)))))))))))
(TLattices.sup2I1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((((cLattices.sup_class.sup @ V0) @ V3) @ V1) @ V2)))))))))))
(TLattices.sup2I2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((((cLattices.sup_class.sup @ V3) @ V0) @ V1) @ V2)))))))))))
(TLifting.NEG_POS,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLifting.NEG @ V0) @ V1)) @ ((cLifting.POS @ V1) @ V0)))))))
(TLifting.NEG_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLifting.NEG @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TLifting.POS_NEG,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLifting.POS @ V0) @ V1)) @ ((cLifting.NEG @ V1) @ V0)))))))
(TLifting.POS_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLifting.POS @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TList.Bleast_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.Bleast @ V0) @ V1)) @ (cOrderings.ord_class.Least @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))))))))
(TList.UNIV_coset,((cHOL.eq @ cOrderings.top_class.top) @ (cList.coset @ cList.list.Nil)))
(TList.append_def,((c== @ cList.append) @ (^[V0]: (((cList.list.list_rec @ (^[V1]: V1)) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cList.list.Cons @ V1) @ (V3 @ V4))))))) @ V0))))
(TList.bind_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.bind @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ ((cList.append @ (V2 @ V0)) @ ((cList.bind @ V1) @ V2))))))))))
(TList.bind_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.bind @ cList.list.Nil) @ V0)) @ cList.list.Nil))))
(TList.butlast_tl,(call @ (^[V0]: ((cHOL.eq @ (cList.butlast @ (cList.tl @ V0))) @ (cList.tl @ (cList.butlast @ V0))))))
(TList.concat_def,((c== @ cList.concat) @ (^[V0]: (((cList.list.list_rec @ cList.list.Nil) @ (^[V1]: (^[V2]: (^[V3]: ((cList.append @ V1) @ V3))))) @ V0))))
(TList.drop.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cNat.nat.nat_case @ ((cList.list.Cons @ V1) @ V2)) @ (^[V3]: ((cList.drop @ V3) @ V2))) @ V0)))))))))
(TList.drop.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.drop @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.drop_Cons',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cList.list.Cons @ V1) @ V2)) @ ((cList.drop @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V2))))))))))
(TList.filter_def,((c== @ cList.filter) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ (V5 @ V2)) @ ((cList.list.Cons @ V2) @ (V4 @ V5))) @ (V4 @ V5))))))) @ V1) @ V0)))))
(TList.filter_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.filter @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ V1) @ ((cList.filter @ ((cFun.comp @ V0) @ V1)) @ V2))))))))))
(TList.filter_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.filter @ V0) @ (cList.set @ V1))) @ (cList.set @ ((cList.filter @ V0) @ V1))))))))
(TList.find.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.find @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ (V0 @ V1)) @ (cOption.option.Some @ V1)) @ ((cList.find @ V0) @ V2))))))))))
(TList.find.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.find @ V0) @ cList.list.Nil)) @ cOption.option.None))))
(TList.finite_set,(call @ (^[V0]: (cFinite_Set.finite @ (cList.set @ V0)))))
(TList.fold.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.fold @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cFun.comp @ ((cList.fold @ V0) @ V2)) @ (V0 @ V1))))))))))
(TList.fold.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.fold @ V0) @ cList.list.Nil)) @ cFun.id))))
(TList.fold_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.fold @ V0) @ ((cList.list.Cons @ V1) @ V2)) @ V3)) @ (((cList.fold @ V0) @ V2) @ ((V0 @ V1) @ V3))))))))))))
(TList.fold_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.fold @ V0) @ cList.list.Nil) @ V1)) @ V1))))))
(TList.foldl_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ (cList.set @ V2))) @ ((cHOL.eq @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))) @ ((cHOL.eq @ (((cList.foldl @ V4) @ V0) @ V2)) @ (((cList.foldl @ V5) @ V1) @ V3))))))))))))))))))
(TList.foldr_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ (cList.set @ V2))) @ ((cHOL.eq @ ((V4 @ V7) @ V6)) @ ((V5 @ V7) @ V6)))))))) @ ((cHOL.eq @ (((cList.foldr @ V4) @ V2) @ V0)) @ (((cList.foldr @ V5) @ V3) @ V1))))))))))))))))))
(TList.foldr_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V2) @ (cList.set @ V0))) @ ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V3)) @ (V1 @ V2))) @ ((cFun.comp @ (V1 @ V2)) @ (V1 @ V3)))))))))) @ ((cHOL.eq @ ((cList.foldr @ V1) @ V0)) @ ((cList.fold @ V1) @ V0))))))))
(TList.hd_Cons_tl,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ ((cList.list.Cons @ (cList.hd @ V0)) @ (cList.tl @ V0))) @ V0)))))
(TList.hd_append2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.hd @ ((cList.append @ V0) @ V1))) @ (cList.hd @ V0))))))))
(TList.in_listspD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cList.listsp @ V0) @ V1)) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: (V0 @ V2)))))))))
(TList.in_listspI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cList.listsp @ V1) @ V0)))))))
(TList.in_set_zip,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ ((cList.zip @ V1) @ V2)))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ ((cList.nth @ V1) @ V3)) @ (cProduct_Type.fst @ V0))) @ ((cHOL.conj @ ((cHOL.eq @ ((cList.nth @ V2) @ V3)) @ (cProduct_Type.snd @ V0))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V2)))))))))))))))
(TList.inj_on_rev,(call @ (^[V0]: ((cFun.inj_on @ cList.rev) @ V0))))
(TList.insert_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.insert @ V0) @ cList.list.Nil)) @ ((cList.list.Cons @ V0) @ cList.list.Nil)))))
(TList.insert_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.insert @ V0) @ V1)) @ (((cHOL.If @ ((cSet.member @ V0) @ (cList.set @ V1))) @ V1) @ ((cList.list.Cons @ V0) @ V1))))))))
(TList.last.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.last @ ((cList.list.Cons @ V0) @ V1))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ V0) @ (cList.last @ V1))))))))
(TList.last_ConsL,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ (cList.last @ ((cList.list.Cons @ V1) @ V0))) @ V1)))))))
(TList.last_ConsR,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.last @ ((cList.list.Cons @ V1) @ V0))) @ (cList.last @ V0))))))))
(TList.length_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.map @ V0) @ V1))) @ (cNat.size_class.size @ V1)))))))
(TList.length_rev,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.rev @ V0))) @ (cNat.size_class.size @ V0)))))
(TList.length_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.upt @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))))))
(TList.length_zip,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.zip @ V0) @ V1))) @ ((cOrderings.ord_class.min @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))
(TList.lenlex_def,(call @ (^[V0]: ((cHOL.eq @ (cList.lenlex @ V0)) @ ((cRelation.inv_image @ ((cWellfounded.lex_prod @ cWellfounded.less_than) @ (cList.lex @ V0))) @ (^[V1]: ((cProduct_Type.Pair @ (cNat.size_class.size @ V1)) @ V1)))))))
(TList.lexn.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.lexn @ V0) @ (cNat.Suc @ V1))) @ ((cLattices.inf_class.inf @ ((cSet.image @ ((cProduct_Type.map_pair @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cList.list.Cons @ V2) @ V3))))) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cList.list.Cons @ V2) @ V3)))))) @ ((cWellfounded.lex_prod @ V0) @ ((cList.lexn @ V0) @ V1)))) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ (cNat.size_class.size @ V3)) @ (cNat.Suc @ V1))))))))))))))
(TList.lexn.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.lexn @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cOrderings.bot_class.bot))))
(TList.lexord_def,(call @ (^[V0]: ((cHOL.eq @ (cList.lexord @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.disj @ ((cHOL.eq @ V2) @ ((cList.append @ V1) @ ((cList.list.Cons @ V3) @ V4)))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ V0)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V5) @ ((cList.list.Cons @ V6) @ V8)))) @ ((cHOL.eq @ V2) @ ((cList.append @ V5) @ ((cList.list.Cons @ V7) @ V9))))))))))))))))))))))))))))
(TList.lexord_lex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.lex @ V2))) @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.lexord @ V2))) @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1)))))))))))
(TList.list.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list.list_case @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ ((V1 @ V2) @ V3)))))))))))
(TList.list.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list.list_case @ V0) @ V1) @ cList.list.Nil)) @ V0))))))
(TList.list.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list.list_rec @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ (((V1 @ V2) @ V3) @ (((cList.list.list_rec @ V0) @ V1) @ V3))))))))))))
(TList.list.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list.list_rec @ V0) @ V1) @ cList.list.Nil)) @ V0))))))
(TList.list.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list.list_case @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ ((V1 @ V2) @ V3)))))))))))
(TList.list.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list.list_case @ V0) @ V1) @ cList.list.Nil)) @ V0))))))
(TList.list.simps_3,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ cList.list.Nil)))))))
(TList.list.simps_2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cList.list.Nil) @ ((cList.list.Cons @ V0) @ V1))))))))
(TList.list.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TList.list.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cList.list.list_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))
(TList.list_all2I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ (cList.set @ ((cList.zip @ V0) @ V1))) @ (^[V3]: ((cProduct_Type.prod.prod_case @ V2) @ V3)))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ (((cList.list_all2 @ V2) @ V0) @ V1))))))))))
(TList.listrel1I1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V3)) @ ((cList.list.Cons @ V1) @ V3))) @ (cList.listrel1 @ V2))))))))))))
(TList.listrel1I2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel1 @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V0)) @ ((cList.list.Cons @ V3) @ V1))) @ (cList.listrel1 @ V2))))))))))))
(TList.lists.Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (cList.lists @ V1))) @ ((cSet.member @ ((cList.list.Cons @ V0) @ V2)) @ (cList.lists @ V1)))))))))))
(TList.lists_IntI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.lists @ V1))) @ ((c==> @ ((cSet.member @ V0) @ (cList.lists @ V2))) @ ((cSet.member @ V0) @ (cList.lists @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))))
(TList.lists_UNIV,((cHOL.eq @ (cList.lists @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(TList.lists_accD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.lists @ (cWellfounded.acc @ V1)))) @ ((cSet.member @ V0) @ (cWellfounded.acc @ (cList.listrel1 @ V1)))))))))
(TList.lists_accI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ (cList.listrel1 @ V1)))) @ ((cSet.member @ V0) @ (cList.lists @ (cWellfounded.acc @ V1)))))))))
(TList.lists_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.lists @ V0)) @ (cList.lists @ V1))))))))
(TList.listsp.Nil,(call @ (^[V0]: ((cList.listsp @ V0) @ cList.list.Nil))))
(TList.listsp_def,((c== @ cList.listsp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: ((cHOL.disj @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V3) @ V4))) @ ((cHOL.conj @ (V0 @ V3)) @ (V1 @ V4))))))))))))))
(TList.map_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.append @ V1) @ V2))) @ ((cList.append @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V0) @ V2))))))))))
(TList.map_concat,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ V0) @ (cList.concat @ V1))) @ (cList.concat @ ((cList.map @ (cList.map @ V0)) @ V1))))))))
(TList.map_inj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V0) @ V2))) @ ((c==> @ ((cFun.inj_on @ V0) @ ((cLattices.sup_class.sup @ (cList.set @ V1)) @ (cList.set @ V2)))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TList.map_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cList.map @ V0) @ (((cList.list_update @ V1) @ V2) @ V3))) @ (((cList.list_update @ ((cList.map @ V0) @ V1)) @ V2) @ (V0 @ V3))))))))))))
(TList.maps_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cList.maps @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.maps_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.maps @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.append @ (V0 @ V1)) @ ((cList.maps @ V0) @ V2))))))))))
(TList.member_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.member @ V0) @ V1)) @ ((cSet.member @ V1) @ (cList.set @ V0))))))))
(TList.member_rec_2,(call @ (^[V0]: ((cHOL.eq @ ((cList.member @ cList.list.Nil) @ V0)) @ cHOL.False))))
(TList.member_rec_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.member @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V2)) @ ((cList.member @ V1) @ V2))))))))))
(TList.nth_Cons_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))
(TList.nth_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.append @ V0) @ V1)) @ V2)) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cList.nth @ V0) @ V2)) @ ((cList.nth @ V1) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ (cNat.size_class.size @ V0))))))))))))
(TList.rev_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rev @ ((cList.append @ V0) @ V1))) @ ((cList.append @ (cList.rev @ V1)) @ (cList.rev @ V0))))))))
(TList.rev_concat,(call @ (^[V0]: ((cHOL.eq @ (cList.rev @ (cList.concat @ V0))) @ (cList.concat @ ((cList.map @ cList.rev) @ (cList.rev @ V0)))))))
(TList.rev_filter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rev @ ((cList.filter @ V0) @ V1))) @ ((cList.filter @ V0) @ (cList.rev @ V1))))))))
(TList.rev_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cList.append @ V3) @ ((cList.list.Cons @ V2) @ cList.list.Nil))))))))) @ (V0 @ V1))))))))
(TList.rev_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (cList.rev @ (((cList.list_update @ V1) @ V0) @ V2))) @ (((cList.list_update @ (cList.rev @ V1)) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V1)) @ V0)) @ cNat.one_nat_inst.one_nat)) @ V2))))))))))
(TList.rotate_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.rotate @ (cNat.Suc @ V0)) @ V1)) @ (cList.rotate1 @ ((cList.rotate @ V0) @ V1))))))))
(TList.rotate_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rotate @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ ((cFun.comp @ (cList.rotate @ V0)) @ (cList.rotate @ V1))))))))
(TList.rotate_def,(call @ (^[V0]: ((cHOL.eq @ (cList.rotate @ V0)) @ ((cNat.compow @ V0) @ cList.rotate1)))))
(TList.rotate_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.rotate @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ V1) @ ((cList.rotate @ V0) @ V2))))))))))
(TList.rotate_rev,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.rotate @ V0) @ (cList.rev @ V1))) @ (cList.rev @ ((cList.rotate @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.size_class.size @ V1)))) @ V1))))))))
(TList.set_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.append @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cList.set @ V0)) @ (cList.set @ V1))))))))
(TList.set_concat,(call @ (^[V0]: ((cHOL.eq @ (cList.set @ (cList.concat @ V0))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cList.set @ V0)) @ (^[V1]: (cList.set @ V1)))))))
(TList.set_empty2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (cList.set @ V0))) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.set_filter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.filter @ V0) @ V1))) @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ (cList.set @ V1))) @ (V0 @ V2))))))))))
(TList.set_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.insert @ V0) @ V1))) @ ((cSet.insert @ V0) @ (cList.set @ V1))))))))
(TList.set_rotate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.rotate @ V0) @ V1))) @ (cList.set @ V1)))))))
(TList.sorted_upt,(call @ (^[V0]: (call @ (^[V1]: (cList.linorder_class.sorted @ ((cList.upt @ V0) @ V1)))))))
(TList.splice_def,((c== @ cList.splice) @ (^[V0]: (^[V1]: (cList.splice_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TList.split_list,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V1) @ ((cList.append @ V2) @ ((cList.list.Cons @ V0) @ V3)))))))))))))
(TList.take.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cNat.nat.nat_case @ cList.list.Nil) @ (^[V3]: ((cList.list.Cons @ V1) @ ((cList.take @ V3) @ V2)))) @ V0)))))))))
(TList.take.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.take @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.take_Cons',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cList.list.Nil) @ ((cList.list.Cons @ V1) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V2)))))))))))
(TList.tl_append2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.tl @ ((cList.append @ V0) @ V1))) @ ((cList.append @ (cList.tl @ V0)) @ V1))))))))
(TList.update_zip,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_update @ ((cList.zip @ V0) @ V1)) @ V2) @ V3)) @ ((cList.zip @ (((cList.list_update @ V0) @ V2) @ (cProduct_Type.fst @ V3))) @ (((cList.list_update @ V1) @ V2) @ (cProduct_Type.snd @ V3)))))))))))))
(TList.upto.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TList.upto.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.upto @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.list.Cons @ V4) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))) @ cList.list.Nil))) @ V3)))))))) @ V3)))))))))))
(TList.upto.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cList.list.Cons @ V0) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1))) @ cList.list.Nil)))))))
(TList.upto_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cHOL.eq @ ((cList.upto @ V1) @ V0)) @ cList.list.Nil)))))))
(TList.zip_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.zip @ ((cList.append @ V0) @ V2)) @ ((cList.append @ V1) @ V3))) @ ((cList.append @ ((cList.zip @ V0) @ V1)) @ ((cList.zip @ V2) @ V3)))))))))))))
(TList.zip_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cList.zip @ (((cList.list_update @ V0) @ V1) @ V2)) @ (((cList.list_update @ V3) @ V1) @ V4))) @ (((cList.list_update @ ((cList.zip @ V0) @ V3)) @ V1) @ ((cProduct_Type.Pair @ V2) @ V4))))))))))))))
(TMap.dom_fun_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cMap.dom @ (((cFun.fun_upd @ V0) @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V2) @ cOption.option.None)) @ ((cGroups.minus_class.minus @ (cMap.dom @ V0)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet.insert @ V1) @ (cMap.dom @ V0)))))))))))
(TMap.dom_map_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.dom @ ((cMap.map_add @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cMap.dom @ V1)) @ (cMap.dom @ V0))))))))
(TMap.map_add_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMap.map_add @ V0) @ V1)) @ (^[V2]: (((cOption.option.option_case @ (V0 @ V2)) @ (^[V3]: (cOption.option.Some @ V3))) @ (V1 @ V2)))))))))
(TMap.map_add_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cMap.map_add @ V0) @ (((cFun.fun_upd @ V1) @ V2) @ (cOption.option.Some @ V3)))) @ (((cFun.fun_upd @ ((cMap.map_add @ V0) @ V1)) @ V2) @ (cOption.option.Some @ V3))))))))))))
(TMap.map_le_refl,(call @ (^[V0]: ((cMap.map_le @ V0) @ V0))))
(TMap.map_le_upds,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cMap.map_le @ V0) @ V1)) @ ((cMap.map_le @ (((cMap.map_upds @ V0) @ V2) @ V3)) @ (((cMap.map_upds @ V1) @ V2) @ V3))))))))))))
(TMap.ran_map_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ cOption.option.None)) @ ((cHOL.eq @ (cMap.ran @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2)))) @ ((cSet.insert @ V2) @ (cMap.ran @ V0)))))))))))
(TMap.restrict_in,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ (((cMap.restrict_map @ V2) @ V1) @ V0)) @ (V2 @ V0))))))))))
(TMeson.COMBB_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cMeson.COMBB @ V0) @ V1) @ V2)) @ (V0 @ (V1 @ V2))))))))))
(TMeson.COMBC_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cMeson.COMBC @ V0) @ V1) @ V2)) @ ((V0 @ V2) @ V1)))))))))
(TMeson.COMBI_def,(call @ (^[V0]: ((cHOL.eq @ (cMeson.COMBI @ V0)) @ V0))))
(TMeson.COMBK_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMeson.COMBK @ V0) @ V1)) @ V0))))))
(TMeson.COMBS_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cMeson.COMBS @ V0) @ V1) @ V2)) @ ((V0 @ V2) @ (V1 @ V2))))))))))
(TMeson.TruepropI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ V1)) @ ((c== @ V0) @ V1)))))))
(TMeson.conj_exD1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ V1)))))))))
(TMeson.conj_exD2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ V0) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ V0) @ (V1 @ V2))))))))))
(TMeson.disj_comm,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ V1) @ V0)))))))
(TMeson.disj_exD1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ V1)))))))))
(TMeson.disj_exD2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ V0) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.disj @ V0) @ (V1 @ V2))))))))))
(TMeson.not_conjD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(TMeson.not_disjD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(TNat.Nat.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat.Nat @ V0)) @ ((c==> @ (V1 @ cNat.Zero_Rep)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNat.Nat @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cNat.Suc_Rep @ V2))))))) @ (V1 @ V0)))))))))
(TNat.Nat_Rep_Nat,(call @ (^[V0]: (cNat.Nat @ (cNat.Rep_Nat @ V0)))))
(TNat.One_nat_def,((cHOL.eq @ cNat.one_nat_inst.one_nat) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))
(TNat.Suc_diff_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V1)) @ V0)) @ (cNat.Suc @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))))))))
(TNat.Suc_le_mono,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.Suc_less_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat.Suc_n_not_n,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNat.Suc @ V0)) @ V0)))))
(TNat.add_0_right,(call @ (^[V0]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V0))))
(TNat.add_le_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V3)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3)))))))))))))
(TNat.bot_nat_def,((cHOL.eq @ cNat.bot_nat_inst.bot_nat) @ cNat.zero_nat_inst.zero_nat))
(TNat.comp_funpow,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ V0) @ (cFun.comp @ V1))) @ (cFun.comp @ ((cNat.compow @ V0) @ V1))))))))
(TNat.diff_0_eq_0,(call @ (^[V0]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TNat.diff_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2)))))))))
(TNat.diff_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((V0 @ V3) @ cNat.zero_nat_inst.zero_nat)))) @ ((c==> @ (call @ (^[V3]: ((V0 @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V3))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ (cNat.Suc @ V3)) @ (cNat.Suc @ V4)))))))) @ ((V0 @ V1) @ V2)))))))))))
(TNat.dvd.antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.dvd.eq_refl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.dvd.le_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.dvd.less_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TNat.dvd.max_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cOrderings.ord.max @ cRings.dvd_class.dvd) @ V0) @ V1)) @ (((cHOL.If @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ V1) @ V0)))))))
(TNat.dvd.min_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cOrderings.ord.min @ cRings.dvd_class.dvd) @ V0) @ V1)) @ (((cHOL.If @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ V0) @ V1)))))))
(TNat.dvd_1_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TNat.dvd_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.eq_diff_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V0))) @ ((cHOL.eq @ V1) @ V2)))))))))))
(TNat.funpow_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.compow @ V0) @ ((cNat.compow @ V1) @ V2))) @ ((cNat.compow @ ((cNat.times_nat_inst.times_nat @ V1) @ V0)) @ V2)))))))))
(TNat.inf_nat_def,((cHOL.eq @ cNat.inf_nat_inst.inf_nat) @ cOrderings.ord_class.min))
(TNat.le_add_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2)) @ V0))))))))))
(TNat.le_diff_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V0))) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)))))))))))
(TNat.less_Suc_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.max_Suc_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ (cNat.Suc @ ((cOrderings.ord_class.max @ V0) @ V1))))))))
(TNat.min_Suc_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ (cNat.Suc @ ((cOrderings.ord_class.min @ V0) @ V1))))))))
(TNat.n_not_Suc_n,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ V0) @ (cNat.Suc @ V0))))))
(TNat.nat.Rep_Nat,(call @ (^[V0]: ((cSet.member @ (cNat.Rep_Nat @ V0)) @ (cSet.Collect @ (^[V1]: (cNat.Nat @ V1)))))))
(TNat.nat.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TNat.nat.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.Suc @ V2))) @ V1)))) @ V1)))))))
(TNat.nat.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNat.Suc @ V2)))))) @ (V0 @ V1))))))))
(TNat.nat_distrib_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))))))))))
(TNat.nat_distrib_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.nat_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))))))))))
(TNat.nat_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.nat_less_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TNat.nat_neq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V0))))))))
(TNat.nat_rec_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ (cNat.Suc @ V2))) @ ((V1 @ V2) @ (((cNat.nat.nat_rec @ V0) @ V1) @ V2))))))))))
(TNat.not_less_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.Suc @ V0))))))))
(TNat.sup_nat_def,((cHOL.eq @ cNat.sup_nat_inst.sup_nat) @ cOrderings.ord_class.max))
(TNat.zero_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ (cNat.Suc @ V2))) @ (V0 @ V2))))) @ (V0 @ cNat.zero_nat_inst.zero_nat))))))))
(TNitpick.num_def,((c== @ cNitpick.num) @ ((cFun.comp @ cProduct_Type.fst) @ cNitpick.Rep_Frac)))
(TNitpick.wf'_def,(call @ (^[V0]: ((c== @ (cNitpick.wf' @ V0)) @ ((cHOL.conj @ (cTransitive_Closure.acyclic @ V0)) @ ((cHOL.disj @ (cFinite_Set.finite @ V0)) @ cNitpick.unknown))))))
(TNum.Suc_numeral,(call @ (^[V0]: ((cHOL.eq @ (cNat.Suc @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.arith_simps_65,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.arith_simps_64,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.arith_simps_63,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TNum.arith_simps_62,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TNum.arith_simps_61,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_simps_60,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_simps_59,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_simps_58,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_simps_57,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TNum.arith_simps_56,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.zero_class.zero) @ V0)) @ (cGroups.uminus_class.uminus @ V0)))))
(TNum.arith_simps_55,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNum.arith_simps_54,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_simps_53,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_simps_52,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TNum.arith_simps_51,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNum.arith_simps_50,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNum.arith_simps_49,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.arith_simps_48,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TNum.arith_simps_47,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TNum.arith_simps_46,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TNum.arith_simps_45,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_simps_44,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNum.arith_simps_43,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TNum.arith_simps_42,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_simps_41,((cHOL.eq @ (cGroups.abs_class.abs @ cGroups.one_class.one)) @ cGroups.one_class.one))
(TNum.arith_simps_40,((cHOL.eq @ (cGroups.abs_class.abs @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNum.arith_simps_39,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))))))
(TNum.arith_simps_38,((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ cGroups.one_class.one)) @ cGroups.one_class.one))
(TNum.arith_simps_37,((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ cGroups.zero_class.zero)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNum.arith_simps_36,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit1 @ V0))))))
(TNum.arith_simps_35,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))))))
(TNum.arith_simps_34,((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))))
(TNum.arith_simps_33,((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ cGroups.zero_class.zero)) @ cGroups.one_class.one))
(TNum.arith_simps_32,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.BitM @ V0))))))
(TNum.arith_simps_31,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.arith_simps_30,((cHOL.eq @ (cNum.neg_numeral_class.dbl @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNum.arith_simps_29,((cHOL.eq @ (cNum.neg_numeral_class.dbl @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNum.arith_simps_28,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.arith_simps_27,(call @ (^[V0]: ((cHOL.eq @ (cNum.BitM @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ V0))))))
(TNum.arith_simps_26,(call @ (^[V0]: ((cHOL.eq @ (cNum.BitM @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit1 @ (cNum.BitM @ V0))))))
(TNum.arith_simps_25,((cHOL.eq @ (cNum.BitM @ cNum.num.One)) @ cNum.num.One))
(TNum.arith_simps_24,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.neg_numeral_class.dbl @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.arith_simps_23,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.neg_numeral_class.dbl_inc @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.arith_simps_22,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.neg_numeral_class.dbl_dec @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.arith_simps_21,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.neg_numeral_class.dbl @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.arith_simps_20,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.arith_simps_19,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))))))
(TNum.arith_simps_18,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.arith_simps_17,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.BitM @ V0))))))
(TNum.arith_simps_16,((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ cNum.num.One)) @ cGroups.zero_class.zero))
(TNum.arith_simps_15,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))))
(TNum.arith_simps_14,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ V1))))))))
(TNum.arith_simps_13,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ (cNum.num.Bit1 @ V1)))))))))
(TNum.arith_simps_12,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ V1)))))))))
(TNum.arith_simps_11,(call @ (^[V0]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ cNum.num.One) @ V0)) @ V0))))
(TNum.arith_simps_10,(call @ (^[V0]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ V0) @ cNum.num.One)) @ V0))))
(TNum.arith_simps_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)) @ cNum.num.One))))))))
(TNum.arith_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_simps_7,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.arith_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_simps_4,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cNum.num.Bit1 @ V0)))))
(TNum.arith_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.arith_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit1 @ V0)))))
(TNum.arith_simps_1,((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ cNum.num.One)) @ (cNum.num.Bit0 @ cNum.num.One)))
(TNum.nat_1_add_1,((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ cNat.one_nat_inst.one_nat) @ cNat.one_nat_inst.one_nat)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNum.num.One_def,((c== @ cNum.num.One) @ (cNum.Abs_num @ (cDatatype.In0 @ cHOL.undefined))))
(TNum.num.Rep_num,(call @ (^[V0]: ((cSet.member @ (cNum.Rep_num @ V0)) @ (cSet.Collect @ cNum.num.num_rep_set)))))
(TNum.num.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TNum.num.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cNum.num.One)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNum.num.Bit0 @ V2))) @ V1)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNum.num.Bit1 @ V2))) @ V1)))) @ V1))))))))
(TNum.num.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cNum.num.One)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNum.num.Bit0 @ V2)))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNum.num.Bit1 @ V2)))))) @ (V0 @ V1)))))))))
(TOption.bind_def,((c== @ cOption.bind) @ (^[V0]: (((cOption.option.option_rec @ (^[V1]: cOption.option.None)) @ (^[V1]: (^[V2]: (V2 @ V1)))) @ V0))))
(TOption.elem_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cOption.set @ V1))) @ ((cHOL.eq @ V1) @ (cOption.option.Some @ V0))))))))
(TOption.inj_Some,(call @ (^[V0]: ((cFun.inj_on @ cOption.option.Some) @ V0))))
(TOption.map.comp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (cOption.map @ V0)) @ (cOption.map @ V1))) @ (cOption.map @ ((cFun.comp @ V0) @ V1))))))))
(TOption.map_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cOption.option.Some @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cOption.map @ V2) @ V0)) @ ((cOption.map @ V3) @ V1)))))))))))))
(TOrderings.bot1E,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.bot_class.bot @ V0)) @ V1))))))
(TOrderings.bot2E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.bot_class.bot @ V0) @ V1)) @ V2))))))))
(TOrderings.top1I,(call @ (^[V0]: (cOrderings.top_class.top @ V0))))
(TOrderings.top2I,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.top_class.top @ V0) @ V1))))))
(TPredicate.bindE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPredicate.eval @ ((cPredicate.bind @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cPredicate.eval @ V0) @ V4)) @ ((c==> @ ((cPredicate.eval @ (V1 @ V4)) @ V2)) @ V3))))) @ V3)))))))))))
(TPredicate.bindI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPredicate.eval @ V0) @ V1)) @ ((c==> @ ((cPredicate.eval @ (V2 @ V1)) @ V3)) @ ((cPredicate.eval @ ((cPredicate.bind @ V0) @ V2)) @ V3))))))))))))
(TPredicate.supI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ V0) @ V1)) @ ((cPredicate.eval @ ((cLattices.sup_class.sup @ V0) @ V2)) @ V1)))))))))
(TPredicate.supI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ V0) @ V1)) @ ((cPredicate.eval @ ((cLattices.sup_class.sup @ V2) @ V0)) @ V1)))))))))
(TPresburger.aset_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V1) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ V2) @ V2)))))))))))
(TPresburger.aset_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V1)) @ (^[V5]: ((cSet.Ball @ V2) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ V4) @ V3)))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.plus_int_inst.plus_int @ V4) @ V1)) @ V3)))))))))))))))))
(TPresburger.aset_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V1)) @ (^[V5]: ((cSet.Ball @ V2) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ V4) @ V3))) @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.plus_int_inst.plus_int @ V4) @ V1)) @ V3))))))))))))))))
(TPresburger.aset_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V1) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ V2) @ V3)) @ ((cInt.ord_int_inst.less_eq_int @ V2) @ ((cInt.plus_int_inst.plus_int @ V3) @ V0))))))))))))))
(TPresburger.aset_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V1) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V2) @ V3)) @ ((cInt.ord_int_inst.less_int @ V2) @ ((cInt.plus_int_inst.plus_int @ V3) @ V0))))))))))))))
(TPresburger.aset_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ V3) @ V0)) @ V1))))))))))))))
(TPresburger.aset_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V3) @ V1)) @ ((cInt.ord_int_inst.less_int @ ((cInt.plus_int_inst.plus_int @ V3) @ V0)) @ V1))))))))))))))
(TPresburger.aset_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V1))) @ (cHOL.Not @ ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ V3) @ V0)) @ V1)))))))))))))))
(TPresburger.aset_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ V1)) @ ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ V3) @ V0)) @ V1))))))))))))))
(TPresburger.aset_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V2 @ V4)) @ (V2 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))))))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V3 @ V4)) @ (V3 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))))))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ ((cHOL.disj @ (V2 @ V4)) @ (V3 @ V4))) @ ((cHOL.disj @ (V2 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))) @ (V3 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))))))))))))))))))
(TPresburger.aset_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V2 @ V4)) @ (V2 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))))))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V3 @ V4)) @ (V3 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))))))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ ((cHOL.conj @ (V2 @ V4)) @ (V3 @ V4))) @ ((cHOL.conj @ (V2 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))) @ (V3 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))))))))))))))))))
(TPresburger.bset_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V1) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ V2) @ V2)))))))))))
(TPresburger.bset_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V1)) @ (^[V5]: ((cSet.Ball @ V2) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ V4) @ V3)))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.minus_int_inst.minus_int @ V4) @ V1)) @ V3)))))))))))))))))
(TPresburger.bset_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V1)) @ (^[V5]: ((cSet.Ball @ V2) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ V4) @ V3))) @ ((cRings.dvd_class.dvd @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.minus_int_inst.minus_int @ V4) @ V1)) @ V3))))))))))))))))
(TPresburger.bset_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int)) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V3)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ ((cInt.minus_int_inst.minus_int @ V3) @ V0)))))))))))))))
(TPresburger.bset_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V1) @ V3)) @ ((cInt.ord_int_inst.less_int @ V1) @ ((cInt.minus_int_inst.minus_int @ V3) @ V0)))))))))))))))
(TPresburger.bset_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V1) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.minus_int_inst.minus_int @ V3) @ V0)) @ V2)))))))))))))
(TPresburger.bset_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V1) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V3) @ V2)) @ ((cInt.ord_int_inst.less_int @ ((cInt.minus_int_inst.minus_int @ V3) @ V0)) @ V2)))))))))))))
(TPresburger.bset_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V1))) @ (cHOL.Not @ ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ V3) @ V0)) @ V1)))))))))))))))
(TPresburger.bset_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cSet.member @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int)) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ V3) @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ V1)) @ ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ V3) @ V0)) @ V1))))))))))))))
(TPresburger.bset_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V2 @ V4)) @ (V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))))))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V3 @ V4)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))))))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ ((cHOL.disj @ (V2 @ V4)) @ (V3 @ V4))) @ ((cHOL.disj @ (V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))))))))))))))))))
(TPresburger.bset_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V2 @ V4)) @ (V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))))))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V3 @ V4)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))))))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V1) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ ((cHOL.conj @ (V2 @ V4)) @ (V3 @ V4))) @ ((cHOL.conj @ (V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))))))))))))))))))
(TPresburger.cpmi,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V5) @ V4)) @ ((cHOL.eq @ (V1 @ V5)) @ (V2 @ V5)))))))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V3) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V1 @ V4)) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V4) @ V0))))))) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ (V2 @ V4)) @ (V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ ((cInt.times_int_inst.times_int @ V5) @ V0))))))))) @ ((cHOL.eq @ (cHOL.Ex @ (^[V4]: (V1 @ V4)))) @ ((cHOL.disj @ ((cSet.Bex @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: (V2 @ V4)))) @ ((cSet.Bex @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Bex @ V3) @ (^[V5]: (V1 @ ((cInt.plus_int_inst.plus_int @ V5) @ V4)))))))))))))))))))))
(TPresburger.cppi,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cHOL.eq @ (V1 @ V5)) @ (V2 @ V5)))))))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V5]: ((cSet.Ball @ V3) @ (^[V6]: (cHOL.Not @ ((cHOL.eq @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V5)))))))) @ ((cHOL.implies @ (V1 @ V4)) @ (V1 @ ((cInt.plus_int_inst.plus_int @ V4) @ V0))))))) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ (V2 @ V4)) @ (V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ ((cInt.times_int_inst.times_int @ V5) @ V0))))))))) @ ((cHOL.eq @ (cHOL.Ex @ (^[V4]: (V1 @ V4)))) @ ((cHOL.disj @ ((cSet.Bex @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: (V2 @ V4)))) @ ((cSet.Bex @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V4]: ((cSet.Bex @ V3) @ (^[V5]: (V1 @ ((cInt.minus_int_inst.minus_int @ V5) @ V4)))))))))))))))))))))
(TPresburger.minf_11,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cHOL.eq @ V0) @ V0)))))))))
(TPresburger.minf_10,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V3) @ V2)) @ ((cHOL.eq @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1)))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1))))))))))))))
(TPresburger.minf_9,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V3) @ V2)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1)))))))))))))
(TPresburger.minf_8,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ cHOL.False)))))))))
(TPresburger.minf_7,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V2)) @ cHOL.False)))))))))
(TPresburger.minf_6,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ cHOL.True)))))))))
(TPresburger.minf_5,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V2) @ V0)) @ cHOL.True)))))))))
(TPresburger.minf_4,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V2) @ V0))) @ cHOL.True)))))))))
(TPresburger.minf_3,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ V2) @ V0)) @ cHOL.False)))))))))
(TPresburger.minf_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cHOL.eq @ (V0 @ V5)) @ (V1 @ V5)))))))) @ ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cHOL.eq @ (V2 @ V5)) @ (V3 @ V5)))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cHOL.eq @ ((cHOL.disj @ (V0 @ V5)) @ (V2 @ V5))) @ ((cHOL.disj @ (V1 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TPresburger.minf_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cHOL.eq @ (V0 @ V5)) @ (V1 @ V5)))))))) @ ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cHOL.eq @ (V2 @ V5)) @ (V3 @ V5)))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cHOL.eq @ ((cHOL.conj @ (V0 @ V5)) @ (V2 @ V5))) @ ((cHOL.conj @ (V1 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TPresburger.pinf_11,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ V0) @ V0)))))))))
(TPresburger.pinf_10,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cHOL.eq @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1)))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1))))))))))))))
(TPresburger.pinf_9,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V1)))))))))))))
(TPresburger.pinf_8,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ cHOL.True)))))))))
(TPresburger.pinf_7,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V2)) @ cHOL.True)))))))))
(TPresburger.pinf_6,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ cHOL.False)))))))))
(TPresburger.pinf_5,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V2) @ V0)) @ cHOL.False)))))))))
(TPresburger.pinf_4,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V2) @ V0))) @ cHOL.True)))))))))
(TPresburger.pinf_3,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ V2) @ V0)) @ cHOL.False)))))))))
(TPresburger.pinf_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cHOL.eq @ (V0 @ V5)) @ (V1 @ V5)))))))) @ ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cHOL.eq @ (V2 @ V5)) @ (V3 @ V5)))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.disj @ (V0 @ V5)) @ (V2 @ V5))) @ ((cHOL.disj @ (V1 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TPresburger.pinf_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cHOL.eq @ (V0 @ V5)) @ (V1 @ V5)))))))) @ ((c==> @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cHOL.eq @ (V2 @ V5)) @ (V3 @ V5)))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.conj @ (V0 @ V5)) @ (V2 @ V5))) @ ((cHOL.conj @ (V1 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TPure.remdups_rl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ V0) @ ((c==> @ V1) @ V1))))))))
(TPure.transitive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c== @ V0) @ V1)) @ ((c==> @ ((c== @ V1) @ V2)) @ ((c== @ V0) @ V2))))))))))
(TQuotient.QT_all,(call @ (^[V0]: ((c==> @ (cQuotient.Quot_True @ (cHOL.All @ V0))) @ (cQuotient.Quot_True @ V0)))))
(TQuotient.QT_ex1,(call @ (^[V0]: ((c==> @ (cQuotient.Quot_True @ (cHOL.Ex1 @ V0))) @ (cQuotient.Quot_True @ V0)))))
(TQuotient.QT_ext,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (cQuotient.Quot_True @ (V0 @ V3))) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((c==> @ (cQuotient.Quot_True @ V0)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TQuotient.QT_imp,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (cQuotient.Quot_True @ V0)) @ (cQuotient.Quot_True @ V1)))))))
(TQuotient.QT_lam,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuotient.Quot_True @ V0)) @ (cQuotient.Quot_True @ (V0 @ V1))))))))
(TQuotient.ex_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cSet.Bex @ (cLifting.Respects @ V0)) @ (((cFun.map_fun @ V1) @ cFun.id) @ V3))) @ (cHOL.Ex @ V3))))))))))))
(TQuotient.ex_reg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((c==> @ (cHOL.Ex @ V0)) @ (cHOL.Ex @ V1))))))))
(TQuotient.id_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cFun.map_fun @ V2) @ V1) @ cFun.id)) @ cFun.id)))))))))
(TQuotient.id_rsp,(call @ (^[V0]: ((((cTransfer.fun_rel @ V0) @ V0) @ cFun.id) @ cFun.id))))
(TQuotient.if_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cFun.map_fun @ cFun.id) @ ((cFun.map_fun @ V2) @ ((cFun.map_fun @ V2) @ V1))) @ cHOL.If)) @ cHOL.If)))))))))
(TQuotient.if_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ V0))) @ cHOL.If) @ cHOL.If)))))))))
(TRandom.next_def,((c== @ cRandom.next) @ (^[V0]: ((cProduct_Type.prod.prod_rec @ (^[V1]: (^[V2]: ((cHOL.Let @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (^[V3]: ((cHOL.Let @ (((cRandom.minus_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ ((cCode_Numeral.div_natural_inst.mod_natural @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ V3) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))))) @ (^[V4]: ((cHOL.Let @ ((cCode_Numeral.div_natural_inst.div_natural @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (^[V5]: ((cHOL.Let @ (((cRandom.minus_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ ((cCode_Numeral.div_natural_inst.mod_natural @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ V5) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))))))) @ (^[V6]: ((cHOL.Let @ ((cCode_Numeral.plus_natural_inst.plus_natural @ (((cRandom.minus_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))) @ cCode_Numeral.one_natural_inst.one_natural)) @ (^[V7]: ((cProduct_Type.Pair @ V7) @ ((cProduct_Type.Pair @ V4) @ V6))))))))))))))) @ V0))))
(TRandom.pick_def,((c== @ cRandom.pick) @ (^[V0]: (((cList.list.list_rec @ cHOL.undefined) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ (cProduct_Type.fst @ V1))) @ (cProduct_Type.snd @ V1)) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ (cProduct_Type.fst @ V1))))))))) @ V0))))
(TRecord.abst_def,((c== @ cRecord.abst) @ (^[V0]: ((cRecord.tuple_isomorphism.tuple_isomorphism_rec @ (^[V1]: (^[V2]: V2))) @ V0))))
(TRecord.repr_def,((c== @ cRecord.repr) @ (^[V0]: ((cRecord.tuple_isomorphism.tuple_isomorphism_rec @ (^[V1]: (^[V2]: V1))) @ V0))))
(TRelation.Id_O_R,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcomp @ cRelation.Id) @ V0)) @ V0))))
(TRelation.Id_def,((cHOL.eq @ cRelation.Id) @ (cSet.Collect @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V1) @ V1))))))))
(TRelation.Id_onE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Id_on @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V3))) @ V2))))) @ V2)))))))))
(TRelation.Id_onI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V0)) @ (cRelation.Id_on @ V1))))))))
(TRelation.ImageE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cRelation.Image @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V0)) @ V1)) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ V3))))) @ V3)))))))))))
(TRelation.ImageI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ V0) @ V3)) @ ((cSet.member @ V1) @ ((cRelation.Image @ V2) @ V3)))))))))))))
(TRelation.R_O_Id,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcomp @ V0) @ cRelation.Id)) @ V0))))
(TRelation.RangeE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Range @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V0)) @ V1)) @ V2)))) @ V2)))))))))
(TRelation.reflpD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.reflp @ V0)) @ ((V0 @ V1) @ V1)))))))
(TRelation.reflpE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ ((c==> @ ((V0 @ V1) @ V1)) @ V2)) @ V2)))))))))
(TRelation.reflpI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((V0 @ V1) @ V1)))) @ (cRelation.reflp @ V0)))))
(TRelation.sym_Id,(cRelation.sym @ cRelation.Id))
(TRelation.sym_Un,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.sym @ V0)) @ ((c==> @ (cRelation.sym @ V1)) @ (cRelation.sym @ ((cLattices.sup_class.sup @ V0) @ V1)))))))))
(TRelation.transD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRelation.trans @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V0)))))))))))))
(TRelation.transE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRelation.trans @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)) @ ((c==> @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V0)) @ V4)) @ V4)))))))))))))))
(TRelation.transI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V0)))))))))) @ (cRelation.trans @ V0)))))
(TSMT.array_rules_6,(call @ (^[V0]: ((cHOL.eq @ (cSMT.fun_app @ V0)) @ V0))))
(TSMT.array_rules_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cFun.fun_upd @ (((cFun.fun_upd @ V0) @ V1) @ V2)) @ V1) @ V3)) @ (((cFun.fun_upd @ V0) @ V1) @ V3)))))))))))
(TSMT.array_rules_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ ((((cFun.fun_upd @ V2) @ V1) @ V3) @ V0)) @ (V2 @ V0))))))))))))
(TSMT.array_rules_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cFun.fun_upd @ V0) @ V1) @ V2) @ V1)) @ V2))))))))
(TSMT.array_rules_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cFun.fun_upd @ V0) @ V1) @ V2) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V3) @ V1)) @ V2) @ (V0 @ V3))))))))))))
(TSMT.array_rules_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.eq @ (^[V2]: (V0 @ V2))) @ (^[V2]: (V1 @ V2)))))))))
(TSMT.fun_app_def,(call @ (^[V0]: ((cHOL.eq @ (cSMT.fun_app @ V0)) @ V0))))
(TSMT.trigger_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSMT.trigger @ V0) @ V1)) @ V1))))))
(TSet.Diff_cancel,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V0)) @ cOrderings.bot_class.bot))))
(TSet.Diff_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V2)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))
(TSet.Diff_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V0))))))
(TSet.Int_Collect,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cLattices.inf_class.inf @ V1) @ (cSet.Collect @ (^[V3]: (V2 @ V3)))))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V1)) @ (V2 @ V0))))))))))
(TSet.Int_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ V0)) @ V0)))))))
(TSet.Int_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0)))))))
(TSet.Int_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V1) @ V0)))))))
(TSet.Un_Diff_Int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ V0))))))
(TSet.all_bool_eq,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ ((cHOL.conj @ (V0 @ cHOL.True)) @ (V0 @ cHOL.False))))))
(TSet.basic_monos_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.implies @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.basic_monos_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ (cSet.Collect @ V0)) @ (cSet.Collect @ V1))))))))
(TSet.basic_monos_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(TSet.basic_monos_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V2) @ V3)) @ ((cHOL.implies @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V3)))))))))))))
(TSet.basic_monos_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V2) @ V3)) @ ((cHOL.implies @ ((cHOL.disj @ V0) @ V2)) @ ((cHOL.disj @ V1) @ V3)))))))))))))
(TSet.basic_monos_2,(call @ (^[V0]: ((cHOL.implies @ V0) @ V0))))
(TSet.basic_monos_1,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ V0))))
(TSet.bool_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cHOL.True)) @ ((c==> @ (V0 @ cHOL.False)) @ (V0 @ V1))))))))
(TSet.bot_set_def,((cHOL.eq @ cOrderings.bot_class.bot) @ (cSet.Collect @ cOrderings.bot_class.bot)))
(TSet.double_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V1) @ ((cGroups.minus_class.minus @ V2) @ V0))) @ V0))))))))))
(TSet.image_empty,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TSet.image_ident,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ (^[V1]: V1)) @ V0)) @ V0))))
(TSet.image_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ V0) @ ((cSet.image @ V1) @ V2))) @ ((cSet.image @ (^[V3]: (V0 @ (V1 @ V3)))) @ V2)))))))))
(TSet.inf_set_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (cSet.Collect @ ((cLattices.inf_class.inf @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1))))))))))
(TSet.insert_Diff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.insert @ V0) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))) @ V1)))))))
(TSet.insert_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cSet.insert @ V2) @ V0)) @ ((cSet.insert @ V2) @ V1))))))))))
(TSet.rev_subsetD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.set_diff_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ (cHOL.Not @ ((cSet.member @ V2) @ V1)))))))))))
(TSet.subset_UNIV,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.top_class.top))))
(TSet.subset_refl,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ V0))))
(TSet.sup_set_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (cSet.Collect @ ((cLattices.sup_class.sup @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1))))))))))
(TSet.the_elem_eq,(call @ (^[V0]: ((cHOL.eq @ (cSet.the_elem @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0))))
(TSet.top_set_def,((cHOL.eq @ cOrderings.top_class.top) @ (cSet.Collect @ cOrderings.top_class.top)))
(TSet.vimage_Diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cSet.vimage @ V0) @ V1)) @ ((cSet.vimage @ V0) @ V2))))))))))
(TSet.vimage_UNIV,(call @ (^[V0]: ((cHOL.eq @ ((cSet.vimage @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))))
(TSet.vimage_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cSet.vimage @ V2) @ V0)) @ ((cSet.vimage @ V2) @ V1))))))))))
(TTransfer.OO_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcompp @ V0) @ V1)) @ (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V0 @ V2) @ V4)) @ ((V1 @ V4) @ V3))))))))))))
(TWellfounded.wfI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: V2)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V5)) @ V0)) @ (V4 @ V6))))) @ (V4 @ V5))))) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ (V4 @ V3))))))))) @ (cWellfounded.wf @ V0))))))))))
(TATP.fequal_table_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cATP.fequal @ V0) @ V1)) @ cATP.fFalse)))))))
(TATP.fequal_table_1,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fequal @ V0) @ V0)) @ cATP.fTrue))))
(TATP.fimplies_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fimplies @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(TDatatype.In0_UN1,(call @ (^[V0]: ((cHOL.eq @ (cDatatype.In0 @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (cDatatype.In0 @ (V0 @ V1))))))))
(TDatatype.In0_def,(call @ (^[V0]: ((c== @ (cDatatype.In0 @ V0)) @ ((cDatatype.Scons @ (cDatatype.Numb @ cNat.zero_nat_inst.zero_nat)) @ V0)))))
(TDatatype.In1_UN1,(call @ (^[V0]: ((cHOL.eq @ (cDatatype.In1 @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (cDatatype.In1 @ (V0 @ V1))))))))
(TDatatype.In1_def,(call @ (^[V0]: ((c== @ (cDatatype.In1 @ V0)) @ ((cDatatype.Scons @ (cDatatype.Numb @ cNat.one_nat_inst.one_nat)) @ V0)))))
(TDatatype.Lim_def,(call @ (^[V0]: ((c== @ (cDatatype.Lim @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ ((cSet.image @ (cDatatype.Push_Node @ (cSum_Type.Inl @ V2))) @ (V0 @ V2))))))))))))
(TDatatype.inj_In0,((cFun.inj_on @ cDatatype.In0) @ cOrderings.top_class.top))
(TDatatype.inj_In1,((cFun.inj_on @ cDatatype.In1) @ cOrderings.top_class.top))
(TDatatype.uprodE2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cDatatype.Scons @ V0) @ V1)) @ ((cDatatype.uprod @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V2)) @ ((c==> @ ((cSet.member @ V1) @ V3)) @ V4))) @ V4)))))))))))))
(TDivides.div_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)))))))
(TDivides.mod_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ V0)))))))
(TDivides.zdiv_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1))) @ ((cDivides.div_int_inst.div_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TDivides.zmod_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))) @ ((cDivides.div_int_inst.mod_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TEnum.exists_code,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ (cEnum.enum_class.enum_ex @ V0)))))
(TEnum.max_extp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cWellfounded.max_extp @ V0) @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cWellfounded.max_ext @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4)))))))))))))))
(TEnum.vimage_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.vimage @ V0) @ V1)) @ (cList.set @ ((cList.filter @ (^[V2]: ((cSet.member @ (V0 @ V2)) @ V1))) @ cEnum.enum_class.enum))))))))
(TFun.bij_betw_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ V2))))))))))
(TFun.bij_betw_inv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (((cFun.bij_betw @ V3) @ V2) @ V1)))))))))))
(TFun.bij_swap_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.bij_betw @ (((cFun.swap @ V0) @ V1) @ V2)) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ (((cFun.bij_betw @ V2) @ cOrderings.top_class.top) @ cOrderings.top_class.top)))))))))
(TFun.comp_eq_dest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ ((cFun.comp @ V2) @ V3))) @ ((cHOL.eq @ (V0 @ (V1 @ V4))) @ (V2 @ (V3 @ V4)))))))))))))))
(TFun.comp_eq_elim,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ ((cFun.comp @ V2) @ V3))) @ ((c==> @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ (V0 @ (V1 @ V5))) @ (V2 @ (V3 @ V5)))))) @ V4)) @ V4)))))))))))))
(TFun.fun_upd_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cFun.comp @ V0) @ (((cFun.fun_upd @ V1) @ V2) @ V3))) @ (((cFun.fun_upd @ ((cFun.comp @ V0) @ V1)) @ V2) @ (V0 @ V3))))))))))))
(TFun.fun_upd_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ V2)) @ ((cHOL.eq @ (((cFun.fun_upd @ V0) @ V1) @ V2)) @ V0)))))))))
(TFun.fun_upd_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cFun.fun_upd @ V0) @ V1) @ V2) @ V1)) @ V2))))))))
(TFun.fun_upd_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cFun.fun_upd @ V0) @ V1) @ (V0 @ V1))) @ V0))))))
(TFun.inj_on_INTER,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cFun.inj_on @ V1) @ (V2 @ V3)))))) @ ((cFun.inj_on @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3)))))))))))))
(TFun.inj_on_Inter,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cFun.inj_on @ V1) @ V2))))) @ ((cFun.inj_on @ V1) @ (cComplete_Lattices.Inf_class.Inf @ V0)))))))))
(TFun.inj_on_empty,(call @ (^[V0]: ((cFun.inj_on @ V0) @ cOrderings.bot_class.bot))))
(TFun.map_fun.comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cFun.comp @ ((cFun.map_fun @ V0) @ V1)) @ ((cFun.map_fun @ V2) @ V3))) @ ((cFun.map_fun @ ((cFun.comp @ V2) @ V0)) @ ((cFun.comp @ V1) @ V3))))))))))))
(TFun.range_ex1_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.member @ V1) @ ((cSet.image @ V0) @ cOrderings.top_class.top))) @ (cHOL.Ex1 @ (^[V2]: ((cHOL.eq @ V1) @ (V0 @ V2)))))))))))
(TFun.set.identity,((cHOL.eq @ (cSet.vimage @ (^[V0]: V0))) @ cFun.id))
(TFun.swap_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.swap @ V0) @ V1) @ V2)) @ (((cFun.swap @ V1) @ V0) @ V2)))))))))
(TFunDef.comp_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ (V0 @ (V1 @ V2))) @ (V3 @ (V4 @ V5)))) @ ((cHOL.eq @ (((cFun.comp @ V0) @ V1) @ V2)) @ (((cFun.comp @ V3) @ V4) @ V5))))))))))))))))
(TFunDef.wf_in_rel,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wfP @ (cFunDef.in_rel @ V0))))))
(THOL.atomize_conj,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPure.conjunction @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V1)))))))
(THOL.conj_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V1) @ V0)))))))
(THOL.contrapos_nn,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ V0)) @ ((c==> @ ((c==> @ V1) @ V0)) @ (cHOL.Not @ V1))))))))
(THOL.contrapos_np,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ V0)) @ ((c==> @ ((c==> @ (cHOL.Not @ V1)) @ V0)) @ V1)))))))
(THOL.contrapos_pn,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((c==> @ V1) @ (cHOL.Not @ V0))) @ (cHOL.Not @ V1))))))))
(THOL.contrapos_pp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((c==> @ (cHOL.Not @ V1)) @ (cHOL.Not @ V0))) @ V1)))))))
(THOL.disj_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ V1) @ V0)))))))
(THOL.if_eq_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cHOL.If @ ((cHOL.eq @ V0) @ V1)) @ V1) @ V0)) @ V0))))))
(THOL.if_weak_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cHOL.If @ V0) @ V2) @ V3)) @ (((cHOL.If @ V1) @ V2) @ V3))))))))))))
(THOL.induct_trueI,cHOL.True)
(THOL.split_if_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cHOL.If @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ V1) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.conj @ (cHOL.Not @ V1)) @ (cHOL.Not @ (V0 @ V3)))))))))))))))
(THOL.the_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cHOL.eq @ V2) @ V1))))) @ ((cHOL.eq @ (cHOL.The @ (^[V2]: (V0 @ V2)))) @ V1))))))))
(TInt.Nats_numeral,(call @ (^[V0]: ((cSet.member @ (cNum.numeral_class.numeral @ V0)) @ cNat.semiring_1_class.Nats))))
(TInt.Quotient_int,((((cLifting.Quotient @ cInt.intrel) @ cInt.Abs_Integ) @ cInt.Rep_Integ) @ cInt.cr_int))
(TInt.eq_Abs_Integ,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (cInt.Abs_Integ @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V1)))))) @ V1))))))
(TInt.half_gt_zero,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TInt.int.bi_total,(cTransfer.bi_total @ cInt.cr_int))
(TInt.int_transfer,((((cTransfer.fun_rel @ cHOL.eq) @ cInt.cr_int) @ (^[V0]: ((cProduct_Type.Pair @ V0) @ cNat.zero_nat_inst.zero_nat))) @ cNat.semiring_1_class.of_nat))
(TInt.less_int.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ ((cTransfer.fun_rel @ cInt.intrel) @ cHOL.eq)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TInt.less_int_def,((c== @ cInt.ord_int_inst.less_int) @ (((cFun.map_fun @ cInt.Rep_Integ) @ ((cFun.map_fun @ cInt.Rep_Integ) @ cFun.id)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1)))))))))))
(TInt.nat.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ cHOL.eq) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))))) @ cInt.nat))
(TInt.nat_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cInt.nat @ V0)) @ V1)) @ ((cInt.ord_int_inst.less_int @ V0) @ (cNat.semiring_1_class.of_nat @ V1)))))))))
(TInt.nat_mono_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cInt.nat @ V1)) @ (cInt.nat @ V0))) @ ((cInt.ord_int_inst.less_int @ V1) @ V0))))))))
(TInt.nat_power_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ (cInt.nat @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ (cInt.nat @ V0)) @ V1))))))))
(TInt.negative_zle,(call @ (^[V0]: (call @ (^[V1]: ((cInt.ord_int_inst.less_eq_int @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V1)))))))
(TInt.of_int_eq_id,((cHOL.eq @ cInt.ring_1_class.of_int) @ cFun.id))
(TInt.one_int_code,((cHOL.eq @ cInt.one_int_inst.one_int) @ (cInt.Pos @ cNum.num.One)))
(TInt.plus_int.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ ((cTransfer.fun_rel @ cInt.intrel) @ cInt.intrel)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3))))))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3))))))))))
(TInt.plus_int_def,((c== @ cInt.plus_int_inst.plus_int) @ (((cFun.map_fun @ cInt.Rep_Integ) @ ((cFun.map_fun @ cInt.Rep_Integ) @ cInt.Abs_Integ)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3)))))))))))
(TInt.zero_int.rsp,((cInt.intrel @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)) @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TInt.zero_int_def,((c== @ cInt.zero_int_inst.zero_int) @ (cInt.Abs_Integ @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat))))
(TInt.zero_zle_int,(call @ (^[V0]: ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TInt.zle_diff1_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ V0) @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int))) @ ((cInt.ord_int_inst.less_int @ V0) @ V1)))))))
(TInt.zle_iff_zadd,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ ((cInt.plus_int_inst.plus_int @ V0) @ (cNat.semiring_1_class.of_nat @ V2)))))))))))
(TLattices.inf_min,((cHOL.eq @ cLattices.inf_class.inf) @ cOrderings.ord_class.min))
(TLattices.sup_max,((cHOL.eq @ cLattices.sup_class.sup) @ cOrderings.ord_class.max))
(TLifting.fun_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cTransfer.fun_rel @ V1) @ V2)) @ ((cTransfer.fun_rel @ V0) @ V3)))))))))))))
(TList.Bleast_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.Bleast @ (cList.set @ V0)) @ V1)) @ (((cList.list.list_case @ ((cList.abort_Bleast @ (cList.set @ V0)) @ V1)) @ (^[V2]: (^[V3]: V2))) @ ((cList.filter @ V1) @ ((cList.linorder_class.sort_key @ (^[V2]: V2)) @ V0)))))))))
(TList.Cons_in_lex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cList.lex @ V4))) @ ((cHOL.disj @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ V4)) @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cList.lex @ V4))))))))))))))))
(TList.ListMem_def,((c== @ cList.ListMem) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V3) @ V4)))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V5) @ V4))) @ ((V0 @ V3) @ V4))))))))))))))))
(TList.ListMem_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.ListMem @ V0) @ V1)) @ ((cSet.member @ V0) @ (cList.set @ V1))))))))
(TList.append_Nil2,(call @ (^[V0]: ((cHOL.eq @ ((cList.append @ V0) @ cList.list.Nil)) @ V0))))
(TList.atLeast_upt,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.lessThan @ V0)) @ (cList.set @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ V0))))))
(TList.atMost_upto,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ (cList.set @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V0)))))))
(TList.butlast_def,((c== @ cList.butlast) @ (^[V0]: (((cList.list.list_rec @ cList.list.Nil) @ (^[V1]: (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ cList.list.Nil) @ ((cList.list.Cons @ V1) @ V3)))))) @ V0))))
(TList.card_length,(call @ (^[V0]: ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ (cList.set @ V0))) @ (cNat.size_class.size @ V0)))))
(TList.compl_coset,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cList.coset @ V0))) @ (cList.set @ V0)))))
(TList.distinct_tl,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ (cList.tl @ V0))))))
(TList.drop_1_Cons,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.drop @ cNat.one_nat_inst.one_nat) @ ((cList.list.Cons @ V0) @ V1))) @ V1))))))
(TList.drop_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.append @ V1) @ V2))) @ ((cList.append @ ((cList.drop @ V0) @ V1)) @ ((cList.drop @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.size_class.size @ V1))) @ V2))))))))))
(TList.drop_eq_Nil,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.drop @ V0) @ V1)) @ cList.list.Nil)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V1)) @ V0)))))))
(TList.eq_Nil_null,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cList.null @ V0)))))
(TList.ex_map_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cList.map @ V1) @ V2))))) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V2) @ (V1 @ V3))))))))))))
(TList.ex_nat_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V0)) @ (V1 @ V2))))) @ ((cSet.Bex @ ((cSet_Interval.ord_class.atLeastAtMost @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (^[V2]: (V1 @ V2)))))))))
(TList.filter_True,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cHOL.eq @ ((cList.filter @ V1) @ V0)) @ V0)))))))
(TList.filter_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V1))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cList.filter @ V2) @ V0)) @ ((cList.filter @ V3) @ V1)))))))))))))
(TList.finite_list,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ (cList.set @ V1)) @ V0)))))))
(TList.fold_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.fold @ V0) @ ((cList.append @ V1) @ V2))) @ ((cFun.comp @ ((cList.fold @ V0) @ V2)) @ ((cList.fold @ V0) @ V1))))))))))
(TList.foldl.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ (((cList.foldl @ V0) @ ((V0 @ V1) @ V2)) @ V3)))))))))))
(TList.foldl.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ cList.list.Nil)) @ V1))))))
(TList.foldr.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.foldr @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cFun.comp @ (V0 @ V1)) @ ((cList.foldr @ V0) @ V2))))))))))
(TList.foldr.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.foldr @ V0) @ cList.list.Nil)) @ cFun.id))))
(TList.hd_conv_nth,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.hd @ V0)) @ ((cList.nth @ V0) @ cNat.zero_nat_inst.zero_nat))))))
(TList.in_measures_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.measures @ ((cList.list.Cons @ V2) @ V3)))) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V0)) @ (V2 @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ (V2 @ V0)) @ (V2 @ V1))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.measures @ V3))))))))))))))
(TList.in_measures_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.measures @ cList.list.Nil))) @ cHOL.False))))))
(TList.in_set_zipE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.set @ ((cList.zip @ V2) @ V3)))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ (cList.set @ V2))) @ ((c==> @ ((cSet.member @ V1) @ (cList.set @ V3))) @ V4))) @ V4)))))))))))))
(TList.inj_on_mapI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ cList.set) @ V1)))) @ ((cFun.inj_on @ (cList.map @ V0)) @ V1)))))))
(TList.insert_code_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ (cList.coset @ V1))) @ (cList.coset @ ((cList.removeAll @ V0) @ V1))))))))
(TList.insert_code_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ (cList.set @ V1))) @ (cList.set @ ((cList.insert @ V0) @ V1))))))))
(TList.last_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.last @ ((cList.append @ V0) @ V1))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ (cList.last @ V0)) @ (cList.last @ V1))))))))
(TList.last_in_set,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cSet.member @ (cList.last @ V0)) @ (cList.set @ V0))))))
(TList.length_code,((cHOL.eq @ cNat.size_class.size) @ (cList.gen_length @ cNat.zero_nat_inst.zero_nat)))
(TList.length_drop,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.drop @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V1)) @ V0)))))))
(TList.length_take,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.take @ V0) @ V1))) @ ((cOrderings.ord_class.min @ (cNat.size_class.size @ V1)) @ V0)))))))
(TList.lenlex_conv,(call @ (^[V0]: ((cHOL.eq @ (cList.lenlex @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.lex @ V0))))))))))))
(TList.lexn_length,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cList.lexn @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ V3)) @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ V3))))))))))))
(TList.lexordp_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.lexordp @ V0) @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.lexord @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4)))))))))))))))
(TList.list.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cList.list.Cons @ V2) @ V3)))))))) @ (V0 @ V1))))))))
(TList.list.inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TList.list.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cList.list.list_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ (cHOL.Not @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))))
(TList.list.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cList.list.list_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))
(TList.list_ex_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list_ex @ V0) @ V1)) @ ((cSet.Bex @ (cList.set @ V1)) @ V0)))))))
(TList.list_ex_rev,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list_ex @ V0) @ (cList.rev @ V1))) @ ((cList.list_ex @ V0) @ V1)))))))
(TList.listrel.Nil,(call @ (^[V0]: ((cSet.member @ ((cProduct_Type.Pair @ cList.list.Nil) @ cList.list.Nil)) @ (cList.listrel @ V0)))))
(TList.listrel_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.Image @ (cList.listrel @ V0)) @ ((cSet.insert @ cList.list.Nil) @ cOrderings.bot_class.bot))) @ ((cSet.insert @ cList.list.Nil) @ cOrderings.bot_class.bot)))))
(TList.listrel_def,((c== @ cList.listrel) @ (^[V0]: (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (((cList.listrelp @ (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)))) @ V1) @ V2))))))))
(TList.listrel_sym,(call @ (^[V0]: ((c==> @ (cRelation.sym @ V0)) @ (cRelation.sym @ (cList.listrel @ V0))))))
(TList.lists.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.lists @ V1))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V2)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ V4))) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((c==> @ ((cSet.member @ V4) @ (cList.lists @ V1))) @ V2)))))))) @ V2))))))))))
(TList.lists.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.lists @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ ((cSet.member @ V2) @ V1)) @ ((cSet.member @ V3) @ (cList.lists @ V1)))))))))))))))
(TList.lists_empty,((cHOL.eq @ (cList.lists @ cOrderings.bot_class.bot)) @ ((cSet.insert @ cList.list.Nil) @ cOrderings.bot_class.bot)))
(TList.lists_image,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.lists @ ((cSet.image @ V0) @ V1))) @ ((cSet.image @ (cList.map @ V0)) @ (cList.lists @ V1))))))))
(TList.listset_def,((c== @ cList.listset) @ (^[V0]: (((cList.list.list_rec @ ((cSet.insert @ cList.list.Nil) @ cOrderings.bot_class.bot)) @ (^[V1]: (^[V2]: (^[V3]: ((cList.set_Cons @ V1) @ V3))))) @ V0))))
(TList.listsp.Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ ((cList.listsp @ V0) @ V2)) @ ((cList.listsp @ V0) @ ((cList.list.Cons @ V1) @ V2)))))))))))
(TList.listsp_infI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.listsp @ V0) @ V1)) @ ((c==> @ ((cList.listsp @ V2) @ V1)) @ ((cList.listsp @ ((cLattices.inf_class.inf @ V0) @ V2)) @ V1))))))))))
(TList.listsp_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.listsp @ V0)) @ (cList.listsp @ V1))))))))
(TList.map_Suc_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ cNat.Suc) @ ((cList.upt @ V0) @ V1))) @ ((cList.upt @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))))))))
(TList.map_butlast,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ V0) @ (cList.butlast @ V1))) @ (cList.butlast @ ((cList.map @ V0) @ V1))))))))
(TList.map_eq_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V2) @ V1))) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V3]: ((cHOL.eq @ (V0 @ V3)) @ (V2 @ V3))))))))))))
(TList.map_fst_zip,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.map @ cProduct_Type.fst) @ ((cList.zip @ V0) @ V1))) @ V0)))))))
(TList.map_fun_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((cHOL.eq @ ((cList.map @ (((cFun.fun_upd @ V2) @ V0) @ V3)) @ V1)) @ ((cList.map @ V2) @ V1))))))))))))
(TList.map_snd_zip,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.map @ cProduct_Type.snd) @ ((cList.zip @ V0) @ V1))) @ V1)))))))
(TList.map_zip_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.zip @ ((cList.map @ V1) @ V2)) @ V3))) @ ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ (V1 @ V4)) @ V5)))))) @ ((cList.zip @ V2) @ V3))))))))))))
(TList.n_lists_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.n_lists @ V0) @ cList.list.Nil)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil)) @ cList.list.Nil)))))
(TList.n_lists_def,((c== @ cList.n_lists) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil))) @ (^[V1]: (^[V2]: (^[V3]: (cList.concat @ ((cList.map @ (^[V4]: ((cList.map @ (^[V5]: ((cList.list.Cons @ V5) @ V4))) @ V3))) @ (V2 @ V3))))))) @ V0))))
(TList.nth_butlast,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ (cList.butlast @ V1)))) @ ((cHOL.eq @ ((cList.nth @ (cList.butlast @ V1)) @ V0)) @ ((cList.nth @ V1) @ V0))))))))
(TList.nth_map_upt,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ ((cHOL.eq @ ((cList.nth @ ((cList.map @ V3) @ ((cList.upt @ V2) @ V1))) @ V0)) @ (V3 @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0)))))))))))))
(TList.partition_P,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.partition @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: (V0 @ V4)))) @ ((cSet.Ball @ (cList.set @ V3)) @ (^[V4]: (cHOL.Not @ (V0 @ V4)))))))))))))))
(TList.product_def,((c== @ cList.product) @ (^[V0]: (((cList.list.list_rec @ (^[V1]: cList.list.Nil)) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cList.append @ ((cList.map @ (cProduct_Type.Pair @ V1)) @ V4)) @ (V3 @ V4))))))) @ V0))))
(TList.product_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2)))) @ ((cHOL.eq @ ((cList.nth @ ((cList.product @ V1) @ V2)) @ V0)) @ ((cProduct_Type.Pair @ ((cList.nth @ V1) @ ((cDivides.div_nat_inst.div_nat @ V0) @ (cNat.size_class.size @ V2)))) @ ((cList.nth @ V2) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.size_class.size @ V2)))))))))))))
(TList.remdups_def,((c== @ cList.remdups) @ (^[V0]: (((cList.list.list_rec @ cList.list.Nil) @ (^[V1]: (^[V2]: (^[V3]: (((cHOL.If @ ((cSet.member @ V1) @ (cList.set @ V2))) @ V3) @ ((cList.list.Cons @ V1) @ V3)))))) @ V0))))
(TList.remove1_def,((c== @ cList.remove1) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ ((cHOL.eq @ V5) @ V2)) @ V3) @ ((cList.list.Cons @ V2) @ (V4 @ V5)))))))) @ V1) @ V0)))))
(TList.remove_code_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.remove @ V0) @ (cList.coset @ V1))) @ (cList.coset @ ((cList.insert @ V0) @ V1))))))))
(TList.remove_code_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.remove @ V0) @ (cList.set @ V1))) @ (cList.set @ ((cList.removeAll @ V0) @ V1))))))))
(TList.rev_exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V1)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ cList.list.Nil)))) @ V1)))))) @ V1)))))))
(TList.rotate1_def,((c== @ cList.rotate1) @ (^[V0]: (((cList.list.list_rec @ cList.list.Nil) @ (^[V1]: (^[V2]: (^[V3]: ((cList.append @ V2) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))) @ V0))))
(TList.set_n_lists,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.n_lists @ V0) @ V1))) @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ V0)) @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ (cList.set @ V1)))))))))))
(TList.set_relcomp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcomp @ (cList.set @ V0)) @ (cList.set @ V1))) @ (cList.set @ (cList.concat @ ((cList.map @ (^[V2]: (cList.concat @ ((cList.map @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ (cProduct_Type.snd @ V2)) @ (cProduct_Type.fst @ V3))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cProduct_Type.fst @ V2)) @ (cProduct_Type.snd @ V3))) @ cList.list.Nil)) @ cList.list.Nil))) @ V1)))) @ V0)))))))))
(TList.set_remdups,(call @ (^[V0]: ((cHOL.eq @ (cList.set @ (cList.remdups @ V0))) @ (cList.set @ V0)))))
(TList.set_rotate1,(call @ (^[V0]: ((cHOL.eq @ (cList.set @ (cList.rotate1 @ V0))) @ (cList.set @ V0)))))
(TList.set_sublist,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.sublist @ V0) @ V1))) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.nth @ V0) @ V3))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V0))) @ ((cSet.member @ V3) @ V1)))))))))))))
(TList.setsum_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ (cList.set @ V1))) @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ (cList.remdups @ V1)))))))))
(TList.sorted_upto,(call @ (^[V0]: (call @ (^[V1]: (cList.linorder_class.sorted @ ((cList.upto @ V0) @ V1)))))))
(TList.splice_Nil2,(call @ (^[V0]: ((cHOL.eq @ ((cList.splice @ V0) @ cList.list.Nil)) @ V0))))
(TList.sublist_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.sublist @ V0) @ V1)) @ ((cList.map @ cProduct_Type.fst) @ ((cList.filter @ (^[V2]: ((cSet.member @ (cProduct_Type.snd @ V2)) @ V1))) @ ((cList.zip @ V0) @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V0)))))))))))
(TList.sublist_nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.sublist @ cList.list.Nil) @ V0)) @ cList.list.Nil))))
(TList.subset_code_3,((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cList.coset @ cList.list.Nil)) @ (cList.set @ cList.list.Nil))) @ cHOL.False))
(TList.subset_code_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cList.coset @ V1))) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: (cHOL.Not @ ((cSet.member @ V2) @ V0))))))))))
(TList.subset_code_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cList.set @ V0)) @ V1)) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cSet.member @ V2) @ V1)))))))))
(TList.take_1_Cons,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.take @ cNat.one_nat_inst.one_nat) @ ((cList.list.Cons @ V0) @ V1))) @ ((cList.list.Cons @ V0) @ cList.list.Nil)))))))
(TList.take_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.append @ V1) @ V2))) @ ((cList.append @ ((cList.take @ V0) @ V1)) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.size_class.size @ V1))) @ V2))))))))))
(TList.take_eq_Nil,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.take @ V0) @ V1)) @ cList.list.Nil)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ cList.list.Nil))))))))
(TList.those.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.those @ ((cList.list.Cons @ V0) @ V1))) @ (((cOption.option.option_case @ cOption.option.None) @ (^[V2]: ((cOption.map @ (cList.list.Cons @ V2)) @ (cList.those @ V1)))) @ V0)))))))
(TList.those.simps_1,((cHOL.eq @ (cList.those @ cList.list.Nil)) @ (cOption.option.Some @ cList.list.Nil)))
(TList.tl_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0)) @ cList.tl) @ cList.tl))))
(TList.upt.upt_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upt @ V0) @ (cNat.Suc @ V1))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cList.append @ ((cList.upt @ V0) @ V1)) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ cList.list.Nil)))))))
(TList.upto.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)) @ ((V0 @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TList.upto.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.upto @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cList.upto_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.list.Cons @ V4) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))) @ cList.list.Nil))) @ ((c==> @ ((cWellfounded.accp @ cList.upto_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TList.upto.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cList.upto_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cList.upto @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cList.list.Cons @ V0) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1))) @ cList.list.Nil))))))))
(TList.wf_measures,(call @ (^[V0]: (cWellfounded.wf @ (cList.measures @ V0)))))
(TList.zip_append1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ ((cList.append @ V0) @ V1)) @ V2)) @ ((cList.append @ ((cList.zip @ V0) @ ((cList.take @ (cNat.size_class.size @ V0)) @ V2))) @ ((cList.zip @ V1) @ ((cList.drop @ (cNat.size_class.size @ V0)) @ V2)))))))))))
(TList.zip_append2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ V0) @ ((cList.append @ V1) @ V2))) @ ((cList.append @ ((cList.zip @ ((cList.take @ (cNat.size_class.size @ V1)) @ V0)) @ V1)) @ ((cList.zip @ ((cList.drop @ (cNat.size_class.size @ V1)) @ V0)) @ V2))))))))))
(TList.zip_eq_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.zip @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ ((cList.map @ cProduct_Type.fst) @ V2)) @ V0)) @ ((cHOL.eq @ ((cList.map @ cProduct_Type.snd) @ V2)) @ V1)))))))))))
(TList.zip_map_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cList.zip @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V2) @ V3))) @ ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cProduct_Type.Pair @ (V0 @ V4)) @ (V2 @ V5)))))) @ ((cList.zip @ V1) @ V3))))))))))))
(TMap.dom_map_upds,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cMap.dom @ (((cMap.map_upds @ V0) @ V1) @ V2))) @ ((cLattices.sup_class.sup @ (cList.set @ ((cList.take @ (cNat.size_class.size @ V2)) @ V1))) @ (cMap.dom @ V0))))))))))
(TMap.dom_restrict,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.dom @ ((cMap.restrict_map @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cMap.dom @ V0)) @ V1)))))))
(TMap.map_add_None,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (((cMap.map_add @ V0) @ V1) @ V2)) @ cOption.option.None)) @ ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ cOption.option.None)) @ ((cHOL.eq @ (V0 @ V2)) @ cOption.option.None))))))))))
(TMap.map_add_comm,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cMap.dom @ V0)) @ (cMap.dom @ V1))) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cMap.map_add @ V0) @ V1)) @ ((cMap.map_add @ V1) @ V0))))))))
(TMap.map_add_upds,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cMap.map_add @ V0) @ (((cMap.map_upds @ V1) @ V2) @ V3))) @ (((cMap.map_upds @ ((cMap.map_add @ V0) @ V1)) @ V2) @ V3)))))))))))
(TMap.map_comp_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMap.map_comp @ V0) @ V1)) @ (^[V2]: (((cOption.option.option_case @ cOption.option.None) @ (^[V3]: (V0 @ V3))) @ (V1 @ V2)))))))))
(TMap.map_le_empty,(call @ (^[V0]: ((cMap.map_le @ (^[V1]: cOption.option.None)) @ V0))))
(TMap.map_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cMap.map_le @ V0) @ V1)) @ ((c==> @ ((cMap.map_le @ V1) @ V2)) @ ((cMap.map_le @ V0) @ V2))))))))))
(TMap.map_of.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.map_of @ ((cList.list.Cons @ V0) @ V1))) @ (((cFun.fun_upd @ (cMap.map_of @ V1)) @ (cProduct_Type.fst @ V0)) @ (cOption.option.Some @ (cProduct_Type.snd @ V0)))))))))
(TMap.map_of.simps_1,((cHOL.eq @ (cMap.map_of @ cList.list.Nil)) @ (^[V0]: cOption.option.None)))
(TMap.map_of_SomeD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cMap.map_of @ V0) @ V1)) @ (cOption.option.Some @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.set @ V0))))))))))
(TMap.map_upd_eqD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2))) @ (((cFun.fun_upd @ V3) @ V1) @ (cOption.option.Some @ V4)))) @ ((cHOL.eq @ V2) @ V4)))))))))))))
(TMap.map_upd_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (cOption.option.Some @ V2))) @ ((cHOL.eq @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2))) @ V0)))))))))
(TMap.map_upds_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cMap.map_upds @ V0) @ V1) @ V2)) @ ((cMap.map_add @ V0) @ (cMap.map_of @ (cList.rev @ ((cList.zip @ V1) @ V2))))))))))))
(TMap.ran_distinct,(call @ (^[V0]: ((c==> @ (cList.distinct @ ((cList.map @ cProduct_Type.fst) @ V0))) @ ((cHOL.eq @ (cMap.ran @ (cMap.map_of @ V0))) @ ((cSet.image @ cProduct_Type.snd) @ (cList.set @ V0)))))))
(TMap.restrict_out,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ (((cMap.restrict_map @ V2) @ V1) @ V0)) @ cOption.option.None)))))))))
(TMeson.disj_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.disj @ ((cHOL.disj @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V1) @ V2))))))))))
(TMeson.ex_forward,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(TMeson.skolem_def,((cHOL.eq @ cMeson.skolem) @ (^[V0]: V0)))
(TMetis.eq_lambdaI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ V1)) @ ((c== @ V0) @ (cMetis.lambda @ V1))))))))
(TMetis.lambda_def,((cHOL.eq @ cMetis.lambda) @ (^[V0]: V0)))
(TMetis.select_def,((cHOL.eq @ cMetis.select) @ (^[V0]: V0)))
(TNat.Nat.Suc_RepI,(call @ (^[V0]: ((c==> @ (cNat.Nat @ V0)) @ (cNat.Nat @ (cNat.Suc_Rep @ V0))))))
(TNat.Suc_diff_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ (cNat.Suc @ ((cNat.minus_nat_inst.minus_nat @ V1) @ (cNat.Suc @ V0)))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))))))))
(TNat.Suc_eq_plus1,(call @ (^[V0]: ((cHOL.eq @ (cNat.Suc @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ cNat.one_nat_inst.one_nat)))))
(TNat.Suc_le_lessD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat.Suc_neq_Zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.Suc @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ V1))))))
(TNat.Suc_not_Zero,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNat.Suc @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.Zero_nat_def,((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ (cNat.Abs_Nat @ cNat.Zero_Rep)))
(TNat.Zero_neq_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V0))) @ V1))))))
(TNat.Zero_not_Suc,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V0))))))
(TNat.add_le_mono1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TNat.diff_Suc_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)))))))
(TNat.diff_cancel2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V2)))))))))
(TNat.diff_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V2)) @ V1)))))))))
(TNat.diff_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2)))))))))))
(TNat.diff_is_0_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.diff_le_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))))))))))
(TNat.diff_le_self,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V0))))))
(TNat.dvd.mono_def,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.order.mono @ cRings.dvd_class.dvd) @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat.dvd_diff_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2)))))))))))
(TNat.funpow.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ (cNat.Suc @ V0)) @ V1)) @ ((cFun.comp @ V1) @ ((cNat.compow @ V0) @ V1))))))))
(TNat.funpow.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cFun.id))))
(TNat.funpow_swap1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ (((cNat.compow @ V1) @ V0) @ V2))) @ (((cNat.compow @ V1) @ V0) @ (V0 @ V2))))))))))
(TNat.gr0_conv_Suc,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNat.Suc @ V1))))))))
(TNat.le_diff_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TNat.less_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.mult_0_right,(call @ (^[V0]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat))))
(TNat.mult_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))))))))))
(TNat.mult_cancel2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V2) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))))
(TNat.mult_le_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V3)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V3)))))))))))))
(TNat.nat.distinct_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNat.Suc @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.nat.distinct_1,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V0))))))
(TNat.nat.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)) @ cHOL.True))
(TNat.nat.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.nat.eq.simps_2,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V0))) @ cHOL.False))))
(TNat.nat.eq.simps_1,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ (cNat.Suc @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ cHOL.False))))
(TNat.nat.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNat.Suc @ V1))))))))
(TNat.nat_case_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ (cNat.Suc @ V2))) @ (V1 @ V2)))))))))
(TNat.of_nat_eq_id,((cHOL.eq @ cNat.semiring_1_class.of_nat) @ cFun.id))
(TNat.plus_nat_def,((c== @ cNat.plus_nat_inst.plus_nat) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: V1)) @ (^[V1]: (^[V2]: (^[V3]: (cNat.Suc @ (V2 @ V3)))))) @ V0))))
(TNat.subst_equals,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V0)) @ ((cHOL.eq @ V2) @ V1))))))))))
(TNitpick.Frac_def,((c== @ cNitpick.Frac) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cNitpick.int_gcd @ V0) @ V1)) @ cInt.one_int_inst.one_int)))))))
(TNitpick.frac_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cNitpick.frac @ V0) @ V1)) @ (cNitpick.Abs_Frac @ ((cNitpick.norm_frac @ V0) @ V1))))))))
(TNitpick.prod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.prod @ V0) @ V1)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V3) @ V1))))))))))))
(TNum.add_2_eq_Suc,(call @ (^[V0]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ (cNat.Suc @ (cNat.Suc @ V0))))))
(TNum.eq_num_simps_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.eq_num_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ cHOL.False))))))
(TNum.eq_num_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ cHOL.False))))))
(TNum.eq_num_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.eq_num_simps_5,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.eq_num_simps_4,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.eq_num_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ cHOL.False))))
(TNum.eq_num_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ cHOL.False))))
(TNum.eq_num_simps_1,((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ cNum.num.One)) @ cHOL.True))
(TNum.le_num_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.le_num_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.le_num_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.le_num_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.le_num_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.le_num_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.le_num_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ cNum.num.One) @ V0)) @ cHOL.True))))
(TNum.less_2_cases,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))
(TNum.less_num_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V1))))))))
(TNum.num.Bit0_def,(call @ (^[V0]: ((c== @ (cNum.num.Bit0 @ V0)) @ (cNum.Abs_num @ (cDatatype.In1 @ (cDatatype.In0 @ (cNum.Rep_num @ V0))))))))
(TNum.num.Bit1_def,(call @ (^[V0]: ((c== @ (cNum.num.Bit1 @ V0)) @ (cNum.Abs_num @ (cDatatype.In1 @ (cDatatype.In1 @ (cNum.Rep_num @ V0))))))))
(TNum.num.distinct_6,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))))))))
(TNum.num.distinct_5,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))))))))
(TNum.num.distinct_4,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)))))
(TNum.num.distinct_3,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit1 @ V0))))))
(TNum.num.distinct_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)))))
(TNum.num.distinct_1,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit0 @ V0))))))
(TNum.num.eq.simps_9,((c== @ ((cHOL.equal_class.equal @ cNum.num.One) @ cNum.num.One)) @ cHOL.True))
(TNum.num.eq.simps_8,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.eq.simps_7,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.eq.simps_6,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ cHOL.False))))
(TNum.num.eq.simps_5,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.num.eq.simps_4,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ cHOL.False))))
(TNum.num.eq.simps_3,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNum.num.eq.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ cHOL.False))))))
(TNum.num.eq.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ cHOL.False))))))
(TNum.num.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cNum.num.One)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNum.num.Bit0 @ V1))))) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNum.num.Bit1 @ V1)))))))))
(TNum.plus_num_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)) @ (cNum.num_of_nat @ ((cNat.plus_nat_inst.plus_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V1)))))))))
(TOption.bind_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cOption.option.Some @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cOption.bind @ V0) @ V2)) @ ((cOption.bind @ V1) @ V3)))))))))))))
(TOption.set.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cOption.set @ (cOption.option.Some @ V0))) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TOption.set.simps_1,((cHOL.eq @ (cOption.set @ cOption.option.None)) @ cOrderings.bot_class.bot))
(TOption.the.simps,(call @ (^[V0]: ((cHOL.eq @ (cOption.the @ (cOption.option.Some @ V0))) @ V0))))
(TOption.these_def,(call @ (^[V0]: ((cHOL.eq @ (cOption.these @ V0)) @ ((cSet.image @ cOption.the) @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cSet.member @ V1) @ V0)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOption.option.None))))))))))
(TOrderings.xtrans_24,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V1))))))))))))))
(TOrderings.xtrans_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xtrans_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V1))))))))))))))
(TOrderings.xtrans_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xtrans_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less @ V2) @ (V3 @ V1))))))))))))))
(TOrderings.xtrans_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xtrans_18,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V3 @ V0))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V3 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ V2) @ (V3 @ V1))))))))))))))
(TOrderings.xtrans_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V5)) @ (V0 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ (V0 @ V3)) @ V2)))))))))))))
(TOrderings.xtrans_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V0)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V5)) @ (V2 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ V3) @ (V2 @ V1))))))))))))))
(TOrderings.xtrans_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V5)) @ (V1 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V0)))))))))))))
(TOrderings.xtrans_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V0)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V2 @ V5)) @ (V2 @ V4)))))))) @ ((cOrderings.ord_class.less @ V3) @ (V2 @ V1))))))))))))))
(TOrderings.xtrans_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V5) @ V4)) @ ((cOrderings.ord_class.less @ (V1 @ V5)) @ (V1 @ V4)))))))) @ ((cOrderings.ord_class.less @ (V1 @ V3)) @ V0)))))))))))))
(TOrderings.xtrans_12,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.xtrans_11,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.xtrans_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xtrans_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)))))))))
(TOrderings.xtrans_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xtrans_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xtrans_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))))))))
(TOrderings.xtrans_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.xtrans_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))))))))
(TOrderings.xtrans_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V0))))))))))
(TOrderings.xtrans_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.xtrans_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cOrderings.ord_class.less @ V2) @ V0))))))))))
(TPower.power2_sum,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ ((cGroups.plus_class.plus @ V0) @ V1)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ V1))))))))
(TPredicate.eq_def,((c== @ cPredicate.eq) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3))))))))))
(TPredicate.map.id,((cHOL.eq @ (cPredicate.map @ cFun.id)) @ cFun.id))
(TPredicate.the_eq,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.the @ V0)) @ ((cPredicate.singleton @ (^[V1]: ((cString.Code.abort @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))) @ (^[V2]: (cPredicate.the @ V0))))) @ V0)))))
(TPure.equals_cong,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c== @ V0) @ V1)) @ ((c== @ V0) @ V1)))))))
(TPure.norm_hhf_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c==> @ V0) @ (call @ (^[V2]: (V1 @ V2))))) @ (call @ (^[V2]: ((c==> @ V0) @ (V1 @ V2))))))))))
(TPure.swap_params,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (call @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (call @ (^[V1]: (call @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TQuotient.all_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cSet.Ball @ (cLifting.Respects @ V0)) @ (((cFun.map_fun @ V1) @ cFun.id) @ V3))) @ (cHOL.All @ V3))))))))))))
(TQuotient.all_reg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((c==> @ (cHOL.All @ V0)) @ (cHOL.All @ V1))))))))
(TQuotient.bex_reg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ V3) @ V0)) @ ((cHOL.implies @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((c==> @ ((cSet.Bex @ V0) @ V1)) @ ((cSet.Bex @ V0) @ V2))))))))))
(TQuotient.bex_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((((cTransfer.fun_rel @ V0) @ cHOL.eq) @ V1) @ V2)) @ ((cHOL.eq @ ((cSet.Bex @ (cLifting.Respects @ V0)) @ V1)) @ ((cSet.Bex @ (cLifting.Respects @ V0)) @ V2))))))))))
(TQuotient.ex1_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((((cFun.map_fun @ ((cFun.map_fun @ V1) @ cFun.id)) @ cFun.id) @ (cQuotient.Bex1_rel @ V0)) @ V3)) @ (cHOL.Ex1 @ V3))))))))))))
(TQuotient.let_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cFun.map_fun @ V5) @ ((cFun.map_fun @ ((cFun.map_fun @ V4) @ V2)) @ V1)) @ cHOL.Let)) @ cHOL.Let))))))))))))))))
(TQuotient.let_rsp,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ V1)) @ cHOL.Let) @ cHOL.Let))))))
(TRandom.log.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TRandom.log.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cRandom.log @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ ((cRandom.log @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))) @ V3)))))))) @ V3)))))))))))
(TRandom.log.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom.log @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V0))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ ((cRandom.log @ V0) @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ V0))))))))))
(TRandom.pick_same,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cRandom.pick @ ((cList.map @ (cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (cCode_Numeral.natural_of_nat @ V0))) @ ((cList.nth @ V1) @ V0))))))))
(TRandom.range_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom.range @ V0)) @ ((cProduct_Type.scomp @ (((cRandom.iterate @ ((cRandom.log @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ V0)) @ (^[V1]: ((cProduct_Type.scomp @ cRandom.next) @ (^[V2]: (cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V2) @ ((cCode_Numeral.times_natural_inst.times_natural @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))))))))) @ cCode_Numeral.one_natural_inst.one_natural)) @ (^[V1]: (cProduct_Type.Pair @ ((cCode_Numeral.div_natural_inst.mod_natural @ V1) @ V0))))))))
(TRelation.DomainE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Domain @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ V1)) @ V2)))) @ V2)))))))))
(TRelation.O_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcomp @ ((cRelation.relcomp @ V0) @ V1)) @ V2)) @ ((cRelation.relcomp @ V0) @ ((cRelation.relcomp @ V1) @ V2))))))))))
(TRelation.RangePI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cRelation.Rangep @ V0) @ V2)))))))))
(TRelation.RangepE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Rangep @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((V0 @ V3) @ V1)) @ V2)))) @ V2)))))))))
(TRelation.refl_Id,((cRelation.refl_on @ cOrderings.top_class.top) @ cRelation.Id))
(TRelation.subrelI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TRelation.sym_Int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.sym @ V0)) @ ((c==> @ (cRelation.sym @ V1)) @ (cRelation.sym @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TRelation.sym_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.sym @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0))))))))))
(TRelation.transpD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRelation.transp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V0 @ V1) @ V3)))))))))))))
(TRelation.transpE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRelation.transp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((c==> @ ((V0 @ V1) @ V3)) @ V4)) @ V4)))))))))))))))
(TRelation.transpI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V0 @ V1) @ V3)))))))))) @ (cRelation.transp @ V0)))))
(TSMT.pattern.recs,(call @ (^[V0]: ((cHOL.eq @ ((cSMT.pattern.pattern_rec @ V0) @ cSMT.pattern.Pattern)) @ V0))))
(TSMT.pattern.size_2,((cHOL.eq @ (cSMT.pattern.size_pattern_inst.size_pattern @ cSMT.pattern.Pattern)) @ cNat.zero_nat_inst.zero_nat))
(TSMT.pattern.size_1,((cHOL.eq @ (cSMT.pattern.pattern_size @ cSMT.pattern.Pattern)) @ cNat.zero_nat_inst.zero_nat))
(TSet.Collect_cong,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.eq @ (cSet.Collect @ (^[V2]: (V0 @ V2)))) @ (cSet.Collect @ (^[V2]: (V1 @ V2))))))))))
(TSet.Collect_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ (cSet.Collect @ V0)) @ (cSet.Collect @ V1))))))))
(TSet.Compl_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cSet.insert @ V0) @ V1))) @ ((cGroups.minus_class.minus @ (cGroups.uminus_class.uminus @ V1)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))))
(TSet.Diff_insert0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V0) @ V2))) @ ((cGroups.minus_class.minus @ V1) @ V2))))))))))
(TSet.Diff_insert2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ V2)))))))))
(TSet.Int_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2)))))))))))
(TSet.UNIV_witness,(cHOL.Ex @ (^[V0]: ((cSet.member @ V0) @ cOrderings.top_class.top))))
(TSet.Un_Int_crazy,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V2) @ V0))) @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ V2) @ V0))))))))))
(TSet.Un_UNIV_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ cOrderings.top_class.top) @ V0)) @ cOrderings.top_class.top))))
(TSet.atomize_ball,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: (V1 @ V2)))))))))
(TSet.eq_mem_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.image_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cSet.insert @ (V0 @ V1)) @ ((cSet.image @ V0) @ V2))))))))))
(TSet.insert_Diff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cSet.insert @ V0) @ V2)) @ V1)) @ ((cGroups.minus_class.minus @ V2) @ V1))))))))))
(TSet.insert_compr,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cHOL.disj @ ((cHOL.eq @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.insert_ident,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V2))) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ ((cSet.insert @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2)))))))))))
(TSet.insert_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.insert @ (V2 @ V0)) @ ((cSet.image @ V2) @ V1))) @ ((cSet.image @ V2) @ V1))))))))))
(TSet.insert_is_Un,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ V1)))))))
(TSet.is_empty_def,(call @ (^[V0]: ((cHOL.eq @ (cSet.is_empty @ V0)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TSet.less_set_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1)))))))))
(TSet.split_if_eq1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ V3)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TSet.split_if_eq2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ V0) @ (((cHOL.If @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ V1) @ ((cHOL.eq @ V0) @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ ((cHOL.eq @ V0) @ V3)))))))))))))
(TSet.subset_Un_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V1)))))))
(TSet.subset_empty,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TSet.subset_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet.the_elem_def,(call @ (^[V0]: ((cHOL.eq @ (cSet.the_elem @ V0)) @ (cHOL.The @ (^[V1]: ((cHOL.eq @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))
(TSet.vimage_Compl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.vimage @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cSet.vimage @ V0) @ V1))))))))
(TSet.vimage_const,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.vimage @ (^[V2]: V0)) @ V1)) @ (((cHOL.If @ ((cSet.member @ V0) @ V1)) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot)))))))
(TSet.vimage_empty,(call @ (^[V0]: ((cHOL.eq @ ((cSet.vimage @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TSet.vimage_ident,(call @ (^[V0]: ((cHOL.eq @ ((cSet.vimage @ (^[V1]: V1)) @ V0)) @ V0))))
(TSet_Interval.BIJ,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (cHOL.Ex @ (^[V2]: (((cFun.bij_betw @ V2) @ V0) @ V1)))) @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))))))))))
(TString.UNIV_char,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.image @ (cProduct_Type.prod.prod_case @ cString.char.Char)) @ ((cProduct_Type.Sigma @ cOrderings.top_class.top) @ (^[V0]: cOrderings.top_class.top)))))
(TString.char.recs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cString.char.char_rec @ V0) @ ((cString.char.Char @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TString.char.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cString.char.size_char_inst.size_char @ ((cString.char.Char @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TString.char.size_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cString.char.char_size @ ((cString.char.Char @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TString.char_size,(call @ (^[V0]: ((cHOL.eq @ (cString.char.char_size @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TString.size_char,(call @ (^[V0]: ((cHOL.eq @ (cString.char.size_char_inst.size_char @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TSum_Type.Inl_def,((cHOL.eq @ cSum_Type.Inl) @ ((cFun.comp @ cSum_Type.Abs_sum) @ cSum_Type.Inl_Rep)))
(TSum_Type.Inr_def,((cHOL.eq @ cSum_Type.Inr) @ ((cFun.comp @ cSum_Type.Abs_sum) @ cSum_Type.Inr_Rep)))
(TSum_Type.inj_Inl,(call @ (^[V0]: ((cFun.inj_on @ cSum_Type.Inl) @ V0))))
(TSum_Type.inj_Inr,(call @ (^[V0]: ((cFun.inj_on @ cSum_Type.Inr) @ V0))))
(TSum_Type.sum_def,((cHOL.eq @ cSum_Type.sum) @ (cSet.Collect @ (^[V0]: ((cHOL.disj @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cSum_Type.Inl_Rep @ V1))))) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cSum_Type.Inr_Rep @ V1)))))))))
(TTransfer.Rel_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransfer.Rel @ V0) @ V4) @ V5)) @ (((cTransfer.Rel @ V1) @ (V2 @ V4)) @ (V3 @ V5)))))))) @ (((cTransfer.Rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ (^[V4]: (V2 @ V4))) @ (^[V4]: (V3 @ V4)))))))))))))
(TTransfer.Rel_app,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransfer.Rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ V2) @ V3)) @ ((c==> @ (((cTransfer.Rel @ V0) @ V4) @ V5)) @ (((cTransfer.Rel @ V1) @ (V2 @ V4)) @ (V3 @ V5)))))))))))))))))
(TTransfer.Rel_def,(call @ (^[V0]: ((c== @ (cTransfer.Rel @ V0)) @ V0))))
(TATP.fimplies_laws_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cATP.fNot @ ((cATP.fimplies @ V0) @ V1))) @ ((cATP.fconj @ V0) @ (cATP.fNot @ V1))))))))
(TATP.fimplies_laws_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cATP.fimplies @ V0) @ V1)) @ ((cATP.fdisj @ (cHOL.Not @ V0)) @ V1)))))))
(TDatatype.Atom_def,((c== @ cDatatype.Atom) @ (^[V0]: ((cSet.insert @ (cDatatype.Abs_Node @ ((cProduct_Type.Pair @ (^[V1]: (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat))) @ V0))) @ cOrderings.bot_class.bot))))
(TDatatype.Case_In0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cDatatype.Case @ V0) @ V1) @ (cDatatype.In0 @ V2))) @ (V0 @ V2)))))))))
(TDatatype.Case_In1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cDatatype.Case @ V0) @ V1) @ (cDatatype.In1 @ V2))) @ (V1 @ V2)))))))))
(TDatatype.Case_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cDatatype.Case @ V0) @ V1) @ V2)) @ (cHOL.The @ (^[V3]: ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cDatatype.In0 @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4)))))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cDatatype.In1 @ V4))) @ ((cHOL.eq @ V3) @ (V1 @ V4))))))))))))))))
(TDatatype.In0_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cDatatype.In0 @ V0)) @ (cDatatype.In0 @ V1))))))))
(TDatatype.In1_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cDatatype.In1 @ V0)) @ (cDatatype.In1 @ V1))))))))
(TDatatype.Leaf_def,((c== @ cDatatype.Leaf) @ ((cFun.comp @ cDatatype.Atom) @ cSum_Type.Inl)))
(TDatatype.Node_def,((cHOL.eq @ cDatatype.Node) @ (cSet.Collect @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((cHOL.eq @ (V1 @ V3)) @ (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat)))))))))))))
(TDatatype.Numb_def,((c== @ cDatatype.Numb) @ ((cFun.comp @ cDatatype.Atom) @ cSum_Type.Inr)))
(TDatatype.Push_def,((c== @ cDatatype.Push) @ (^[V0]: (^[V1]: ((cNat.nat.nat_case @ V0) @ V1)))))
(TDatatype.dsum_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cDatatype.dsum @ V0) @ V1)) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cSet.insert @ ((cProduct_Type.Pair @ (cDatatype.In0 @ V2)) @ (cDatatype.In0 @ V3))) @ cOrderings.bot_class.bot)))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cSet.insert @ ((cProduct_Type.Pair @ (cDatatype.In1 @ V2)) @ (cDatatype.In1 @ V3))) @ cOrderings.bot_class.bot))))))))))))
(TDatatype.inj_Atom,((cFun.inj_on @ cDatatype.Atom) @ cOrderings.top_class.top))
(TDatatype.inj_Leaf,((cFun.inj_on @ cDatatype.Leaf) @ cOrderings.top_class.top))
(TDatatype.inj_Numb,((cFun.inj_on @ cDatatype.Numb) @ cOrderings.top_class.top))
(TDatatype.ntrunc_0,(call @ (^[V0]: ((cHOL.eq @ ((cDatatype.ntrunc @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cOrderings.bot_class.bot))))
(TDatatype.usum_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cDatatype.usum @ V0) @ V1)) @ ((cLattices.sup_class.sup @ ((cSet.image @ cDatatype.In0) @ V0)) @ ((cSet.image @ cDatatype.In1) @ V1))))))))
(TDivides.adjust_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.adjust @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((cHOL.Let @ ((cInt.minus_int_inst.minus_int @ V2) @ V0)) @ (^[V3]: (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V3)) @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)) @ cInt.one_int_inst.one_int)) @ V3)) @ ((cProduct_Type.Pair @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)) @ V2))))))))))))
(TDivides.mod2_gr_0,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cNat.one_nat_inst.one_nat)))))
(TDivides.mod_eq_0D,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TDivides.mod_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V0))) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V2) @ V0)))))))))))))
(TDivides.split_div,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cDivides.div_nat_inst.div_nat @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ (V0 @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V4) @ V2)) @ ((cHOL.implies @ ((cHOL.eq @ V1) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V3)) @ V4))) @ (V0 @ V3)))))))))))))))))
(TDivides.split_mod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ (V0 @ V1))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V4) @ V2)) @ ((cHOL.implies @ ((cHOL.eq @ V1) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V3)) @ V4))) @ (V0 @ V4)))))))))))))))))
(TEnum.Collect_code,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ V0)) @ (cList.set @ ((cList.filter @ V0) @ cEnum.enum_class.enum))))))
(TEnum.enum.enum_ex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.eq @ V2) @ cHOL.Ex)))))))))
(TEnum.enum.in_enum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cSet.member @ V3) @ (cList.set @ V0))))))))))))
(TEnum.enum_fun_def,((cHOL.eq @ cEnum.enum_class.enum) @ ((cList.map @ (^[V0]: ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ cEnum.enum_class.enum) @ V0))))) @ ((cList.n_lists @ (cNat.size_class.size @ cEnum.enum_class.enum)) @ cEnum.enum_class.enum))))
(TEnum.enum_set_def,((cHOL.eq @ cEnum.enum_class.enum) @ ((cList.map @ cList.set) @ (cList.sublists @ cEnum.enum_class.enum))))
(TEnum.enum_sum_def,((cHOL.eq @ cEnum.enum_class.enum) @ ((cList.append @ ((cList.map @ cSum_Type.Inl) @ cEnum.enum_class.enum)) @ ((cList.map @ cSum_Type.Inr) @ cEnum.enum_class.enum))))
(TEnum.enum_the_def,((cHOL.eq @ cEnum.enum_the) @ cHOL.The))
(TEnum.exists1_code,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex1 @ (^[V1]: (V0 @ V1)))) @ ((cList.list_ex1 @ V0) @ cEnum.enum_class.enum)))))
(TFields.sign_simps_24,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)))))))))
(TFields.sign_simps_23,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)))))))))
(TFields.sign_simps_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TFields.sign_simps_21,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TFields.sign_simps_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TFields.sign_simps_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.sign_simps_18,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TFields.sign_simps_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.sign_simps_16,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cGroups.minus_class.minus @ V0) @ V1)))))))
(TFields.sign_simps_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)))))))))
(TFields.sign_simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.sign_simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.sign_simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.sign_simps_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cGroups.minus_class.minus @ V1) @ V0)))))))
(TFields.sign_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.sign_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TFields.sign_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.sign_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.sign_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.sign_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.sign_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.sign_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.sign_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.sign_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFun.UNION_fun_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (((cFun.fun_upd @ V1) @ V2) @ V3))) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ V1)) @ (((cHOL.If @ ((cSet.member @ V2) @ V0)) @ V3) @ cOrderings.bot_class.bot))))))))))))
(TFun.apply_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ V2)) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V3 @ V5)) @ ((cHOL.eq @ (V4 @ (V0 @ V5))) @ V5))))) @ ((c==> @ (V3 @ V1)) @ ((cHOL.eq @ V1) @ (V4 @ V2))))))))))))))))
(TFun.bij_betw_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cHOL.eq @ (V1 @ V4)) @ (V2 @ V4)))))) @ ((cHOL.eq @ (((cFun.bij_betw @ V1) @ V0) @ V3)) @ (((cFun.bij_betw @ V2) @ V0) @ V3))))))))))))
(TFun.bij_image_INT,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cSet.image @ V0) @ (V2 @ V3)))))))))))))
(TFun.fun_upd_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cFun.fun_upd @ V0) @ V1) @ V2) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V3) @ V1)) @ V2) @ (V0 @ V3))))))))))))
(TFun.fun_upd_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.image @ (((cFun.fun_upd @ V0) @ V1) @ V2)) @ V3)) @ (((cHOL.If @ ((cSet.member @ V1) @ V3)) @ ((cSet.insert @ V2) @ ((cSet.image @ V0) @ ((cGroups.minus_class.minus @ V3) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))) @ ((cSet.image @ V0) @ V3))))))))))))
(TFun.fun_upd_other,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ ((((cFun.fun_upd @ V2) @ V1) @ V3) @ V0)) @ (V2 @ V0))))))))))))
(TFun.fun_upd_twist,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ (((cFun.fun_upd @ (((cFun.fun_upd @ V2) @ V0) @ V3)) @ V1) @ V4)) @ (((cFun.fun_upd @ (((cFun.fun_upd @ V2) @ V1) @ V4)) @ V0) @ V3))))))))))))))
(TFun.image_compose,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cSet.image @ V0) @ ((cSet.image @ V1) @ V2))))))))))
(TFun.inj_on_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V2)) @ (V0 @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))))
(TFun.inj_on_imageI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cFun.inj_on @ V0) @ ((cSet.image @ V1) @ V2))))))))))
(TFun.inj_on_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.inj_on @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cHOL.conj @ ((cFun.inj_on @ V0) @ V2)) @ (cHOL.Not @ ((cSet.member @ (V0 @ V1)) @ ((cSet.image @ V0) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))))
(TFun.inj_singleton,((cFun.inj_on @ (^[V0]: ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ cOrderings.top_class.top))
(TFun.map_fun_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cFun.map_fun @ V0) @ V1) @ V2) @ V3)) @ (V1 @ (V2 @ (V0 @ V3)))))))))))))
(TFun.subset_inj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cFun.inj_on @ V0) @ V2))))))))))
(TFun.surj_swap_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ (((cFun.swap @ V0) @ V1) @ V2)) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V2) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)))))))))
(TFun.swap_image_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ ((cSet.image @ (((cFun.swap @ V0) @ V2) @ V3)) @ V1)) @ ((cSet.image @ V3) @ V1)))))))))))))
(TFunDef.in_rel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cFunDef.in_rel @ V0) @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)))))))))
(TFunDef.pair_leqI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V2)) @ ((cProduct_Type.Pair @ V1) @ V3))) @ cFunDef.pair_leq)))))))))))
(TFunDef.pair_leqI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V2)) @ ((cProduct_Type.Pair @ V1) @ V3))) @ cFunDef.pair_leq))))))))))))
(TFunDef.split_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V4) @ V5)) @ V0)) @ ((cHOL.eq @ ((V1 @ V4) @ V5)) @ ((V2 @ V4) @ V5)))))))) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V1) @ V3)) @ ((cProduct_Type.prod.prod_case @ V2) @ V0)))))))))))))
(TFunDef.wf_no_loop,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ ((cRelation.relcomp @ V0) @ V0)) @ cOrderings.bot_class.bot)) @ (cWellfounded.wf @ V0)))))
(TGroups.monoid_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.monoid @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.semigroup @ V0)) @ ((cGroups.monoid_axioms @ V0) @ V1))))))))
(THOL.Let_case_cert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c== @ V0) @ (^[V3]: ((cHOL.Let @ V3) @ V1)))) @ ((c== @ (V0 @ V2)) @ (V1 @ V2))))))))))
(THOL.True_or_False,(call @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cHOL.True)) @ ((cHOL.eq @ V0) @ cHOL.False)))))
(THOL.Trueprop_code,((c== @ cHOL.True) @ cCode_Generator.holds))
(THOL.atomize_conjL,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((c==> @ V0) @ ((c==> @ V1) @ V2))) @ ((c==> @ ((cHOL.conj @ V0) @ V1)) @ V2)))))))))
(THOL.atomize_disjL,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ ((c==> @ V2) @ V1)) @ V1))) @ ((c==> @ ((c==> @ ((cHOL.disj @ V0) @ V2)) @ V1)) @ V1)))))))))
(THOL.atomize_elimL,(call @ (^[V0]: ((c== @ (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ V1)))) @ V0))))
(THOL.context_conjI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((c==> @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V1))))))))
(THOL.eq_reflection,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c== @ V0) @ V1)))))))
(THOL.imp_conv_disj,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)))))))
(THOL.imp_disj_not1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.implies @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ ((cHOL.implies @ V0) @ V2))))))))))
(THOL.imp_disj_not2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.implies @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V2)) @ ((cHOL.implies @ V0) @ V1))))))))))
(THOL.induct_rulify_4,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_equal @ V0) @ V1)) @ ((c== @ V0) @ V1)))))))
(THOL.induct_rulify_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_conj @ V0) @ V1)) @ ((cPure.conjunction @ V0) @ V1)))))))
(THOL.induct_rulify_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_implies @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(THOL.induct_rulify_1,(call @ (^[V0]: ((c== @ (cHOL.induct_forall @ (^[V1]: (V0 @ V1)))) @ (call @ (^[V1]: (V0 @ V1)))))))
(THOL.let_weak_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.Let @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cHOL.Let @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(THOL.rev_conj_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.conj @ V2) @ V0)) @ ((cHOL.conj @ V3) @ V1)))))))))))))
(THOL.simp_impliesE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ V0) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(THOL.simp_impliesI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(THOL.the1_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (V0 @ V1)) @ ((cHOL.eq @ (cHOL.The @ (^[V2]: (V0 @ V2)))) @ V1))))))))
(TInt.Abs_Integ_def,((c== @ cInt.Abs_Integ) @ ((cQuotient.quot_type.abs @ cInt.intrel) @ cInt.Abs_int)))
(TInt.Quotient3_int,(((cQuotient.Quotient3 @ cInt.intrel) @ cInt.Abs_Integ) @ cInt.Rep_Integ))
(TInt.Rep_Integ_def,((c== @ cInt.Rep_Integ) @ (cQuotient.quot_type.rep @ cInt.Rep_int)))
(TInt.divide_minus1,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))) @ (cGroups.uminus_class.uminus @ V0)))))
(TInt.equal_int_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TInt.int_Suc0_eq_1,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ cInt.one_int_inst.one_int))
(TInt.int_eq_0_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TInt.int_ge_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((c==> @ (V2 @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V3)) @ ((c==> @ (V2 @ V3)) @ (V2 @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int))))))) @ (V2 @ V1)))))))))))
(TInt.int_gr_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((c==> @ (V2 @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V3)) @ ((c==> @ (V2 @ V3)) @ (V2 @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int))))))) @ (V2 @ V1)))))))))))
(TInt.int_le_0_conv,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cNat.semiring_1_class.of_nat @ V0)) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TInt.int_le_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((c==> @ (V2 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V1)) @ ((c==> @ (V2 @ V3)) @ (V2 @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))))))) @ (V2 @ V0)))))))))))
(TInt.int_val_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.implies @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ (cInt.abs_int_inst.abs_int @ ((cInt.minus_int_inst.minus_int @ (V1 @ ((cNat.plus_nat_inst.plus_nat @ V3) @ cNat.one_nat_inst.one_nat))) @ (V1 @ V3)))) @ cInt.one_int_inst.one_int))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ (V1 @ cNat.zero_nat_inst.zero_nat)) @ V2)) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ V2) @ (V1 @ V0))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ V3)) @ V2))))))))))))))
(TInt.le_imp_0_less,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ V0))))))
(TInt.less_int_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.Neg @ V0)) @ (cInt.Neg @ V1))) @ ((cNum.ord_num_inst.less_num @ V1) @ V0)))))))
(TInt.less_int_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.Neg @ V0)) @ (cInt.Pos @ V1))) @ cHOL.True))))))
(TInt.less_int_code_7,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.Neg @ V0)) @ cInt.zero_int_inst.zero_int)) @ cHOL.True))))
(TInt.less_int_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.Pos @ V0)) @ (cInt.Neg @ V1))) @ cHOL.False))))))
(TInt.less_int_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.Pos @ V0)) @ (cInt.Pos @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TInt.less_int_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.Pos @ V0)) @ cInt.zero_int_inst.zero_int)) @ cHOL.False))))
(TInt.less_int_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ (cInt.Neg @ V0))) @ cHOL.False))))
(TInt.less_int_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ (cInt.Pos @ V0))) @ cHOL.True))))
(TInt.less_int_code_1,((cHOL.eq @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)) @ cHOL.False))
(TInt.max_number_of_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))))
(TInt.max_number_of_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))))
(TInt.max_number_of_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ (cNum.numeral_class.numeral @ V0))))))))
(TInt.max_number_of_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ V1)) @ (cNum.numeral_class.numeral @ V0))))))))
(TInt.min_number_of_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TInt.min_number_of_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TInt.min_number_of_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TInt.min_number_of_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TInt.minus1_divide,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)) @ (cGroups.uminus_class.uminus @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0))))))
(TInt.minus_int.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ ((cTransfer.fun_rel @ cInt.intrel) @ cInt.intrel)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TInt.minus_int_def,((c== @ cInt.minus_int_inst.minus_int) @ (((cFun.map_fun @ cInt.Rep_Integ) @ ((cFun.map_fun @ cInt.Rep_Integ) @ cInt.Abs_Integ)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2)))))))))))
(TInt.nat_le_eq_zle,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1))) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1))))))))
(TInt.nonneg_eq_int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V2))) @ V1)))) @ V1)))))))
(TInt.of_int_int_eq,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TInt.of_int_setsum,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cInt.ring_1_class.of_int @ (V0 @ V2)))) @ V1)))))))
(TInt.of_nat_setsum,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cNat.semiring_1_class.of_nat @ (V0 @ V2)))) @ V1)))))))
(TInt.plus_int_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cInt.Neg @ V0)) @ (cInt.Neg @ V1))) @ (cInt.Neg @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TInt.plus_int_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cInt.Neg @ V0)) @ (cInt.Pos @ V1))) @ ((cInt.sub @ V1) @ V0)))))))
(TInt.plus_int_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cInt.Pos @ V0)) @ (cInt.Neg @ V1))) @ ((cInt.sub @ V0) @ V1)))))))
(TInt.plus_int_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cInt.Pos @ V0)) @ (cInt.Pos @ V1))) @ (cInt.Pos @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TInt.plus_int_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ cInt.zero_int_inst.zero_int) @ V0)) @ V0))))
(TInt.plus_int_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.zero_int_inst.zero_int)) @ V0))))
(TInt.ring_1.Ints_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cSet.member @ V3) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))))))))))))))))
(TInt.ring_1.Ints_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cSet.member @ V0) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))))))))))))))))
(TInt.times_int.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ ((cTransfer.fun_rel @ cInt.intrel) @ cInt.intrel)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V3)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)))))))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V3)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)))))))))))
(TInt.times_int_def,((c== @ cInt.times_int_inst.times_int) @ (((cFun.map_fun @ cInt.Rep_Integ) @ ((cFun.map_fun @ cInt.Rep_Integ) @ cInt.Abs_Integ)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V3)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))))
(TInt.zadd_int_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cNat.semiring_1_class.of_nat @ V0)) @ ((cInt.plus_int_inst.plus_int @ (cNat.semiring_1_class.of_nat @ V1)) @ V2))) @ ((cInt.plus_int_inst.plus_int @ (cNat.semiring_1_class.of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ V2)))))))))
(TInt.zless_add1_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))) @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TInt.zpower_zpower,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPower.power_class.power @ ((cPower.power_class.power @ V0) @ V1)) @ V2)) @ ((cPower.power_class.power @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TLifting.NEG_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLifting.NEG @ V0) @ V1)) @ ((c==> @ ((cLifting.NEG @ V1) @ V2)) @ ((cLifting.NEG @ V0) @ V2))))))))))
(TLifting.POS_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cLifting.POS @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TLifting.POS_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLifting.POS @ V0) @ V1)) @ ((c==> @ ((cLifting.POS @ V1) @ V2)) @ ((cLifting.POS @ V0) @ V2))))))))))
(TLifting.QuotientI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((cHOL.eq @ (V0 @ (V1 @ V4))) @ V4)))) @ ((c==> @ (call @ (^[V4]: ((V2 @ (V1 @ V4)) @ (V1 @ V4))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((cHOL.conj @ ((V2 @ V4) @ V4)) @ ((cHOL.conj @ ((V2 @ V5) @ V5)) @ ((cHOL.eq @ (V0 @ V4)) @ (V0 @ V5)))))))))) @ ((c==> @ ((cHOL.eq @ V3) @ (^[V4]: (^[V5]: ((cHOL.conj @ ((V2 @ V4) @ V4)) @ ((cHOL.eq @ (V0 @ V4)) @ V5)))))) @ ((((cLifting.Quotient @ V2) @ V0) @ V1) @ V3))))))))))))))
(TLifting.apply_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cTransfer.fun_rel @ V0) @ V4) @ V5) @ V6)) @ ((c==> @ ((V0 @ V7) @ V8)) @ ((V4 @ (V5 @ V7)) @ (V6 @ V8))))))))))))))))))))))))
(TLifting.neg_OO_eq,(call @ (^[V0]: ((cLifting.NEG @ ((cRelation.relcompp @ V0) @ cHOL.eq)) @ V0))))
(TLifting.neg_eq_OO,(call @ (^[V0]: ((cLifting.NEG @ ((cRelation.relcompp @ cHOL.eq) @ V0)) @ V0))))
(TLifting.pos_OO_eq,(call @ (^[V0]: ((cLifting.POS @ ((cRelation.relcompp @ V0) @ cHOL.eq)) @ V0))))
(TLifting.pos_eq_OO,(call @ (^[V0]: ((cLifting.POS @ ((cRelation.relcompp @ cHOL.eq) @ V0)) @ V0))))
(TList.Domainp_list,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((cHOL.eq @ (cRelation.Domainp @ (cList.list_all2 @ V0))) @ (cList.list_all @ V1))))))))
(TList.ListMem.elem,(call @ (^[V0]: (call @ (^[V1]: ((cList.ListMem @ V0) @ ((cList.list.Cons @ V0) @ V1)))))))
(TList.Nil_transfer,(call @ (^[V0]: (((cList.list_all2 @ V0) @ cList.list.Nil) @ cList.list.Nil))))
(TList.all_nat_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V0)) @ (V1 @ V2))))) @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (^[V2]: (V1 @ V2)))))))))
(TList.append.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.append @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ ((cList.list.Cons @ V0) @ ((cList.append @ V1) @ V2))))))))))
(TList.append.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.append @ cList.list.Nil) @ V0)) @ V0))))
(TList.append_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.append @ ((cList.append @ V0) @ V1)) @ V2)) @ ((cList.append @ V0) @ ((cList.append @ V1) @ V2))))))))))
(TList.butlast_drop,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.butlast @ ((cList.drop @ V0) @ V1))) @ ((cList.drop @ V0) @ (cList.butlast @ V1))))))))
(TList.butlast_snoc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.butlast @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))) @ V0))))))
(TList.butlast_take,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (cList.butlast @ ((cList.take @ V0) @ V1))) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V1))))))))
(TList.concat.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.concat @ ((cList.list.Cons @ V0) @ V1))) @ ((cList.append @ V0) @ (cList.concat @ V1))))))))
(TList.concat.simps_1,((cHOL.eq @ (cList.concat @ cList.list.Nil)) @ cList.list.Nil))
(TList.distinct_def,((c== @ cList.distinct) @ (^[V0]: (((cList.list.list_rec @ cHOL.True) @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V1) @ (cList.set @ V2)))) @ V3))))) @ V0))))
(TList.distinct_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.distinct @ ((cList.map @ V0) @ V1))) @ ((cHOL.conj @ (cList.distinct @ V1)) @ ((cFun.inj_on @ V0) @ (cList.set @ V1)))))))))
(TList.distinct_rev,(call @ (^[V0]: ((cHOL.eq @ (cList.distinct @ (cList.rev @ V0))) @ (cList.distinct @ V0)))))
(TList.distinct_upt,(call @ (^[V0]: (call @ (^[V1]: (cList.distinct @ ((cList.upt @ V0) @ V1)))))))
(TList.drop_butlast,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.drop @ V0) @ (cList.butlast @ V1))) @ (cList.butlast @ ((cList.drop @ V0) @ V1))))))))
(TList.filter.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.filter @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ (V0 @ V1)) @ ((cList.list.Cons @ V1) @ ((cList.filter @ V0) @ V2))) @ ((cList.filter @ V0) @ V2))))))))))
(TList.filter.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.filter @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.filter_False,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: (cHOL.Not @ (V1 @ V2))))) @ ((cHOL.eq @ ((cList.filter @ V1) @ V0)) @ cList.list.Nil)))))))
(TList.fold_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cFun.comp @ V1) @ (V2 @ V4))) @ ((cFun.comp @ (V3 @ V4)) @ V1)))))) @ ((cHOL.eq @ ((cFun.comp @ V1) @ ((cList.fold @ V2) @ V0))) @ ((cFun.comp @ ((cList.fold @ V3) @ V0)) @ V1))))))))))))
(TList.foldl_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ ((cList.append @ V2) @ V3))) @ (((cList.foldl @ V0) @ (((cList.foldl @ V0) @ V1) @ V2)) @ V3)))))))))))
(TList.foldr_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.foldr @ V0) @ ((cList.append @ V1) @ V2)) @ V3)) @ (((cList.foldr @ V0) @ V1) @ (((cList.foldr @ V0) @ V2) @ V3))))))))))))
(TList.hd_dropWhile,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ ((cList.dropWhile @ V0) @ V1)) @ cList.list.Nil))) @ (cHOL.Not @ (V0 @ (cList.hd @ ((cList.dropWhile @ V0) @ V1))))))))))
(TList.hd_replicate,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ (cList.hd @ ((cList.replicate @ V0) @ V1))) @ V1)))))))
(TList.in_set_dropD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ ((cList.drop @ V1) @ V2)))) @ ((cSet.member @ V0) @ (cList.set @ V2))))))))))
(TList.in_set_takeD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ ((cList.take @ V1) @ V2)))) @ ((cSet.member @ V0) @ (cList.set @ V2))))))))))
(TList.is_empty_set,(call @ (^[V0]: ((cHOL.eq @ (cSet.is_empty @ (cList.set @ V0))) @ (cList.null @ V0)))))
(TList.last_appendL,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ (cList.last @ ((cList.append @ V1) @ V0))) @ (cList.last @ V1))))))))
(TList.last_appendR,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.last @ ((cList.append @ V1) @ V0))) @ (cList.last @ V0))))))))
(TList.lexord_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cList.lexord @ V4))) @ ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cList.lexord @ V4))))))))))))))))
(TList.lexord_simps_2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil)) @ (cList.lexord @ V1))))))))
(TList.lexord_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ cList.list.Nil) @ V0)) @ (cList.lexord @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V3))))))))))))
(TList.lexord_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.lexord @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cList.lexord @ V2))) @ ((c==> @ (cRelation.trans @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cList.lexord @ V2))))))))))))))
(TList.list.Nil_def,((c== @ cList.list.Nil) @ (cList.Abs_list @ (cDatatype.In0 @ cHOL.undefined))))
(TList.list.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TList.list.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V1)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V3))) @ V1)))))) @ V1)))))))
(TList.list.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cList.list.Cons @ V2) @ V3)))))))) @ (V0 @ V1))))))))
(TList.list_all2_OO,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcompp @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V1))) @ (cList.list_all2 @ ((cRelation.relcompp @ V0) @ V1))))))))
(TList.list_all2_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ (((cList.list_all2 @ cHOL.eq) @ V0) @ V1)))))))
(TList.list_all_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list_all @ V0) @ V1)) @ ((cSet.Ball @ (cList.set @ V1)) @ V0)))))))
(TList.list_all_rev,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list_all @ V0) @ (cList.rev @ V1))) @ ((cList.list_all @ V0) @ V1)))))))
(TList.list_ex1_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list_ex1 @ V0) @ V1)) @ (cHOL.Ex1 @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ (cList.set @ V1))) @ (V0 @ V2))))))))))
(TList.list_ex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V1))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cList.list_ex @ V2) @ V0)) @ ((cList.list_ex @ V3) @ V1)))))))))))))
(TList.list_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((V2 @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V4)) @ (cNat.size_class.size @ V6))) @ ((c==> @ ((V2 @ V4) @ V6)) @ ((V2 @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6))))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.list_induct3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))) @ ((c==> @ (((V3 @ cList.list.Nil) @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V5)) @ (cNat.size_class.size @ V7))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V7)) @ (cNat.size_class.size @ V9))) @ ((c==> @ (((V3 @ V5) @ V7) @ V9)) @ (((V3 @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V6) @ V7)) @ ((cList.list.Cons @ V8) @ V9)))))))))))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))))
(TList.list_induct4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.size_class.size @ V3))) @ ((c==> @ ((((V4 @ cList.list.Nil) @ cList.list.Nil) @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V6)) @ (cNat.size_class.size @ V8))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V8)) @ (cNat.size_class.size @ V10))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V10)) @ (cNat.size_class.size @ V12))) @ ((c==> @ ((((V4 @ V6) @ V8) @ V10) @ V12)) @ ((((V4 @ ((cList.list.Cons @ V5) @ V6)) @ ((cList.list.Cons @ V7) @ V8)) @ ((cList.list.Cons @ V9) @ V10)) @ ((cList.list.Cons @ V11) @ V12))))))))))))))))))))))) @ ((((V4 @ V0) @ V1) @ V2) @ V3)))))))))))))))))
(TList.listrel.Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (cList.listrel @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V3)) @ ((cList.list.Cons @ V1) @ V4))) @ (cList.listrel @ V2)))))))))))))))
(TList.listrel1_def,(call @ (^[V0]: ((cHOL.eq @ (cList.listrel1 @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V3) @ ((cList.list.Cons @ V4) @ V6)))) @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V0)) @ ((cHOL.eq @ V2) @ ((cList.append @ V3) @ ((cList.list.Cons @ V5) @ V6)))))))))))))))))))))
(TList.listrel_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.Image @ (cList.listrel @ V0)) @ ((cSet.insert @ ((cList.list.Cons @ V1) @ V2)) @ cOrderings.bot_class.bot))) @ ((cList.set_Cons @ ((cRelation.Image @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ (cList.listrel @ V0)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))
(TList.listrel_Nil1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ cList.list.Nil) @ V0)) @ (cList.listrel @ V1))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V2)) @ V2)))))))))
(TList.listrel_Nil2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil)) @ (cList.listrel @ V1))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V2)) @ V2)))))))))
(TList.listrel_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.listrel @ V0)) @ (cList.listrel @ V1))))))))
(TList.listrelp.Nil,(call @ (^[V0]: (((cList.listrelp @ V0) @ cList.list.Nil) @ cList.list.Nil))))
(TList.listrelp_def,((c== @ cList.listrelp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ ((cHOL.eq @ V3) @ cList.list.Nil))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V5) @ V7))) @ ((cHOL.conj @ ((V0 @ V4) @ V5)) @ ((V1 @ V6) @ V7))))))))))))))))))))
(TList.lists.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.lists @ V1))) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V3) @ V1)) @ ((c==> @ ((cSet.member @ V4) @ (cList.lists @ V1))) @ ((c==> @ (V2 @ V4)) @ (V2 @ ((cList.list.Cons @ V3) @ V4)))))))))) @ (V2 @ V0)))))))))))
(TList.lists.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (cList.lists @ V1))) @ ((cSet.member @ ((cList.list.Cons @ V0) @ V2)) @ (cList.lists @ V1)))))))))))
(TList.lists.intros_1,(call @ (^[V0]: ((cSet.member @ cList.list.Nil) @ (cList.lists @ V0)))))
(TList.lists_Int_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.lists @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cList.lists @ V0)) @ (cList.lists @ V1))))))))
(TList.lists_eq_set,(call @ (^[V0]: ((cHOL.eq @ (cList.lists @ V0)) @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cList.set @ V1)) @ V0)))))))
(TList.listsp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.listsp @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ V2)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ V4))) @ ((c==> @ (V0 @ V3)) @ ((c==> @ ((cList.listsp @ V0) @ V4)) @ V2)))))))) @ V2))))))))))
(TList.listsp.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.listsp @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ (V0 @ V2)) @ ((cList.listsp @ V0) @ V3))))))))))))))
(TList.listsp_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.listsp @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cHOL.conj @ (V0 @ V1)) @ ((cList.listsp @ V0) @ V2))))))))))
(TList.listsp_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.listsp @ V0) @ cList.list.Nil)) @ cHOL.True))))
(TList.listsum_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cOrderings.ord_class.less_eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: (V1 @ V3))) @ V0))) @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: (V2 @ V3))) @ V0)))))))))))
(TList.map.identity,((cHOL.eq @ (cList.map @ (^[V0]: V0))) @ cFun.id))
(TList.map_comp_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (cList.map @ V0)) @ (cList.map @ V1))) @ (cList.map @ ((cFun.comp @ V0) @ V1))))))))
(TList.map_decr_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ (^[V2]: ((cNat.minus_nat_inst.minus_nat @ V2) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))) @ ((cList.upt @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1)))) @ ((cList.upt @ V0) @ V1)))))))
(TList.map_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V1))) @ cList.map) @ cList.map))))))
(TList.map_zip_map2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.zip @ V1) @ ((cList.map @ V2) @ V3)))) @ ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ V4) @ (V2 @ V5))))))) @ ((cList.zip @ V1) @ V3))))))))))))
(TList.measures_def,(call @ (^[V0]: ((cHOL.eq @ (cList.measures @ V0)) @ ((cRelation.inv_image @ (cList.lex @ cWellfounded.less_than)) @ (^[V1]: ((cList.map @ (^[V2]: (V2 @ V1))) @ V0)))))))
(TList.nat_list_def,(call @ (^[V0]: ((cHOL.eq @ (cList.nat_list @ V0)) @ (cNat_Transfer.nat_set @ (cList.set @ V0))))))
(TList.neq_Nil_conv,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cList.list.Cons @ V1) @ V2))))))))))
(TList.nth.nth_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ (((cNat.nat.nat_case @ V0) @ (^[V3]: ((cList.nth @ V1) @ V3))) @ V2)))))))))
(TList.nth_Cons_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V1)) @ (cNat.Suc @ V2))) @ ((cList.nth @ V1) @ V2)))))))))
(TList.nth_Cons_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V1) @ V2)) @ V0)) @ ((cList.nth @ V2) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)))))))))))
(TList.nth_via_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.drop @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.eq @ ((cList.nth @ V1) @ V0)) @ V2)))))))))))
(TList.product_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.product @ (cList.set @ V0)) @ (cList.set @ V1))) @ (cList.set @ (cList.concat @ ((cList.map @ (^[V2]: ((cList.map @ (^[V3]: ((cProduct_Type.Pair @ V2) @ V3))) @ V1))) @ V0)))))))))
(TList.remove1_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((cHOL.eq @ ((cList.remove1 @ V0) @ V1)) @ V1)))))))
(TList.removeAll_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((cHOL.eq @ ((cList.removeAll @ V0) @ V1)) @ V1)))))))
(TList.rev_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0)) @ cList.rev) @ cList.rev))))
(TList.set_Cons_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.set_Cons @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V3) @ V4))) @ ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ V4) @ V1)))))))))))))))
(TList.set_conv_nth,(call @ (^[V0]: ((cHOL.eq @ (cList.set @ V0)) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.nth @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0)))))))))))
(TList.set_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cLifting_Set.set_rel @ V0)) @ cList.set) @ cList.set))))
(TList.splice.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V2))) @ V1)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V3)) @ cList.list.Nil))) @ V1)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V3)) @ ((cList.list.Cons @ V4) @ V5)))) @ V1)))))))))) @ V1))))))))
(TList.splice.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.splice @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V4)) @ V3)))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ V5))) @ V3)))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V6) @ ((cList.splice @ V5) @ V7))))) @ V3)))))))))))) @ V3)))))))))))))
(TList.splice.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cList.splice @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V2) @ ((cList.splice @ V1) @ V3)))))))))))))
(TList.splice.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.splice @ ((cList.list.Cons @ V0) @ V1)) @ cList.list.Nil)) @ ((cList.list.Cons @ V0) @ V1)))))))
(TList.splice.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.splice @ cList.list.Nil) @ V0)) @ V0))))
(TList.sublist_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.sublist @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ ((cList.append @ (((cHOL.If @ ((cSet.member @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cList.list.Cons @ V0) @ cList.list.Nil)) @ cList.list.Nil)) @ ((cList.sublist @ V1) @ (cSet.Collect @ (^[V3]: ((cSet.member @ (cNat.Suc @ V3)) @ V2)))))))))))))
(TList.sublists_def,((c== @ cList.sublists) @ (^[V0]: (((cList.list.list_rec @ ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil)) @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.Let @ V3) @ (^[V4]: ((cList.append @ ((cList.map @ (cList.list.Cons @ V1)) @ V4)) @ V4))))))) @ V0))))
(TList.take_butlast,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.take @ V0) @ (cList.butlast @ V1))) @ ((cList.take @ V0) @ V1))))))))
(TList.take_hd_drop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.append @ ((cList.take @ V0) @ V1)) @ ((cList.list.Cons @ (cList.hd @ ((cList.drop @ V0) @ V1))) @ cList.list.Nil))) @ ((cList.take @ (cNat.Suc @ V0)) @ V1))))))))
(TList.the_elem_set,(call @ (^[V0]: ((cHOL.eq @ (cSet.the_elem @ (cList.set @ ((cList.list.Cons @ V0) @ cList.list.Nil)))) @ V0))))
(TList.tl_replicate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.tl @ ((cList.replicate @ V0) @ V1))) @ ((cList.replicate @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V1)))))))
(TList.upt_conv_Nil,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cList.upt @ V1) @ V0)) @ cList.list.Nil)))))))
(TList.upto.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cList.upto_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cList.upto_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)) @ ((V2 @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TList.upto_aux_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.upto_aux @ V0) @ V1) @ V2)) @ ((cList.append @ ((cList.upto @ V0) @ V1)) @ V2)))))))))
(TList.upto_aux_rec,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.upto_aux @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ V0)) @ V2) @ (((cList.upto_aux @ V0) @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int)) @ ((cList.list.Cons @ V1) @ V2)))))))))))
(TList.upto_rel_def,((c== @ cList.upto_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)))))))))))))
(TList.zip.zip_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ ((cProduct_Type.Pair @ V3) @ V1)) @ ((cList.zip @ V4) @ V2))))) @ V0)))))))))
(TList.zip_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ (cList.list_all2 @ ((cLifting_Product.prod_rel @ V0) @ V1)))) @ cList.zip) @ cList.zip))))))
(TMap.empty_map_add,(call @ (^[V0]: ((cHOL.eq @ ((cMap.map_add @ (^[V1]: cOption.option.None)) @ V0)) @ V0))))
(TMap.image_map_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ ((cSet.image @ (((cFun.fun_upd @ V2) @ V0) @ (cOption.option.Some @ V3))) @ V1)) @ ((cSet.image @ V2) @ V1))))))))))))
(TMap.map_add_SomeD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (((cMap.map_add @ V0) @ V1) @ V2)) @ (cOption.option.Some @ V3))) @ ((cHOL.disj @ ((cHOL.eq @ (V1 @ V2)) @ (cOption.option.Some @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ cOption.option.None)) @ ((cHOL.eq @ (V0 @ V2)) @ (cOption.option.Some @ V3))))))))))))))
(TMap.map_add_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cMap.map_add @ V0) @ ((cMap.map_add @ V1) @ V2))) @ ((cMap.map_add @ ((cMap.map_add @ V0) @ V1)) @ V2)))))))))
(TMap.map_add_empty,(call @ (^[V0]: ((cHOL.eq @ ((cMap.map_add @ V0) @ (^[V1]: cOption.option.None))) @ V0))))
(TMap.map_of_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.map_of @ ((cList.append @ V0) @ V1))) @ ((cMap.map_add @ (cMap.map_of @ V1)) @ (cMap.map_of @ V0))))))))
(TMap.map_of_eq_dom,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cMap.map_of @ V0)) @ (cMap.map_of @ V1))) @ ((cHOL.eq @ ((cSet.image @ cProduct_Type.fst) @ (cList.set @ V0))) @ ((cSet.image @ cProduct_Type.fst) @ (cList.set @ V1)))))))))
(TMap.map_upds_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cMap.map_upds @ V0) @ ((cList.list.Cons @ V1) @ V2)) @ ((cList.list.Cons @ V3) @ V4))) @ (((cMap.map_upds @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V3))) @ V2) @ V4)))))))))))))
(TMap.map_upds_Nil1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cMap.map_upds @ V0) @ cList.list.Nil) @ V1)) @ V0))))))
(TMap.map_upds_Nil2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cMap.map_upds @ V0) @ V1) @ cList.list.Nil)) @ V0))))))
(TMap.ran_restrictD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cMap.ran @ ((cMap.restrict_map @ V1) @ V2)))) @ ((cSet.Bex @ V2) @ (^[V3]: ((cHOL.eq @ (V1 @ V3)) @ (cOption.option.Some @ V0))))))))))))
(TMeson.all_forward,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(TMetis.not_atomize,(call @ (^[V0]: ((c== @ ((c==> @ (cHOL.Not @ V0)) @ cHOL.False)) @ V0))))
(TNat.Nat.Zero_RepI,(cNat.Nat @ cNat.Zero_Rep))
(TNat.Suc_diff_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V0)) @ V1)) @ (cNat.Suc @ V2))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V2)))))))))
(TNat.Suc_less_SucD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat.add_Suc_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ (cNat.Suc @ V1))) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TNat.add_Suc_shift,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ (cNat.Suc @ V1))))))))
(TNat.add_less_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ V3)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3)))))))))))))
(TNat.def_nat_rec_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c== @ (V0 @ V3)) @ (((cNat.nat.nat_rec @ V1) @ V2) @ V3))))) @ ((cHOL.eq @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ V1)))))))))
(TNat.diff_Suc_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.Suc @ V1))) @ V0)))))))
(TNat.diff_is_0_eq',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)))))))
(TNat.diff_le_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V1)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V0))))))))))
(TNat.diff_less_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ (cNat.Suc @ V0)))))))
(TNat.dvd.Least_def,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord.Least @ cRings.dvd_class.dvd) @ V0)) @ (cHOL.The @ (^[V1]: ((cHOL.conj @ (V0 @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ ((cRings.dvd_class.dvd @ V1) @ V2)))))))))))
(TNat.dvd.less_asym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((c==> @ (cHOL.Not @ V2)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))))) @ V2)))))))))
(TNat.dvd_minus_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V2) @ V3))) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V3) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ ((cRings.dvd_class.dvd @ V3) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V3)) @ V0)))))))))))))))
(TNat.equal_nat_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.le_diff_conv2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0)) @ V1))))))))))
(TNat.less_add_Suc1,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TNat.less_add_Suc2,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V0))))))))
(TNat.less_diff_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V0))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)))))))))))
(TNat.less_not_refl,(call @ (^[V0]: (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ V0)))))
(TNat.minus_nat_def,((c== @ cNat.minus_nat_inst.minus_nat) @ (^[V0]: (^[V1]: ((((cNat.nat.nat_rec @ (^[V2]: V2)) @ (^[V2]: (^[V3]: (^[V4]: (((cNat.nat.nat_case @ cNat.zero_nat_inst.zero_nat) @ (^[V5]: V5)) @ (V3 @ V4)))))) @ V1) @ V0)))))
(TNat.mult_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TNat.mult_le_mono1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.mult_le_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V0)) @ ((cNat.times_nat_inst.times_nat @ V2) @ V1))))))))))
(TNat.nat.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ (cNat.Suc @ V6))) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ (((cNat.nat.nat_case @ V2) @ V4) @ V0)) @ (((cNat.nat.nat_case @ V3) @ V5) @ V1))))))))))))))))))
(TNat.nat.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cNat.nat.nat_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cNat.zero_nat_inst.zero_nat)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cNat.Suc @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TNat.nat_add_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TNat.nat_le_linear,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V0)))))))
(TNat.not_add_less1,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V0)))))))
(TNat.not_add_less2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V1)))))))
(TNat.one_less_mult,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V0)))))))))
(TNat.times_nat_def,((c== @ cNat.times_nat_inst.times_nat) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: cNat.zero_nat_inst.zero_nat)) @ (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ V3) @ (V2 @ V3)))))) @ V0))))
(TNat.trans_le_add1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TNat.trans_le_add2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TNat.zero_less_Suc,(call @ (^[V0]: ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ V0)))))
(TNitpick.Eps_psimp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.Not @ (V0 @ V2))) @ ((c==> @ ((cHOL.eq @ (cHilbert_Choice.Eps @ V0)) @ V2)) @ ((cHOL.eq @ (cHilbert_Choice.Eps @ V0)) @ V1)))))))))))
(TNitpick.The_psimp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ (cHOL.eq @ V1))) @ ((cHOL.eq @ (cHOL.The @ V0)) @ V1)))))))
(TNitpick.card'_def,(call @ (^[V0]: ((c== @ (cNitpick.card' @ V0)) @ (((cHOL.If @ (cFinite_Set.finite @ V0)) @ (cNat.size_class.size @ (cHilbert_Choice.Eps @ (^[V1]: ((cHOL.conj @ ((cHOL.eq @ (cList.set @ V1)) @ V0)) @ (cList.distinct @ V1)))))) @ cNat.zero_nat_inst.zero_nat)))))
(TNitpick.denom_def,((c== @ cNitpick.denom) @ ((cFun.comp @ cProduct_Type.snd) @ cNitpick.Rep_Frac)))
(TNitpick.refl'_def,(call @ (^[V0]: ((c== @ (cNitpick.refl' @ V0)) @ (cHOL.All @ (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ V0)))))))
(TNitpick.word.recs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.word.word_rec @ V0) @ (cNitpick.word.Word @ V1))) @ (V0 @ V1)))))))
(TNitpick.word.size_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cNitpick.word.Word @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TNitpick.word.size_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.word.word_size @ V0) @ (cNitpick.word.Word @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TNum.BitM_plus_one,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.BitM @ V0)) @ cNum.num.One)) @ (cNum.num.Bit0 @ V0)))))
(TNum.Suc3_eq_add_3,(call @ (^[V0]: ((cHOL.eq @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ V0)))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V0)))))
(TNum.add_2_eq_Suc',(call @ (^[V0]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cNat.Suc @ (cNat.Suc @ V0))))))
(TNum.add_num_simps_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)) @ cNum.num.One))))))))
(TNum.add_num_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.add_num_simps_7,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.add_num_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.add_num_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.add_num_simps_4,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cNum.num.Bit1 @ V0)))))
(TNum.add_num_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.add_num_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit1 @ V0)))))
(TNum.add_num_simps_1,((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ cNum.num.One)) @ (cNum.num.Bit0 @ cNum.num.One)))
(TNum.arith_special_10,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNum.arith_special_9,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.arith_special_8,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.neg_numeral_class.sub @ V0) @ cNum.num.One)))))
(TNum.arith_special_7,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0))))))
(TNum.arith_special_6,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0)))))
(TNum.arith_special_5,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0)))))
(TNum.arith_special_4,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0)))))
(TNum.arith_special_3,((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNum.arith_special_2,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0))))))
(TNum.arith_special_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.equal_num_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cNum.num.One)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V1) @ (cNum.num.Bit0 @ V8))) @ ((cHOL.eq @ (V4 @ V8)) @ (V5 @ V8)))))) @ ((c==> @ (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V1) @ (cNum.num.Bit1 @ V8))) @ ((cHOL.eq @ (V6 @ V8)) @ (V7 @ V8)))))) @ ((cHOL.eq @ ((((cNum.num.num_case @ V2) @ V4) @ V6) @ V0)) @ ((((cNum.num.num_case @ V3) @ V5) @ V7) @ V1)))))))))))))))))))))))
(TNum.num.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cNum.num.num_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cNum.num.One)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cNum.num.Bit0 @ V5))) @ (cHOL.Not @ (V0 @ (V2 @ V5))))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cNum.num.Bit1 @ V5))) @ (cHOL.Not @ (V0 @ (V3 @ V5)))))))))))))))))))))
(TNum.one_plus_BitM,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ (cNum.BitM @ V0))) @ (cNum.num.Bit0 @ V0)))))
(TNum.sqr_conv_mult,(call @ (^[V0]: ((cHOL.eq @ (cNum.sqr @ V0)) @ ((cNum.times_num_inst.times_num @ V0) @ V0)))))
(TNum.times_num_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ V0) @ V1)) @ (cNum.num_of_nat @ ((cNat.times_nat_inst.times_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V1)))))))))
(TOption.bind.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOption.bind @ (cOption.option.Some @ V0)) @ V1)) @ (V1 @ V0)))))))
(TOption.bind.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cOption.bind @ cOption.option.None) @ V0)) @ cOption.option.None))))
(TOption.bind_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOption.bind @ ((cOption.bind @ V0) @ V1)) @ V2)) @ ((cOption.bind @ V0) @ (^[V3]: ((cOption.bind @ (V1 @ V3)) @ V2)))))))))))
(TOption.bind_runit,(call @ (^[V0]: ((cHOL.eq @ ((cOption.bind @ V0) @ cOption.option.Some)) @ V0))))
(TOption.bind_rzero,(call @ (^[V0]: ((cHOL.eq @ ((cOption.bind @ V0) @ (^[V1]: cOption.option.None))) @ cOption.option.None))))
(TOrderings.le_funD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TOrderings.le_funE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V1 @ V2))) @ V3)) @ V3)))))))))))
(TOrderings.le_funI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TPower.power2_diff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ V1))))))))
(TPower.power_0_Suc,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ cGroups.zero_class.zero) @ (cNat.Suc @ V0))) @ cGroups.zero_class.zero))))
(TPower.power_Suc_0,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))
(TPower.power_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ cGroups.one_class.one) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ cNat.one_nat_inst.one_nat))))))))))
(TPredicate.Seq_def,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.Seq @ V0)) @ (cPredicate.pred_of_seq @ (V0 @ cProduct_Type.Unity))))))
(TPredicate.map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.map @ V0) @ V1)) @ ((cPredicate.bind @ V1) @ ((cFun.comp @ cPredicate.single) @ V0))))))))
(TPredicate.not_bot,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ V0) @ V2)) @ V1)))) @ V1)))))))
(TPredicate.singleE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ (cPredicate.single @ V0)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ V0)) @ V2)) @ V2)))))))))
(TPredicate.singleI,(call @ (^[V0]: ((cPredicate.eval @ (cPredicate.single @ V0)) @ V0))))
(TPredicate.the_def,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.the @ V0)) @ (cHOL.The @ (^[V1]: ((cPredicate.eval @ V0) @ V1)))))))
(TPredicate.the_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cHOL.The @ (^[V2]: ((cPredicate.eval @ V0) @ V2)))) @ V1)) @ ((cHOL.eq @ (cPredicate.the @ V0)) @ V1)))))))
(TPure.conjunctionI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ V1) @ ((cPure.conjunction @ V0) @ V1))))))))
(TPure.protect_cong,(call @ (^[V0]: ((c== @ (cprop @ V0)) @ (cprop @ V0)))))
(TQuotient.Babs_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ (((cQuotient.Babs @ V1) @ V2) @ V0)) @ (V2 @ V0))))))))))
(TQuotient.babs_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cFun.map_fun @ V2) @ V4) @ ((cQuotient.Babs @ (cLifting.Respects @ V0)) @ (((cFun.map_fun @ V1) @ V5) @ V6)))) @ V6))))))))))))))))))
(TQuotient.babs_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((((cTransfer.fun_rel @ V0) @ V3) @ V4) @ V5)) @ ((((cTransfer.fun_rel @ V0) @ V3) @ ((cQuotient.Babs @ (cLifting.Respects @ V0)) @ V4)) @ ((cQuotient.Babs @ (cLifting.Respects @ V0)) @ V5)))))))))))))))))
(TQuotient.ball_reg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ V3) @ V0)) @ ((cHOL.implies @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((c==> @ ((cSet.Ball @ V0) @ V1)) @ ((cSet.Ball @ V0) @ V2))))))))))
(TQuotient.ball_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((((cTransfer.fun_rel @ V0) @ cHOL.eq) @ V1) @ V2)) @ ((cHOL.eq @ ((cSet.Ball @ (cLifting.Respects @ V0)) @ V1)) @ ((cSet.Ball @ (cLifting.Respects @ V0)) @ V2))))))))))
(TQuotient.bex1_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((((cTransfer.fun_rel @ V0) @ cHOL.eq) @ V1) @ V2)) @ ((cHOL.eq @ (cHOL.Ex1 @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ (cLifting.Respects @ V0))) @ (V1 @ V3))))) @ (cHOL.Ex1 @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ (cLifting.Respects @ V0))) @ (V2 @ V3)))))))))))))
(TQuotient.cond_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (V1 @ (((cHOL.If @ V3) @ (V2 @ V4)) @ (V2 @ V5)))) @ (((cHOL.If @ V3) @ V4) @ V5))))))))))))))))
(TRandom.log.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3)))) @ ((V0 @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TRandom.log.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cRandom.log @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cRandom.log_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ ((cRandom.log @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))) @ ((c==> @ ((cWellfounded.accp @ cRandom.log_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TRandom.log.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cRandom.log_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cRandom.log @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V0))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ ((cRandom.log @ V0) @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ V0)))))))))))
(TRandom.next.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRandom.next @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.Let @ ((cCode_Numeral.div_natural_inst.div_natural @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (^[V2]: ((cHOL.Let @ (((cRandom.minus_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ ((cCode_Numeral.div_natural_inst.mod_natural @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))))) @ (^[V3]: ((cHOL.Let @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (^[V4]: ((cHOL.Let @ (((cRandom.minus_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ ((cCode_Numeral.div_natural_inst.mod_natural @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))))) @ ((cCode_Numeral.times_natural_inst.times_natural @ V4) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))))))) @ (^[V5]: ((cHOL.Let @ ((cCode_Numeral.plus_natural_inst.plus_natural @ (((cRandom.minus_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ V3) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ cCode_Numeral.one_natural_inst.one_natural)) @ (^[V6]: ((cProduct_Type.Pair @ V6) @ ((cProduct_Type.Pair @ V3) @ V5))))))))))))))))))
(TRandom.pick.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRandom.pick @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ (cProduct_Type.fst @ V0))) @ (cProduct_Type.snd @ V0)) @ ((cRandom.pick @ V1) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ (cProduct_Type.fst @ V0))))))))))))
(TRandom.select_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom.select @ V0)) @ ((cProduct_Type.scomp @ (cRandom.range @ (cCode_Numeral.natural_of_nat @ (cNat.size_class.size @ V0)))) @ (^[V1]: (cProduct_Type.Pair @ ((cList.nth @ V0) @ (cCode_Numeral.nat_of_natural @ V1)))))))))
(TRecord.abst.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRecord.abst @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1))) @ V1))))))
(TRecord.prop_subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (V2 @ V1)) @ (V2 @ V0))))))))))
(TRecord.repr.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRecord.repr @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1))) @ V0))))))
(TRelation.DomainPI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cRelation.Domainp @ V0) @ V1)))))))))
(TRelation.DomainpE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Domainp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V3)) @ V2)))) @ V2)))))))))
(TRelation.Field_Un,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.Field @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cRelation.Field @ V0)) @ (cRelation.Field @ V1))))))))
(TRelation.Image_Id,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.Image @ cRelation.Id) @ V0)) @ V0))))
(TRelation.Image_UN,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.Image @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cRelation.Image @ V0) @ (V2 @ V3))))))))))))
(TRelation.Image_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.Image @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cRelation.Image @ V0) @ V1)) @ ((cRelation.Image @ V0) @ V2))))))))))
(TRelation.Powp_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Powp @ V0)) @ (^[V1]: ((cSet.Ball @ V1) @ (^[V2]: (V0 @ V2))))))))
(TRelation.Range_Id,((cHOL.eq @ (cRelation.Range @ cRelation.Id)) @ cOrderings.top_class.top))
(TRelation.Un_Image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.Image @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cRelation.Image @ V0) @ V2)) @ ((cRelation.Image @ V1) @ V2))))))))))
(TRelation.antisymD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRelation.antisym @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0)) @ ((cHOL.eq @ V1) @ V2)))))))))))
(TRelation.antisymI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0)) @ ((cHOL.eq @ V1) @ V2)))))))) @ (cRelation.antisym @ V0)))))
(TRelation.refl_onD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V2)) @ V1))))))))))
(TRelation.refl_onI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V2]: V1)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V2)) @ V0))))) @ ((cRelation.refl_on @ V1) @ V0))))))))
(TRelation.relcompE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cRelation.relcomp @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V6))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ V3)))))))))) @ V3)))))))))))
(TRelation.symp_INF,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cRelation.symp @ (V1 @ V2))))) @ (cRelation.symp @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1))))))))
(TRelation.symp_SUP,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cRelation.symp @ (V1 @ V2))))) @ (cRelation.symp @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))))))))
(TRelation.symp_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.symp @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TRelation.symp_inf,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ (cRelation.symp @ V1)) @ (cRelation.symp @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TRelation.symp_sup,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ (cRelation.symp @ V1)) @ (cRelation.symp @ ((cLattices.sup_class.sup @ V0) @ V1)))))))))
(TRelation.trans_Id,(cRelation.trans @ cRelation.Id))
(TRings.dvd.dvd_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V2) @ ((V0 @ V1) @ V3))))))))))))
(TSMT.pattern.cases,(call @ (^[V0]: ((cHOL.eq @ ((cSMT.pattern.pattern_case @ V0) @ cSMT.pattern.Pattern)) @ V0))))
(TSMT.pattern.simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cSMT.pattern.pattern_rec @ V0) @ cSMT.pattern.Pattern)) @ V0))))
(TSMT.pattern.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cSMT.pattern.pattern_case @ V0) @ cSMT.pattern.Pattern)) @ V0))))
(TSMT.pattern.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cSMT.pattern.pattern_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cSMT.pattern.Pattern)) @ (V0 @ V1))))))))))
(TSMT.term_true_def,((cHOL.eq @ cSMT.term_true) @ cHOL.True))
(TSet.Collect_const,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: V0))) @ (((cHOL.If @ V0) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot)))))
(TSet.Compl_Diff_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cGroups.uminus_class.uminus @ V0)) @ V1)))))))
(TSet.Compl_UNIV_eq,((cHOL.eq @ (cGroups.uminus_class.uminus @ cOrderings.top_class.top)) @ cOrderings.bot_class.bot))
(TSet.Diff_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ cOrderings.bot_class.bot))))))
(TSet.Int_UNIV_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ cOrderings.top_class.top) @ V0)) @ V0))))
(TSet.Pow_not_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cSet.Pow @ V0)) @ cOrderings.bot_class.bot)))))
(TSet.Un_Pow_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (cSet.Pow @ V0)) @ (cSet.Pow @ V1))) @ (cSet.Pow @ ((cLattices.sup_class.sup @ V0) @ V1))))))))
(TSet.Un_UNIV_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))))
(TSet.Un_empty_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ cOrderings.bot_class.bot) @ V0)) @ V0))))
(TSet.Un_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TSet.empty_subsetI,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cOrderings.bot_class.bot) @ V0))))
(TSet.eqset_imp_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.equal_set_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TSet.image_Collect,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ V0) @ (cSet.Collect @ (^[V2]: (V1 @ V2))))) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (V0 @ V3))) @ (V1 @ V3))))))))))))
(TSet.image_subsetI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ (V1 @ V3)) @ V2))))) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V1) @ V0)) @ V2)))))))))
(TSet.insert_absorb,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ V1)))))))
(TSet.insert_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ ((cSet.insert @ V2) @ V3))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3)) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cSet.insert @ V2) @ V4))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V2) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cSet.insert @ V0) @ V4))) @ (cHOL.Not @ ((cSet.member @ V0) @ V4))))))))))))))))))))
(TSet.insert_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet.insert @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cSet.member @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TSet.member_filter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.filter @ V1) @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V2)) @ (V1 @ V0))))))))))
(TSet.member_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.remove @ V1) @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V2)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))))
(TSet.minus_set_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (cSet.Collect @ ((cGroups.minus_class.minus @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1))))))))))
(TSet.psubset_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.rev_image_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ (V3 @ V0))) @ ((cSet.member @ V2) @ ((cSet.image @ V3) @ V1)))))))))))))
(TSet.set_eq_subset,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TSet.singleton_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet.split_if_mem1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ (((cHOL.If @ V0) @ V1) @ V2)) @ V3)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ ((cSet.member @ V1) @ V3))) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ ((cSet.member @ V2) @ V3)))))))))))))
(TSet.split_if_mem2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ V0) @ (((cHOL.If @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ V1) @ ((cSet.member @ V0) @ V2))) @ ((cHOL.implies @ (cHOL.Not @ V1)) @ ((cSet.member @ V0) @ V3)))))))))))))
(TSet.subset_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ ((cSet.insert @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TSet.vimage_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cSet.vimage @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet.vimage @ V0) @ V2))))))))))
(TString.char.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cString.char.char_case @ V0) @ ((cString.char.Char @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TString.char.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cString.char.char_rec @ V0) @ ((cString.char.Char @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TString.char.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cString.char.char_case @ V0) @ ((cString.char.Char @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TString.char.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cString.char.Char @ V0) @ V1)) @ ((cString.char.Char @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TString.char.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cString.char.char_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cString.char.Char @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TSum_Type.Inl_RepI,(call @ (^[V0]: ((cSet.member @ (cSum_Type.Inl_Rep @ V0)) @ cSum_Type.sum))))
(TSum_Type.Inr_RepI,(call @ (^[V0]: ((cSet.member @ (cSum_Type.Inr_Rep @ V0)) @ cSum_Type.sum))))
(TSum_Type.Plus_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSum_Type.Plus @ V0) @ V1)) @ ((cLattices.sup_class.sup @ ((cSet.image @ cSum_Type.Inl) @ V0)) @ ((cSet.image @ cSum_Type.Inr) @ V1))))))))
(TSum_Type.Suml_def,((c== @ cSum_Type.Suml) @ (^[V0]: (^[V1]: ((((cSum_Type.sum.sum_rec @ (^[V2]: (^[V3]: (V3 @ V2)))) @ cHOL.undefined) @ V1) @ V0)))))
(TSum_Type.Sumr_def,((c== @ cSum_Type.Sumr) @ (^[V0]: (^[V1]: ((((cSum_Type.sum.sum_rec @ cHOL.undefined) @ (^[V2]: (^[V3]: (V3 @ V2)))) @ V1) @ V0)))))
(TSum_Type.UNIV_sum,((cHOL.eq @ cOrderings.top_class.top) @ ((cLattices.sup_class.sup @ ((cSet.image @ cSum_Type.Inl) @ cOrderings.top_class.top)) @ ((cSet.image @ cSum_Type.Inr) @ cOrderings.top_class.top))))
(TSum_Type.sum.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_rec @ V0) @ V1) @ (cSum_Type.Inr @ V2))) @ (V1 @ V2)))))))))
(TSum_Type.sum.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_rec @ V0) @ V1) @ (cSum_Type.Inl @ V2))) @ (V0 @ V2)))))))))
(TSum_Type.sum.size_4,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cSum_Type.Inr @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TSum_Type.sum.size_3,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cSum_Type.Inl @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TSum_Type.sum.size_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_size @ V0) @ V1) @ (cSum_Type.Inr @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ (V1 @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TSum_Type.sum.size_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_size @ V0) @ V1) @ (cSum_Type.Inl @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TTransfer.fun_relD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cTransfer.fun_rel @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ (V2 @ V4)) @ (V3 @ V5)))))))))))))))))
(TTransfer.fun_relE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cTransfer.fun_rel @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ ((c==> @ ((V1 @ (V2 @ V4)) @ (V3 @ V5))) @ V6)) @ V6))))))))))))))))))
(TTransfer.fun_relI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ (V2 @ V4)) @ (V3 @ V5)))))))) @ ((((cTransfer.fun_rel @ V0) @ V1) @ V2) @ V3)))))))))))
(TWellfounded.accpI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((V0 @ V2) @ V1)) @ ((cWellfounded.accp @ V0) @ V2))))) @ ((cWellfounded.accp @ V0) @ V1)))))))
(TWellfounded.wf_UN,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cWellfounded.wf @ (V1 @ V2))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ (V1 @ V2)) @ (V1 @ V3)))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cRelation.Domain @ (V1 @ V2))) @ (cRelation.Range @ (V1 @ V3)))) @ cOrderings.bot_class.bot))))))) @ (cWellfounded.wf @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2)))))))))))
(TWellfounded.wf_Un,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (cWellfounded.wf @ V1)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cRelation.Domain @ V0)) @ (cRelation.Range @ V1))) @ cOrderings.bot_class.bot)) @ (cWellfounded.wf @ ((cLattices.sup_class.sup @ V0) @ V1))))))))))
(TATP.fimplies_table_3,((cHOL.eq @ ((cATP.fimplies @ cATP.fTrue) @ cATP.fFalse)) @ cATP.fFalse))
(TATP.fimplies_table_2,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fimplies @ cATP.fFalse) @ V0)) @ cATP.fTrue))))
(TATP.fimplies_table_1,(call @ (^[V0]: ((cHOL.eq @ ((cATP.fimplies @ V0) @ cATP.fTrue)) @ cATP.fTrue))))
(TDatatype.Node_K0_I,(call @ (^[V0]: ((cSet.member @ ((cProduct_Type.Pair @ (^[V1]: (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat))) @ V0)) @ cDatatype.Node))))
(TDatatype.Scons_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cDatatype.Scons @ V0) @ V1)) @ ((cLattices.sup_class.sup @ ((cSet.image @ (cDatatype.Push_Node @ (cSum_Type.Inr @ cNat.one_nat_inst.one_nat))) @ V0)) @ ((cSet.image @ (cDatatype.Push_Node @ (cSum_Type.Inr @ (cNat.Suc @ cNat.one_nat_inst.one_nat)))) @ V1))))))))
(TDatatype.Split_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cDatatype.Split @ V0) @ V1)) @ (cHOL.The @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cDatatype.Scons @ V3) @ V4))) @ ((cHOL.eq @ V2) @ ((V0 @ V3) @ V4)))))))))))))))
(TDatatype.dprod_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cDatatype.dprod @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cSet.insert @ ((cProduct_Type.Pair @ ((cDatatype.Scons @ V2) @ V4)) @ ((cDatatype.Scons @ V3) @ V5))) @ cOrderings.bot_class.bot)))))))))))))))
(TDatatype.dsum_In0I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ (cDatatype.In0 @ V0)) @ (cDatatype.In0 @ V1))) @ ((cDatatype.dsum @ V2) @ V3))))))))))))
(TDatatype.dsum_In1I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ (cDatatype.In1 @ V0)) @ (cDatatype.In1 @ V1))) @ ((cDatatype.dsum @ V3) @ V2))))))))))))
(TDatatype.dsum_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cDatatype.dsum @ V0) @ V2)) @ ((cDatatype.dsum @ V1) @ V3)))))))))))))
(TDatatype.ndepth_K0,(call @ (^[V0]: ((cHOL.eq @ (cDatatype.ndepth @ (cDatatype.Abs_Node @ ((cProduct_Type.Pair @ (^[V1]: (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat))) @ V0)))) @ cNat.zero_nat_inst.zero_nat))))
(TDatatype.uprod_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cDatatype.uprod @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cSet.insert @ ((cDatatype.Scons @ V2) @ V3)) @ cOrderings.bot_class.bot)))))))))))
(TDatatype.usum_In0I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ (cDatatype.In0 @ V0)) @ ((cDatatype.usum @ V1) @ V2))))))))))
(TDatatype.usum_In1I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ (cDatatype.In1 @ V0)) @ ((cDatatype.usum @ V2) @ V1))))))))))
(TDatatype.usum_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cDatatype.usum @ V0) @ V2)) @ ((cDatatype.usum @ V1) @ V3)))))))))))))
(TDivides.adjust_def,(call @ (^[V0]: ((cHOL.eq @ (cDivides.adjust @ V0)) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.minus_int_inst.minus_int @ V2) @ V0))) @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)) @ cInt.one_int_inst.one_int)) @ ((cInt.minus_int_inst.minus_int @ V2) @ V0))) @ ((cProduct_Type.Pair @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)) @ V2)))))))))
(TDivides.le_div_geq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V1) @ V0)) @ (cNat.Suc @ ((cDivides.div_nat_inst.div_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V0))))))))))
(TDivides.le_mod_geq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0)) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V0))))))))
(TDivides.mod_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V4) @ V0)) @ ((cHOL.implies @ (V1 @ V4)) @ (V1 @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ V4)) @ V0))))))) @ ((c==> @ (V1 @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ (V1 @ V3))))))))))))))
(TDivides.split_div',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cDivides.div_nat_inst.div_nat @ V1) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ (V0 @ cNat.zero_nat_inst.zero_nat))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V3)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V1) @ ((cNat.times_nat_inst.times_nat @ V2) @ (cNat.Suc @ V3))))) @ (V0 @ V3)))))))))))))
(TDivides.split_zdiv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cDivides.div_int_inst.div_int @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cInt.zero_int_inst.zero_int)) @ (V0 @ cInt.zero_int_inst.zero_int))) @ ((cHOL.conj @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V2)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V4) @ V2)) @ ((cHOL.eq @ V1) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V2) @ V3)) @ V4))))) @ (V0 @ V3)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V2) @ V4)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V1) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V2) @ V3)) @ V4))))) @ (V0 @ V3)))))))))))))))))
(TDivides.split_zmod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cDivides.div_int_inst.mod_int @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cInt.zero_int_inst.zero_int)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V2)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V4) @ V2)) @ ((cHOL.eq @ V1) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V2) @ V3)) @ V4))))) @ (V0 @ V4)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V2) @ V4)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V1) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V2) @ V3)) @ V4))))) @ (V0 @ V4)))))))))))))))))
(TDivides.zdiv_mono1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.div_int @ V0) @ V2)) @ ((cDivides.div_int_inst.div_int @ V1) @ V2)))))))))))
(TDivides.zdiv_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.div_int @ V0) @ V2)) @ ((cDivides.div_int_inst.div_int @ V0) @ V1))))))))))))
(TDivides.zmod_eq_0D,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cInt.times_int_inst.times_int @ V1) @ V2))))))))))
(TDivides.zmod_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ V0) @ ((cDivides.div_int_inst.mod_int @ V1) @ V2))) @ V2)) @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ V0) @ V1)) @ V2)))))))))
(TDivides.zmod_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V2)) @ V1)) @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ V0) @ V2)) @ V1)))))))))
(TDivides.zmod_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cInt.uminus_int_inst.uminus_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))) @ V1)) @ ((cDivides.div_int_inst.mod_int @ (cInt.uminus_int_inst.uminus_int @ V0)) @ V1)))))))
(TDivides.zmod_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cPower.power_class.power @ ((cDivides.div_class.mod @ V0) @ V1)) @ V2)) @ V1)) @ ((cDivides.div_class.mod @ ((cPower.power_class.power @ V0) @ V2)) @ V1)))))))))
(TDivides.zmod_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ ((cDivides.div_class.mod @ V0) @ V1)) @ V2)) @ V1)) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)))))))))
(TDivides.zmod_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)))))))))
(TDivides.zmod_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)))))))))
(TDivides.zmod_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ ((cDivides.div_class.mod @ V0) @ V1)) @ V2)) @ V1)) @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TEnum.UNIV_finite_1,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cEnum.finite_1.a\<__caret__sub>1) @ cOrderings.bot_class.bot)))
(TEnum.UNIV_finite_2,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cEnum.finite_2.a\<__caret__sub>1) @ ((cSet.insert @ cEnum.finite_2.a\<__caret__sub>2) @ cOrderings.bot_class.bot))))
(TEnum.UNIV_finite_3,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cEnum.finite_3.a\<__caret__sub>1) @ ((cSet.insert @ cEnum.finite_3.a\<__caret__sub>2) @ ((cSet.insert @ cEnum.finite_3.a\<__caret__sub>3) @ cOrderings.bot_class.bot)))))
(TEnum.UNIV_finite_4,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cEnum.finite_4.a\<__caret__sub>1) @ ((cSet.insert @ cEnum.finite_4.a\<__caret__sub>2) @ ((cSet.insert @ cEnum.finite_4.a\<__caret__sub>3) @ ((cSet.insert @ cEnum.finite_4.a\<__caret__sub>4) @ cOrderings.bot_class.bot))))))
(TEnum.UNIV_finite_5,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cEnum.finite_5.a\<__caret__sub>1) @ ((cSet.insert @ cEnum.finite_5.a\<__caret__sub>2) @ ((cSet.insert @ cEnum.finite_5.a\<__caret__sub>3) @ ((cSet.insert @ cEnum.finite_5.a\<__caret__sub>4) @ ((cSet.insert @ cEnum.finite_5.a\<__caret__sub>5) @ cOrderings.bot_class.bot)))))))
(TEnum.card_UNIV_def,((cHOL.eq @ (cEnum.card_UNIV @ cTYPE)) @ (cFinite_Set.card @ cOrderings.top_class.top)))
(TEnum.enum.enum_all,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.eq @ V1) @ cHOL.All)))))))))
(TEnum.enum_bool_def,((cHOL.eq @ cEnum.enum_bool_inst.enum_bool) @ ((cList.list.Cons @ cHOL.False) @ ((cList.list.Cons @ cHOL.True) @ cList.list.Nil))))
(TEnum.enum_fun_code,((cHOL.eq @ cEnum.enum_class.enum) @ ((cHOL.Let @ cEnum.enum_class.enum) @ (^[V0]: ((cList.map @ (^[V1]: ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ V0) @ V1))))) @ ((cList.n_lists @ (cNat.size_class.size @ V0)) @ cEnum.enum_class.enum))))))
(TEnum.enum_prod_def,((cHOL.eq @ cEnum.enum_class.enum) @ ((cList.product @ cEnum.enum_class.enum) @ cEnum.enum_class.enum)))
(TEnum.enum_unit_def,((cHOL.eq @ cEnum.enum_unit_inst.enum_unit) @ ((cList.list.Cons @ cProduct_Type.Unity) @ cList.list.Nil)))
(TEnum.equal_fun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cSet.Ball @ (cList.set @ cEnum.enum_class.enum)) @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TEnum.finite_1.recs,(call @ (^[V0]: ((cHOL.eq @ ((cEnum.finite_1.finite_1_rec @ V0) @ cEnum.finite_1.a\<__caret__sub>1)) @ V0))))
(TEnum.finite_1.size_2,((cHOL.eq @ (cEnum.finite_1.size_finite_1_inst.size_finite_1 @ cEnum.finite_1.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_1.size_1,((cHOL.eq @ (cEnum.finite_1.finite_1_size @ cEnum.finite_1.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_2.recs_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_rec @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>2)) @ V1))))))
(TEnum.finite_2.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_rec @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>1)) @ V0))))))
(TEnum.finite_2.size_4,((cHOL.eq @ (cEnum.finite_2.size_finite_2_inst.size_finite_2 @ cEnum.finite_2.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_2.size_3,((cHOL.eq @ (cEnum.finite_2.size_finite_2_inst.size_finite_2 @ cEnum.finite_2.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_2.size_2,((cHOL.eq @ (cEnum.finite_2.finite_2_size @ cEnum.finite_2.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_2.size_1,((cHOL.eq @ (cEnum.finite_2.finite_2_size @ cEnum.finite_2.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_3.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_rec @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>3)) @ V2))))))))
(TEnum.finite_3.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_rec @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>2)) @ V1))))))))
(TEnum.finite_3.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_rec @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>1)) @ V0))))))))
(TEnum.finite_3.size_6,((cHOL.eq @ (cEnum.finite_3.size_finite_3_inst.size_finite_3 @ cEnum.finite_3.a\<__caret__sub>3)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_3.size_5,((cHOL.eq @ (cEnum.finite_3.size_finite_3_inst.size_finite_3 @ cEnum.finite_3.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_3.size_4,((cHOL.eq @ (cEnum.finite_3.size_finite_3_inst.size_finite_3 @ cEnum.finite_3.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_3.size_3,((cHOL.eq @ (cEnum.finite_3.finite_3_size @ cEnum.finite_3.a\<__caret__sub>3)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_3.size_2,((cHOL.eq @ (cEnum.finite_3.finite_3_size @ cEnum.finite_3.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_3.size_1,((cHOL.eq @ (cEnum.finite_3.finite_3_size @ cEnum.finite_3.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.recs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>4)) @ V3))))))))))
(TEnum.finite_4.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>3)) @ V2))))))))))
(TEnum.finite_4.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>2)) @ V1))))))))))
(TEnum.finite_4.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>1)) @ V0))))))))))
(TEnum.finite_4.size_8,((cHOL.eq @ (cEnum.finite_4.size_finite_4_inst.size_finite_4 @ cEnum.finite_4.a\<__caret__sub>4)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.size_7,((cHOL.eq @ (cEnum.finite_4.size_finite_4_inst.size_finite_4 @ cEnum.finite_4.a\<__caret__sub>3)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.size_6,((cHOL.eq @ (cEnum.finite_4.size_finite_4_inst.size_finite_4 @ cEnum.finite_4.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.size_5,((cHOL.eq @ (cEnum.finite_4.size_finite_4_inst.size_finite_4 @ cEnum.finite_4.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.size_4,((cHOL.eq @ (cEnum.finite_4.finite_4_size @ cEnum.finite_4.a\<__caret__sub>4)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.size_3,((cHOL.eq @ (cEnum.finite_4.finite_4_size @ cEnum.finite_4.a\<__caret__sub>3)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.size_2,((cHOL.eq @ (cEnum.finite_4.finite_4_size @ cEnum.finite_4.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_4.size_1,((cHOL.eq @ (cEnum.finite_4.finite_4_size @ cEnum.finite_4.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.recs_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>5)) @ V4))))))))))))
(TEnum.finite_5.recs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>4)) @ V3))))))))))))
(TEnum.finite_5.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>3)) @ V2))))))))))))
(TEnum.finite_5.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>2)) @ V1))))))))))))
(TEnum.finite_5.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>1)) @ V0))))))))))))
(TEnum.finite_5.size_10,((cHOL.eq @ (cEnum.finite_5.size_finite_5_inst.size_finite_5 @ cEnum.finite_5.a\<__caret__sub>5)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_9,((cHOL.eq @ (cEnum.finite_5.size_finite_5_inst.size_finite_5 @ cEnum.finite_5.a\<__caret__sub>4)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_8,((cHOL.eq @ (cEnum.finite_5.size_finite_5_inst.size_finite_5 @ cEnum.finite_5.a\<__caret__sub>3)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_7,((cHOL.eq @ (cEnum.finite_5.size_finite_5_inst.size_finite_5 @ cEnum.finite_5.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_6,((cHOL.eq @ (cEnum.finite_5.size_finite_5_inst.size_finite_5 @ cEnum.finite_5.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_5,((cHOL.eq @ (cEnum.finite_5.finite_5_size @ cEnum.finite_5.a\<__caret__sub>5)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_4,((cHOL.eq @ (cEnum.finite_5.finite_5_size @ cEnum.finite_5.a\<__caret__sub>4)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_3,((cHOL.eq @ (cEnum.finite_5.finite_5_size @ cEnum.finite_5.a\<__caret__sub>3)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_2,((cHOL.eq @ (cEnum.finite_5.finite_5_size @ cEnum.finite_5.a\<__caret__sub>2)) @ cNat.zero_nat_inst.zero_nat))
(TEnum.finite_5.size_1,((cHOL.eq @ (cEnum.finite_5.finite_5_size @ cEnum.finite_5.a\<__caret__sub>1)) @ cNat.zero_nat_inst.zero_nat))
(TFun.bij_betw_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((c==> @ (((cFun.bij_betw @ V3) @ V2) @ V4)) @ (((cFun.bij_betw @ ((cFun.comp @ V3) @ V0)) @ V1) @ V4))))))))))))))
(TFun.image_set_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2)))))))))))
(TFun.inj_on_contraD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ (V0 @ V2)) @ (V0 @ V3))))))))))))))))
(TFun.inj_on_imageI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cFun.inj_on @ V1) @ V2)))))))))
(TFun.swap_nilpotent,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.swap @ V0) @ V1) @ (((cFun.swap @ V0) @ V1) @ V2))) @ V2))))))))
(TFun.vimage_compose,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cSet.vimage @ V1) @ ((cSet.vimage @ V0) @ V2))))))))))
(TFun.vimage_subsetD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.vimage @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cSet.image @ V0) @ V2)))))))))))
(TFun.vimage_subsetI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cSet.image @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ ((cSet.vimage @ V0) @ V1)) @ V2))))))))))
(TFunDef.measure_fst,(call @ (^[V0]: ((c==> @ (cFunDef.is_measure @ V0)) @ (cFunDef.is_measure @ (^[V1]: (V0 @ (cProduct_Type.fst @ V1))))))))
(TFunDef.measure_snd,(call @ (^[V0]: ((c==> @ (cFunDef.is_measure @ V0)) @ (cFunDef.is_measure @ (^[V1]: (V0 @ (cProduct_Type.snd @ V1))))))))
(TFunDef.pair_lessI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V2)) @ ((cProduct_Type.Pair @ V1) @ V3))) @ cFunDef.pair_less)))))))))))
(TFunDef.pair_lessI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V2)) @ ((cProduct_Type.Pair @ V1) @ V3))) @ cFunDef.pair_less))))))))))))
(TFunDef.smax_emptyI,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cSet.member @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ V0)) @ cFunDef.max_strict))))))
(TFunDef.smin_emptyI,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ cOrderings.bot_class.bot)) @ cFunDef.min_strict)))))
(TFunDef.wmax_emptyI,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ V0)) @ cFunDef.max_weak)))))
(TFunDef.wmin_emptyI,(call @ (^[V0]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ cOrderings.bot_class.bot)) @ cFunDef.min_weak))))
(TGroebner_Basis.dnf_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ V1) @ V0)))))))
(TGroebner_Basis.dnf_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V1) @ V0)))))))
(TGroebner_Basis.dnf_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ ((cHOL.disj @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V2))))))))))
(TGroebner_Basis.dnf_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V2))))))))))
(TGroups.sgn_if.sgn0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cGroups.class.sgn_if @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ (V1 @ V3)) @ V3)))))))))))))
(THOL.False_neq_True,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ cHOL.False) @ cHOL.True)) @ V0))))
(THOL.False_not_True,(cHOL.Not @ ((cHOL.eq @ cHOL.False) @ cHOL.True)))
(THOL.True_not_False,(cHOL.Not @ ((cHOL.eq @ cHOL.True) @ cHOL.False)))
(THOL.arity_type_fun,(cHOL.type_class @ cTYPE))
(THOL.conj_left_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V2))))))))))
(THOL.de_Morgan_conj,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(THOL.de_Morgan_disj,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(THOL.disj_left_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.disj @ V0) @ V2)) @ ((cHOL.disj @ V1) @ V2))))))))))
(THOL.equal.eq_equal,(call @ (^[V0]: ((c==> @ (cHOL.class.equal @ V0)) @ ((c== @ cHOL.eq) @ V0)))))
(THOL.equal.equal_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.class.equal @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((cHOL.eq @ V1) @ V2))))))))))
(THOL.ex1_implies_ex,(call @ (^[V0]: ((c==> @ (cHOL.Ex1 @ (^[V1]: (V0 @ V1)))) @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))))))
(THOL.induct_atomize_4,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c== @ V0) @ V1)) @ ((cHOL.induct_equal @ V0) @ V1)))))))
(THOL.induct_atomize_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPure.conjunction @ V0) @ V1)) @ ((cHOL.induct_conj @ V0) @ V1)))))))
(THOL.induct_atomize_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c==> @ V0) @ V1)) @ ((cHOL.induct_implies @ V0) @ V1)))))))
(THOL.induct_atomize_1,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (cHOL.induct_forall @ (^[V1]: (V0 @ V1)))))))
(THOL.induct_conj_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPure.conjunction @ V0) @ V1)) @ ((cHOL.induct_conj @ V0) @ V1)))))))
(THOL.induct_rulify'_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_conj @ V0) @ V1)) @ ((cPure.conjunction @ V0) @ V1)))))))
(THOL.induct_rulify'_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_implies @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(THOL.induct_rulify'_1,(call @ (^[V0]: ((c== @ (cHOL.induct_forall @ (^[V1]: (V0 @ V1)))) @ (call @ (^[V1]: (V0 @ V1)))))))
(THOL.the_eq_trivial,(call @ (^[V0]: ((cHOL.eq @ (cHOL.The @ (^[V1]: ((cHOL.eq @ V1) @ V0)))) @ V0))))
(TInductive.coinduct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ (V0 @ ((cLattices.sup_class.sup @ V1) @ (cInductive.complete_lattice_class.gfp @ V0))))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cInductive.complete_lattice_class.gfp @ V0)))))))))
(TInductive.gfp_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.gfp @ V0)) @ (cInductive.complete_lattice_class.gfp @ V1))))))))
(TInductive.lfp_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ (cInductive.complete_lattice_class.lfp @ V1))))))))
(TInt.abs_zmult_eq_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ ((cInt.times_int_inst.times_int @ V0) @ V1))) @ cInt.one_int_inst.one_int)) @ ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ V0)) @ cInt.one_int_inst.one_int)))))))
(TInt.arity_type_int,(cHOL.type_class @ cTYPE))
(TInt.diff_nat_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ (cInt.nat @ V0)) @ ((cHOL.Let @ ((cInt.minus_int_inst.minus_int @ V0) @ V1)) @ (^[V2]: (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int)) @ cNat.zero_nat_inst.zero_nat) @ (cInt.nat @ V2)))))))))))
(TInt.dvd_imp_le_int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ (cInt.abs_int_inst.abs_int @ V1)) @ (cInt.abs_int_inst.abs_int @ V0)))))))))
(TInt.eq_nat_nat_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TInt.equal_int_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cInt.Neg @ V0)) @ (cInt.Neg @ V1))) @ ((cHOL.equal_class.equal @ V0) @ V1)))))))
(TInt.equal_int_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cInt.Neg @ V0)) @ (cInt.Pos @ V1))) @ cHOL.False))))))
(TInt.equal_int_code_7,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cInt.Neg @ V0)) @ cInt.zero_int_inst.zero_int)) @ cHOL.False))))
(TInt.equal_int_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cInt.Pos @ V0)) @ (cInt.Neg @ V1))) @ cHOL.False))))))
(TInt.equal_int_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cInt.Pos @ V0)) @ (cInt.Pos @ V1))) @ ((cHOL.equal_class.equal @ V0) @ V1)))))))
(TInt.equal_int_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cInt.Pos @ V0)) @ cInt.zero_int_inst.zero_int)) @ cHOL.False))))
(TInt.equal_int_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ cInt.zero_int_inst.zero_int) @ (cInt.Neg @ V0))) @ cHOL.False))))
(TInt.equal_int_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ cInt.zero_int_inst.zero_int) @ (cInt.Pos @ V0))) @ cHOL.False))))
(TInt.equal_int_code_1,((cHOL.eq @ ((cHOL.equal_class.equal @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)) @ cHOL.True))
(TInt.equal_int_refl,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TInt.int.abs_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cInt.Abs_Integ @ V0)) @ (cInt.Abs_Integ @ V1))) @ ((cInt.intrel @ V0) @ V1)))))))
(TInt.int.abs_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cInt.Abs_Integ @ V2))))) @ (V0 @ V1)))))))
(TInt.int_diff_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cInt.minus_int_inst.minus_int @ (cNat.semiring_1_class.of_nat @ V2)) @ (cNat.semiring_1_class.of_nat @ V3)))) @ V1)))))) @ V1))))))
(TInt.le_minus_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cGroups.uminus_class.uminus @ V0))) @ ((cOrderings.ord_class.less_eq @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))))))
(TInt.minus_int_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ (cInt.Neg @ V0)) @ (cInt.Neg @ V1))) @ ((cInt.sub @ V1) @ V0)))))))
(TInt.minus_int_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ (cInt.Neg @ V0)) @ (cInt.Pos @ V1))) @ (cInt.Neg @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TInt.minus_int_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ (cInt.Pos @ V0)) @ (cInt.Neg @ V1))) @ (cInt.Pos @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TInt.minus_int_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ (cInt.Pos @ V0)) @ (cInt.Pos @ V1))) @ ((cInt.sub @ V0) @ V1)))))))
(TInt.minus_int_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V0)))))
(TInt.minus_int_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.zero_int_inst.zero_int)) @ V0))))
(TInt.minus_le_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)))))
(TInt.nat_zminus_int,(call @ (^[V0]: ((cHOL.eq @ (cInt.nat @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ V0)))) @ cNat.zero_nat_inst.zero_nat))))
(TInt.negative_zle_0,(call @ (^[V0]: ((cInt.ord_int_inst.less_eq_int @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ V0))) @ cInt.zero_int_inst.zero_int))))
(TInt.negative_zless,(call @ (^[V0]: (call @ (^[V1]: ((cInt.ord_int_inst.less_int @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V0)))) @ (cNat.semiring_1_class.of_nat @ V1)))))))
(TInt.numeral_1_eq_1,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ cGroups.one_class.one))
(TInt.odd_less_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ ((cInt.plus_int_inst.plus_int @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ V0)) @ V0)) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)))))
(TInt.of_int_setprod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (cInt.ring_1_class.of_int @ (V0 @ V2)))) @ V1)))))))
(TInt.of_nat_setprod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (cNat.semiring_1_class.of_nat @ (V0 @ V2)))) @ V1)))))))
(TInt.one_int.abs_eq,((cHOL.eq @ cInt.one_int_inst.one_int) @ (cInt.Abs_Integ @ ((cProduct_Type.Pair @ cNat.one_nat_inst.one_nat) @ cNat.zero_nat_inst.zero_nat))))
(TInt.times_int_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cInt.Neg @ V0)) @ (cInt.Neg @ V1))) @ (cInt.Pos @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TInt.times_int_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cInt.Neg @ V0)) @ (cInt.Pos @ V1))) @ (cInt.Neg @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TInt.times_int_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cInt.Pos @ V0)) @ (cInt.Neg @ V1))) @ (cInt.Neg @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TInt.times_int_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cInt.Pos @ V0)) @ (cInt.Pos @ V1))) @ (cInt.Pos @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TInt.times_int_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ cInt.zero_int_inst.zero_int) @ V0)) @ cInt.zero_int_inst.zero_int))))
(TInt.times_int_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ V0) @ cInt.zero_int_inst.zero_int)) @ cInt.zero_int_inst.zero_int))))
(TInt.uminus_int.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ cInt.intrel) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cProduct_Type.Pair @ V1) @ V0))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cProduct_Type.Pair @ V1) @ V0))))))
(TInt.uminus_int_def,((c== @ cInt.uminus_int_inst.uminus_int) @ (((cFun.map_fun @ cInt.Rep_Integ) @ cInt.Abs_Integ) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cProduct_Type.Pair @ V1) @ V0)))))))
(TInt.zdvd_not_zless,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))))
(TInt.zle_add1_eq_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)))))))
(TInt.zless_nat_conj,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_int @ V0) @ V1))))))))
(TInt.zmult_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ cInt.one_int_inst.one_int)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cInt.one_int_inst.one_int)) @ ((cHOL.eq @ V1) @ cInt.one_int_inst.one_int))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))) @ ((cHOL.eq @ V1) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))))))))))
(TLattices.inf_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLattices.inf_class.inf @ V0) @ V1) @ V2)) @ ((cLattices.inf_class.inf @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TLattices.sup_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLattices.sup_class.sup @ V0) @ V1) @ V2)) @ ((cLattices.sup_class.sup @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TLattices.sup_boolE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLattices.sup_bool_inst.sup_bool @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ V2)) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(TLifting.apply_rsp',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cTransfer.fun_rel @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ (V2 @ V4)) @ (V3 @ V5)))))))))))))))))
(TLifting.map_fun_id,((cHOL.eq @ ((cFun.map_fun @ cFun.id) @ cFun.id)) @ cFun.id))
(TLifting.reflp'_def,(call @ (^[V0]: ((c== @ (cLifting.reflp' @ V0)) @ (cRelation.reflp @ V0)))))
(TLifting.reflp_fun1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.is_equality @ V0)) @ ((c==> @ (cLifting.reflp' @ V1)) @ (cRelation.reflp @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TLifting.reflp_fun2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.is_equality @ V0)) @ ((c==> @ (cTransfer.is_equality @ V1)) @ (cRelation.reflp @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TList.Cons_eq_map_D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.map @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (V2 @ V4))) @ ((cHOL.eq @ V1) @ ((cList.map @ V2) @ V5))))))))))))))))))
(TList.Cons_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.list.Cons) @ cList.list.Cons))))
(TList.ListMem.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.ListMem @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ V4))) @ V2))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V5) @ V4))) @ ((c==> @ ((cList.ListMem @ V3) @ V4)) @ V2)))))))))) @ V2))))))))))
(TList.ListMem.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.ListMem @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V2) @ V3)))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V3))) @ ((cList.ListMem @ V2) @ V3))))))))))))))))
(TList.Nil_notin_lex,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ cList.list.Nil) @ V0)) @ (cList.lex @ V1))))))))
(TList.Quotient_list,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((((cLifting.Quotient @ (cList.list_all2 @ V0)) @ (cList.map @ V1)) @ (cList.map @ V2)) @ (cList.list_all2 @ V3))))))))))))
(TList.butlast.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.butlast @ ((cList.list.Cons @ V0) @ V1))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ cList.list.Nil) @ ((cList.list.Cons @ V0) @ (cList.butlast @ V1)))))))))
(TList.butlast.simps_1,((cHOL.eq @ (cList.butlast @ cList.list.Nil)) @ cList.list.Nil))
(TList.card_distinct,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ (cFinite_Set.card @ (cList.set @ V0))) @ (cNat.size_class.size @ V0))) @ (cList.distinct @ V0)))))
(TList.concat_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.concat @ ((cList.append @ V0) @ V1))) @ ((cList.append @ (cList.concat @ V0)) @ (cList.concat @ V1))))))))
(TList.distinct_card,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ (cList.set @ V0))) @ (cNat.size_class.size @ V0))))))
(TList.distinct_drop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.drop @ V1) @ V0))))))))
(TList.distinct_take,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.take @ V1) @ V0))))))))
(TList.distinct_upto,(call @ (^[V0]: (call @ (^[V1]: (cList.distinct @ ((cList.upto @ V0) @ V1)))))))
(TList.drop.drop_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.drop @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.dropWhile_def,((c== @ cList.dropWhile) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ (V5 @ V2)) @ (V4 @ V5)) @ ((cList.list.Cons @ V2) @ V3))))))) @ V1) @ V0)))))
(TList.dropWhile_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.dropWhile @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ V1) @ ((cList.dropWhile @ ((cFun.comp @ V0) @ V1)) @ V2))))))))))
(TList.dropWhile_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ ((cList.dropWhile @ V1) @ V2)))) @ ((cHOL.eq @ ((cList.nth @ ((cList.dropWhile @ V1) @ V2)) @ V0)) @ ((cList.nth @ V2) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ (cNat.size_class.size @ ((cList.takeWhile @ V1) @ V2)))))))))))))
(TList.drop_Suc_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ (cNat.Suc @ V0)) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.drop @ V0) @ V2)))))))))
(TList.drop_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.drop) @ cList.drop))))
(TList.equiv_listrel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((cEquiv_Relations.equiv @ (cList.lists @ V0)) @ (cList.listrel @ V1))))))))
(TList.filter_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.filter @ V0) @ ((cList.append @ V1) @ V2))) @ ((cList.append @ ((cList.filter @ V0) @ V1)) @ ((cList.filter @ V0) @ V2))))))))))
(TList.filter_concat,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.filter @ V0) @ (cList.concat @ V1))) @ (cList.concat @ ((cList.map @ (cList.filter @ V0)) @ V1))))))))
(TList.filter_filter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.filter @ V0) @ ((cList.filter @ V1) @ V2))) @ ((cList.filter @ (^[V3]: ((cHOL.conj @ (V1 @ V3)) @ (V0 @ V3)))) @ V2)))))))))
(TList.find_None_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.find @ V0) @ V1)) @ cOption.option.None)) @ (cHOL.Not @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ (cList.set @ V1))) @ (V0 @ V2)))))))))))
(TList.find_Some_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cList.find @ V0) @ V1)) @ (cOption.option.Some @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V1))) @ ((cHOL.conj @ (V0 @ ((cList.nth @ V1) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.nth @ V1) @ V3))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V4) @ V3)) @ (cHOL.Not @ (V0 @ ((cList.nth @ V1) @ V4)))))))))))))))))))
(TList.find_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cLifting_Option.option_rel @ V0))) @ cList.find) @ cList.find))))
(TList.finite_maxlen,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ (cNat.size_class.size @ V2)) @ V1)))))))))
(TList.fold.fold_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.fold @ V0) @ cList.list.Nil)) @ cFun.id))))
(TList.fold_Cons_rev,(call @ (^[V0]: ((cHOL.eq @ ((cList.fold @ cList.list.Cons) @ V0)) @ (cList.append @ (cList.rev @ V0))))))
(TList.fold_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ V1))) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ V1) @ V1))) @ cList.fold) @ cList.fold))))))
(TList.in_set_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cHOL.eq @ ((cList.insert @ V0) @ V1)) @ V1)))))))
(TList.in_set_member,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cList.member @ V1) @ V0)))))))
(TList.last_conv_nth,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.last @ V0)) @ ((cList.nth @ V0) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat)))))))
(TList.length_0_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.length_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.append @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))
(TList.length_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ (cNat.size_class.size @ V3)) @ (cNat.size_class.size @ V2))) @ (V0 @ V3))))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TList.length_rotate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.rotate @ V0) @ V1))) @ (cNat.size_class.size @ V1)))))))
(TList.length_splice,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.splice @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))
(TList.lexord_linear,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V3) @ V4)) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)))))))) @ ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.lexord @ V0))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ (cList.lexord @ V0))))))))))))
(TList.lexord_transI,(call @ (^[V0]: ((c==> @ (cRelation.trans @ V0)) @ (cRelation.trans @ (cList.lexord @ V0))))))
(TList.list.Cons_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cList.list.Cons @ V0) @ V1)) @ (cList.Abs_list @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V0)) @ (cList.Rep_list @ V1))))))))))
(TList.list.Rep_list,(call @ (^[V0]: ((cSet.member @ (cList.Rep_list @ V0)) @ (cSet.Collect @ cList.list.list_rep_set)))))
(TList.list.distinct_2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ cList.list.Nil)))))))
(TList.list.distinct_1,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cList.list.Nil) @ ((cList.list.Cons @ V0) @ V1))))))))
(TList.list.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cList.list.Nil) @ cList.list.Nil)) @ cHOL.True))
(TList.list.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TList.list.eq.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ cList.list.Nil) @ ((cList.list.Cons @ V0) @ V1))) @ cHOL.False))))))
(TList.list.eq.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ ((cList.list.Cons @ V0) @ V1)) @ cList.list.Nil)) @ cHOL.False))))))
(TList.list.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cList.list.Cons @ V1) @ V2))))))))))
(TList.list_all2_Nil,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ cList.list.Nil) @ V1)) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.list_all2_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))) @ ((cSet.Ball @ (cList.set @ ((cList.zip @ V1) @ V2))) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4))))))))))))))
(TList.list_all2_eq',((cHOL.eq @ (cList.list_all2 @ cHOL.eq)) @ cHOL.eq))
(TList.list_all2_rev,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ (cList.rev @ V1)) @ (cList.rev @ V2))) @ (((cList.list_all2 @ V0) @ V1) @ V2)))))))))
(TList.list_all_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V1))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cList.list_all @ V2) @ V0)) @ ((cList.list_all @ V3) @ V1)))))))))))))
(TList.list_ball_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V3]: (V2 @ V3)))) @ (V2 @ ((cList.nth @ V1) @ V0)))))))))))
(TList.list_ex_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cList.list_ex @ V0) @ cList.list.Nil)) @ cHOL.False))))
(TList.list_ex_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_ex @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cHOL.disj @ (V0 @ V1)) @ ((cList.list_ex @ V0) @ V2))))))))))
(TList.list_induct2',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V0 @ ((cList.list.Cons @ V3) @ V4)) @ cList.list.Nil)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V0 @ cList.list.Nil) @ ((cList.list.Cons @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((V0 @ V4) @ V6)) @ ((V0 @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6)))))))))))) @ ((V0 @ V1) @ V2))))))))))))
(TList.list_size_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list.list_size @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.list.list_size @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TList.listrel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ V3))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ V6))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V5) @ V7))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ (cList.listrel @ V2))) @ V3))))))))))))) @ V3))))))))))))
(TList.listrel.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V6))) @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ (cList.listrel @ V2))))))))))))))))))))))
(TList.listrel1_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.listrel1 @ V0)) @ (cList.listrel1 @ V1))))))))
(TList.listrel1p_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.listrel1p @ V0) @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.listrel1 @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4)))))))))))))))
(TList.listrel_Cons1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ (cList.listrel @ V3))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V5) @ V6))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V5)) @ V3)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V6)) @ (cList.listrel @ V3))) @ V4)))))))) @ V4)))))))))))))
(TList.listrel_Cons2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (cList.listrel @ V3))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V5) @ V6))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ V3)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V2)) @ (cList.listrel @ V3))) @ V4)))))))) @ V4)))))))))))))
(TList.listrel_trans,(call @ (^[V0]: ((c==> @ (cRelation.trans @ V0)) @ (cRelation.trans @ (cList.listrel @ V0))))))
(TList.listrelp.Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ (((cList.listrelp @ V0) @ V3) @ V4)) @ (((cList.listrelp @ V0) @ ((cList.list.Cons @ V1) @ V3)) @ ((cList.list.Cons @ V2) @ V4)))))))))))))))
(TList.lists.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.lists @ V1))) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V3) @ V1)) @ ((c==> @ ((cSet.member @ V4) @ (cList.lists @ V1))) @ ((c==> @ (V2 @ V4)) @ (V2 @ ((cList.list.Cons @ V3) @ V4)))))))))) @ (V2 @ V0)))))))))))
(TList.listset.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.listset @ ((cList.list.Cons @ V0) @ V1))) @ ((cList.set_Cons @ V0) @ (cList.listset @ V1))))))))
(TList.listset.simps_1,((cHOL.eq @ (cList.listset @ cList.list.Nil)) @ ((cSet.insert @ cList.list.Nil) @ cOrderings.bot_class.bot)))
(TList.listsp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.listsp @ V0) @ V1)) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V3)) @ ((c==> @ ((cList.listsp @ V0) @ V4)) @ ((c==> @ (V2 @ V4)) @ (V2 @ ((cList.list.Cons @ V3) @ V4)))))))))) @ (V2 @ V1)))))))))))
(TList.listsp.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ ((cList.listsp @ V0) @ V2)) @ ((cList.listsp @ V0) @ ((cList.list.Cons @ V1) @ V2)))))))))))
(TList.listsp.intros_1,(call @ (^[V0]: ((cList.listsp @ V0) @ cList.list.Nil))))
(TList.listsp_inf_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.listsp @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cList.listsp @ V0)) @ (cList.listsp @ V1))))))))
(TList.map_eq_Cons_D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ (V0 @ V4)) @ V2)) @ ((cHOL.eq @ ((cList.map @ V0) @ V5)) @ V3)))))))))))))))))
(TList.map_injective,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V0) @ V2))) @ ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TList.map_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.replicate @ V1) @ V2))) @ ((cList.replicate @ V1) @ (V0 @ V2))))))))))
(TList.measures_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V1)) @ (V0 @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.measures @ ((cList.list.Cons @ V0) @ V3)))))))))))))
(TList.n_lists.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.n_lists @ (cNat.Suc @ V0)) @ V1)) @ (cList.concat @ ((cList.map @ (^[V2]: ((cList.map @ (^[V3]: ((cList.list.Cons @ V3) @ V2))) @ V1))) @ ((cList.n_lists @ V0) @ V1)))))))))
(TList.n_lists.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.n_lists @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil)))))
(TList.not_Cons_self,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V1) @ V0))))))))
(TList.nth_equalityI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ ((cList.nth @ V0) @ V2)) @ ((cList.nth @ V1) @ V2)))))) @ ((cHOL.eq @ V0) @ V1))))))))
(TList.nth_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cList.nth @ ((cList.replicate @ V1) @ V2)) @ V0)) @ V2)))))))))
(TList.nth_transpose,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ (cList.transpose @ V1)))) @ ((cHOL.eq @ ((cList.nth @ (cList.transpose @ V1)) @ V0)) @ ((cList.map @ (^[V2]: ((cList.nth @ V2) @ V0))) @ ((cList.filter @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V2)))) @ V1)))))))))
(TList.null_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ cHOL.eq) @ cList.null) @ cList.null))))
(TList.pair_list_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cList.map @ cProduct_Type.fst) @ V0)) @ ((cList.map @ cProduct_Type.fst) @ V1))) @ ((c==> @ ((cHOL.eq @ ((cList.map @ cProduct_Type.snd) @ V0)) @ ((cList.map @ cProduct_Type.snd) @ V1))) @ ((cHOL.eq @ V0) @ V1))))))))
(TList.partition_def,((c== @ cList.partition) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: ((cProduct_Type.Pair @ cList.list.Nil) @ cList.list.Nil))) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((cHOL.Let @ (V4 @ V5)) @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: (((cHOL.If @ (V5 @ V2)) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V6)) @ V7)) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ V2) @ V7)))))))))))) @ V1) @ V0)))))
(TList.partition_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.partition @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cList.set @ V2)) @ (cList.set @ V3))) @ (cList.set @ V1))))))))))))
(TList.product.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.product @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ ((cList.append @ ((cList.map @ (cProduct_Type.Pair @ V0)) @ V2)) @ ((cList.product @ V1) @ V2))))))))))
(TList.product.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.product @ cList.list.Nil) @ V0)) @ cList.list.Nil))))
(TList.remdups.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.remdups @ ((cList.list.Cons @ V0) @ V1))) @ (((cHOL.If @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cList.remdups @ V1)) @ ((cList.list.Cons @ V0) @ (cList.remdups @ V1)))))))))
(TList.remdups.simps_1,((cHOL.eq @ (cList.remdups @ cList.list.Nil)) @ cList.list.Nil))
(TList.remove1.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.remove1 @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V1)) @ V2) @ ((cList.list.Cons @ V1) @ ((cList.remove1 @ V0) @ V2)))))))))))
(TList.remove1.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.remove1 @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.removeAll_def,((c== @ cList.removeAll) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ ((cHOL.eq @ V5) @ V2)) @ (V4 @ V5)) @ ((cList.list.Cons @ V2) @ (V4 @ V5)))))))) @ V1) @ V0)))))
(TList.replicate_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.replicate @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cList.append @ ((cList.replicate @ V0) @ V2)) @ ((cList.replicate @ V1) @ V2))))))))))
(TList.replicate_def,((c== @ cList.replicate) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: cList.list.Nil)) @ (^[V1]: (^[V2]: (^[V3]: ((cList.list.Cons @ V3) @ (V2 @ V3)))))) @ V0))))
(TList.rev_conv_fold,(call @ (^[V0]: ((cHOL.eq @ (cList.rev @ V0)) @ (((cList.fold @ cList.list.Cons) @ V0) @ cList.list.Nil)))))
(TList.rev_replicate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rev @ ((cList.replicate @ V0) @ V1))) @ ((cList.replicate @ V0) @ V1)))))))
(TList.rev_rev_ident,(call @ (^[V0]: ((cHOL.eq @ (cList.rev @ (cList.rev @ V0))) @ V0))))
(TList.rotate1.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rotate1 @ ((cList.list.Cons @ V0) @ V1))) @ ((cList.append @ V1) @ ((cList.list.Cons @ V0) @ cList.list.Nil))))))))
(TList.rotate1.simps_1,((cHOL.eq @ (cList.rotate1 @ cList.list.Nil)) @ cList.list.Nil))
(TList.rotate1_hd_tl,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.rotate1 @ V0)) @ ((cList.append @ (cList.tl @ V0)) @ ((cList.list.Cons @ (cList.hd @ V0)) @ cList.list.Nil)))))))
(TList.rotate_rotate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.rotate @ V0) @ ((cList.rotate @ V1) @ V2))) @ ((cList.rotate @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)))))))))
(TList.set_removeAll,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.removeAll @ V0) @ V1))) @ ((cGroups.minus_class.minus @ (cList.set @ V1)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))))
(TList.set_replicate,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ (cList.set @ ((cList.replicate @ V0) @ V1))) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))
(TList.set_zip_leftD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.set @ ((cList.zip @ V2) @ V3)))) @ ((cSet.member @ V0) @ (cList.set @ V2))))))))))))
(TList.splice.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((V0 @ cList.list.Nil) @ V3)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V0 @ ((cList.list.Cons @ V3) @ V4)) @ cList.list.Nil)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((V0 @ V4) @ V6)) @ ((V0 @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6)))))))))))) @ ((V0 @ V1) @ V2)))))))))))
(TList.splice.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.splice @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V4)) @ ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V4))) @ V3))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ V5))) @ ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ cList.list.Nil))) @ V3))))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V6) @ ((cList.splice @ V5) @ V7))))) @ ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V6) @ V7)))) @ V3))))))))))))) @ V3))))))))))))))
(TList.splice.psimps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3)))) @ ((cHOL.eq @ ((cList.splice @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V2) @ ((cList.splice @ V1) @ V3))))))))))))))
(TList.splice.psimps_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ cList.list.Nil))) @ ((cHOL.eq @ ((cList.splice @ ((cList.list.Cons @ V0) @ V1)) @ cList.list.Nil)) @ ((cList.list.Cons @ V0) @ V1))))))))
(TList.splice.psimps_1,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V0))) @ ((cHOL.eq @ ((cList.splice @ cList.list.Nil) @ V0)) @ V0)))))
(TList.sublist_empty,(call @ (^[V0]: ((cHOL.eq @ ((cList.sublist @ V0) @ cOrderings.bot_class.bot)) @ cList.list.Nil))))
(TList.take.take_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.take @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.takeWhile_def,((c== @ cList.takeWhile) @ (^[V0]: (^[V1]: ((((cList.list.list_rec @ (^[V2]: cList.list.Nil)) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ (V5 @ V2)) @ ((cList.list.Cons @ V2) @ (V4 @ V5))) @ cList.list.Nil)))))) @ V1) @ V0)))))
(TList.takeWhile_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.takeWhile @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ V1) @ ((cList.takeWhile @ ((cFun.comp @ V0) @ V1)) @ V2))))))))))
(TList.takeWhile_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ ((cList.takeWhile @ V1) @ V2)))) @ ((cHOL.eq @ ((cList.nth @ ((cList.takeWhile @ V1) @ V2)) @ V0)) @ ((cList.nth @ V2) @ V0))))))))))
(TList.take_Suc_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ (cNat.Suc @ V0)) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.list.Cons @ V1) @ ((cList.take @ V0) @ V2))))))))))
(TList.take_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.take) @ cList.take))))
(TList.transpose_def,((c== @ cList.transpose) @ (^[V0]: (cList.transpose_sumC @ V0))))
(TList.upt_conv_Cons,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cList.upt @ V0) @ V1)) @ ((cList.list.Cons @ V0) @ ((cList.upt @ (cNat.Suc @ V0)) @ V1)))))))))
(TList.upto_sumC_def,((c== @ cList.upto_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cList.upto_graph @ V0) @ V1))))))
(TList.zip_Cons_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cList.zip @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ V2)) @ ((cList.zip @ V1) @ V3))))))))))))
(TList.zip_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cList.zip @ ((cList.replicate @ V0) @ V1)) @ ((cList.replicate @ V2) @ V3))) @ ((cList.replicate @ ((cOrderings.ord_class.min @ V0) @ V2)) @ ((cProduct_Type.Pair @ V1) @ V3))))))))))))
(TMap.dom_map_of_zip,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (cMap.dom @ (cMap.map_of @ ((cList.zip @ V0) @ V1)))) @ (cList.set @ V0))))))))
(TMap.dom_option_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.dom @ (^[V2]: ((cOption.map @ (V0 @ V2)) @ (V1 @ V2))))) @ (cMap.dom @ V1)))))))
(TMap.empty_upd_none,(call @ (^[V0]: ((cHOL.eq @ (((cFun.fun_upd @ (^[V1]: cOption.option.None)) @ V0) @ cOption.option.None)) @ (^[V1]: cOption.option.None)))))
(TMap.map_comp_empty_2,(call @ (^[V0]: ((cHOL.eq @ ((cMap.map_comp @ (^[V1]: cOption.option.None)) @ V0)) @ (^[V1]: cOption.option.None)))))
(TMap.map_comp_empty_1,(call @ (^[V0]: ((cHOL.eq @ ((cMap.map_comp @ V0) @ (^[V1]: cOption.option.None))) @ (^[V1]: cOption.option.None)))))
(TMap.map_comp_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (cOption.option.Some @ V2))) @ ((cHOL.eq @ (((cMap.map_comp @ V3) @ V0) @ V1)) @ (V3 @ V2))))))))))))
(TMap.map_comp_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ cOption.option.None)) @ ((cHOL.eq @ (((cMap.map_comp @ V2) @ V0) @ V1)) @ cOption.option.None)))))))))
(TMap.map_le_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cMap.map_le @ V0) @ V1)) @ ((c==> @ ((cMap.map_le @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TMap.map_le_map_add,(call @ (^[V0]: (call @ (^[V1]: ((cMap.map_le @ V0) @ ((cMap.map_add @ V1) @ V0)))))))
(TMap.map_of_zip_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.map_of @ ((cList.zip @ V0) @ ((cList.map @ V1) @ V0)))) @ (^[V2]: (((cHOL.If @ ((cSet.member @ V2) @ (cList.set @ V0))) @ (cOption.option.Some @ (V1 @ V2))) @ cOption.option.None))))))))
(TMap.map_of_zip_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.size_class.size @ V1))) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V3) @ (cList.set @ V1)))) @ ((c==> @ ((cHOL.eq @ (((cFun.fun_upd @ (cMap.map_of @ ((cList.zip @ V1) @ V0))) @ V3) @ (cOption.option.Some @ V4))) @ (((cFun.fun_upd @ (cMap.map_of @ ((cList.zip @ V1) @ V2))) @ V3) @ (cOption.option.Some @ V5)))) @ ((cHOL.eq @ (cMap.map_of @ ((cList.zip @ V1) @ V0))) @ (cMap.map_of @ ((cList.zip @ V1) @ V2))))))))))))))))))))
(TMap.map_upds_twist,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((cHOL.eq @ (((cMap.map_upds @ (((cFun.fun_upd @ V2) @ V0) @ (cOption.option.Some @ V3))) @ V1) @ V4)) @ (((cFun.fun_upd @ (((cMap.map_upds @ V2) @ V1) @ V4)) @ V0) @ (cOption.option.Some @ V3)))))))))))))))
(TMeson.conj_forward,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ V2)) @ ((c==> @ ((c==> @ V1) @ V3)) @ ((cHOL.conj @ V2) @ V3)))))))))))))
(TMeson.disj_FalseD1,(call @ (^[V0]: ((c==> @ ((cHOL.disj @ cHOL.False) @ V0)) @ V0))))
(TMeson.disj_FalseD2,(call @ (^[V0]: ((c==> @ ((cHOL.disj @ V0) @ cHOL.False)) @ V0))))
(TMeson.disj_forward,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.disj @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ V2)) @ ((c==> @ ((c==> @ V1) @ V3)) @ ((cHOL.disj @ V2) @ V3)))))))))))))
(TMeson.ext_cong_neq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2)))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2)))) @ (cHOL.Ex @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V3))))))))))))))
(TMeson.iff_to_disjD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)) @ ((cHOL.disj @ (cHOL.Not @ V1)) @ V0))))))))
(TMeson.imp_to_disjD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)))))))
(TNat.Suc_Rep_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.Suc_Rep @ V0)) @ (cNat.Suc_Rep @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.Suc_n_not_le_n,(call @ (^[V0]: (cHOL.Not @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V0)))))
(TNat.add_diff_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V2) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1)) @ V0))))))))))
(TNat.add_less_mono1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TNat.arity_type_ind,(cHOL.type_class @ cTYPE))
(TNat.arity_type_nat,(cHOL.type_class @ cTYPE))
(TNat.arity_zero_nat,(cGroups.zero_class @ cTYPE))
(TNat.diff_add_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1)) @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))))))))))
(TNat.diff_diff_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TNat.diff_less_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2)))))))))))
(TNat.diff_self_eq_0,(call @ (^[V0]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TNat.dvd.dual_order,((cOrderings.class.order @ (^[V0]: (^[V1]: ((cRings.dvd_class.dvd @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.dvd.less_asym',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))) @ V2)))))))))
(TNat.dvd.less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.dvd.order.asym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))) @ cHOL.False)))))))
(TNat.dvd.order.refl,(call @ (^[V0]: ((cRings.dvd_class.dvd @ V0) @ V0))))
(TNat.dvd.order_refl,(call @ (^[V0]: ((cRings.dvd_class.dvd @ V0) @ V0))))
(TNat.dvd_minus_self,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ V1) @ V0)) @ ((cRings.dvd_class.dvd @ V0) @ V1))))))))
(TNat.inj_on_add_nat,(call @ (^[V0]: (call @ (^[V1]: ((cFun.inj_on @ (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ V0))) @ V1))))))
(TNat.le_less_Suc_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.Suc @ V0))) @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.less_Suc_eq_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.less_diff_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ V1)))))))))
(TNat.less_dvd_minus,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))))))))
(TNat.less_eq_Suc_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)))))))
(TNat.less_not_refl2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.less_not_refl3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.less_trans_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ V2))))))))))
(TNat.measure_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V4)) @ (V0 @ V3))) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2)))))))))
(TNat.mono_times_nat,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (cOrderings.order_class.mono @ (cNat.times_nat_inst.times_nat @ V0))))))
(TNat.mult_Suc_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ (cNat.Suc @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))))))))
(TNat.nat_diff_split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ (V0 @ cNat.zero_nat_inst.zero_nat))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3))) @ (V0 @ V3)))))))))))))
(TNat.nat_less_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((V2 @ V1) @ V0))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((V2 @ V1) @ V0))) @ ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ V0)) @ ((V2 @ V1) @ V0))) @ ((V2 @ V1) @ V0)))))))))))
(TNat.nat_mult_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.not_less_eq_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V1)) @ V0)))))))
(TNat.not_less_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.Suc @ V0))) @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.not_less_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.plus_nat.add_0,(call @ (^[V0]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ V0))))
(TNat.plus_nat.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cNat.Suc @ V0)) @ V1)) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TNat.plus_nat.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ V0))))
(TNat.size_class_def,((c== @ (cNat.size_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TNat.zero_less_diff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V0)))))))
(TNitpick.Ex1_unfold,(call @ (^[V0]: ((c== @ (cHOL.Ex1 @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: (V0 @ V2)))) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))
(TNitpick.word.cases,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.word.word_case @ V0) @ (cNitpick.word.Word @ V1))) @ (V0 @ V1)))))))
(TNitpick.word.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.word.word_rec @ V0) @ (cNitpick.word.Word @ V1))) @ (V0 @ V1)))))))
(TNitpick.word.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.word.word_case @ V0) @ (cNitpick.word.Word @ V1))) @ (V0 @ V1)))))))
(TNitpick.word.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNitpick.word.Word @ V0)) @ (cNitpick.word.Word @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.word.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.word.word_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cNitpick.word.Word @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TNum.Suc_eq_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Suc @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ V0) @ (cNum.pred_numeral @ V1))))))))
(TNum.arity_plus_num,(cGroups.plus_class @ cTYPE))
(TNum.arity_type_num,(cHOL.type_class @ cTYPE))
(TNum.eq_numeral_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ (cNum.pred_numeral @ V0)) @ V1)))))))
(TNum.le_Suc_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNum.pred_numeral @ V1))))))))
(TNum.le_numeral_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNat.Suc @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNum.pred_numeral @ V0)) @ V1)))))))
(TNum.less_num_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.less_num_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.less_num_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.less_num_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.less_num_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ cHOL.True))))
(TNum.less_num_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ cHOL.True))))
(TNum.less_num_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ V0) @ cNum.num.One)) @ cHOL.False))))
(TNum.mult_num_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))))
(TNum.mult_num_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ V1))))))))
(TNum.mult_num_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ (cNum.num.Bit1 @ V1)))))))))
(TNum.mult_num_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ V1)))))))))
(TNum.mult_num_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ cNum.num.One) @ V0)) @ V0))))
(TNum.mult_num_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ V0) @ cNum.num.One)) @ V0))))
(TNum.mult_numeral_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ cNum.num.One)) @ V0)) @ V0))))
(TNum.nat_of_num_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNum.nat_of_num @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V1))))))))
(TNum.nat_of_num_def,((c== @ cNum.nat_of_num) @ (^[V0]: ((((cNum.num.num_rec @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ V2)))) @ (^[V1]: (^[V2]: (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V2))))) @ V0))))
(TNum.nat_of_num_inc,(call @ (^[V0]: ((cHOL.eq @ (cNum.nat_of_num @ (cNum.inc @ V0))) @ (cNat.Suc @ (cNum.nat_of_num @ V0))))))
(TNum.nat_of_num_pos,(call @ (^[V0]: ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cNum.nat_of_num @ V0)))))
(TNum.nat_of_num_sqr,(call @ (^[V0]: ((cHOL.eq @ (cNum.nat_of_num @ (cNum.sqr @ V0))) @ ((cNat.times_nat_inst.times_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V0))))))
(TNum.num_of_nat_One,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ (cNum.num_of_nat @ V0)) @ cNum.num.One)))))
(TNum.num_of_nat_def,((c== @ cNum.num_of_nat) @ (^[V0]: (((cNat.nat.nat_rec @ cNum.num.One) @ (^[V1]: (^[V2]: (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ (cNum.inc @ V2)) @ cNum.num.One)))) @ V0))))
(TNum.numeral_2_eq_2,((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNat.Suc @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))
(TNum.numeral_3_eq_3,((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))
(TNum.numeral_eq_Suc,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNat.Suc @ (cNum.pred_numeral @ V0))))))
(TOption.in_these_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cOption.these @ V1))) @ ((cSet.member @ (cOption.option.Some @ V0)) @ V1)))))))
(TOption.is_none_def,(call @ (^[V0]: ((cHOL.eq @ (cOption.is_none @ V0)) @ ((cHOL.eq @ V0) @ cOption.option.None)))))
(TOption.not_None_eq,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOption.option.None))) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cOption.option.Some @ V1))))))))
(TOption.not_Some_eq,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V0) @ (cOption.option.Some @ V1)))))) @ ((cHOL.eq @ V0) @ cOption.option.None)))))
(TOption.option.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cOption.option.option_rec @ V0) @ V1) @ (cOption.option.Some @ V2))) @ (V1 @ V2)))))))))
(TOption.option.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cOption.option.option_rec @ V0) @ V1) @ cOption.option.None)) @ V0))))))
(TOption.option.size_4,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cOption.option.Some @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TOption.option.size_3,((cHOL.eq @ (cNat.size_class.size @ cOption.option.None)) @ cNat.zero_nat_inst.zero_nat))
(TOption.option.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOption.option.option_size @ V0) @ (cOption.option.Some @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TOption.option.size_1,(call @ (^[V0]: ((cHOL.eq @ ((cOption.option.option_size @ V0) @ cOption.option.None)) @ cNat.zero_nat_inst.zero_nat))))
(TOption.these_empty,((cHOL.eq @ (cOption.these @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TOrderings.le_boolD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_bool_inst.less_eq_bool @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(TOrderings.le_boolE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_bool_inst.less_eq_bool @ V0) @ V1)) @ ((c==> @ V0) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(TOrderings.le_boolI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((cOrderings.ord_bool_inst.less_eq_bool @ V0) @ V1)))))))
(TPower.power_0_left,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ cGroups.zero_class.zero) @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cGroups.one_class.one) @ cGroups.zero_class.zero)))))
(TPower.power_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPower.power_class.power @ ((cFields.inverse_class.divide @ V0) @ V1)) @ V2)) @ ((cFields.inverse_class.divide @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V1) @ V2))))))))))
(TPredicate.Sup_bind,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.bind @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ (^[V2]: ((cPredicate.bind @ V2) @ V1))) @ V0))))))))
(TPredicate.bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.bind @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V2]: ((cPredicate.eval @ V0) @ V2)))) @ V1)))))))
(TPredicate.eq.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ V2))))) @ V2)))))))))
(TPredicate.eq.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.eq @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TPredicate.eq_is_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPredicate.eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.eval_Inf,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.eval @ (cComplete_Lattices.Inf_class.Inf @ V0))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ cPredicate.eval)))))
(TPredicate.eval_Sup,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.eval @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ cPredicate.eval)))))
(TPredicate.eval_bot,((cHOL.eq @ (cPredicate.eval @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TPredicate.eval_def,((c== @ cPredicate.eval) @ (^[V0]: ((cPredicate.pred.pred_rec @ (^[V1]: V1)) @ V0))))
(TPredicate.eval_inf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.eval @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1))))))))
(TPredicate.eval_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.eval @ ((cPredicate.map @ V0) @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V2]: ((cPredicate.eval @ V1) @ V2)))) @ (^[V2]: (^[V3]: ((cHOL.eq @ (V0 @ V2)) @ V3))))))))))
(TPredicate.eval_sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.eval @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1))))))))
(TPredicate.eval_top,((cHOL.eq @ (cPredicate.eval @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(TPredicate.holds_eq,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.holds @ V0)) @ ((cPredicate.eval @ V0) @ cProduct_Type.Unity)))))
(TPredicate.if_predE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ (cPredicate.if_pred @ V0)) @ V1)) @ ((c==> @ ((c==> @ V0) @ ((c==> @ ((cHOL.eq @ V1) @ cProduct_Type.Unity)) @ V2))) @ V2)))))))))
(TPredicate.if_predI,(call @ (^[V0]: ((c==> @ V0) @ ((cPredicate.eval @ (cPredicate.if_pred @ V0)) @ cProduct_Type.Unity)))))
(TPredicate.map.comp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (cPredicate.map @ V0)) @ (cPredicate.map @ V1))) @ (cPredicate.map @ ((cFun.comp @ V0) @ V1))))))))
(TPredicate.null_def,((c== @ cPredicate.null) @ (^[V0]: ((((cPredicate.seq.seq_rec @ cHOL.True) @ (^[V1]: (^[V2]: cHOL.False))) @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.conj @ (cPredicate.is_empty @ V1)) @ V3))))) @ V0))))
(TPredicate.pred_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.eval @ V0) @ V2)) @ ((cPredicate.eval @ V1) @ V2))))) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.seq.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ ((cPredicate.seq.Join @ V3) @ V4))) @ (((V2 @ V3) @ V4) @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ V4))))))))))))))
(TPredicate.seq.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ ((cPredicate.seq.Insert @ V3) @ V4))) @ ((V1 @ V3) @ V4)))))))))))))
(TPredicate.seq.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ cPredicate.seq.Empty)) @ V0))))))))
(TPredicate.seq.size_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cPredicate.seq.Join @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TPredicate.seq.size_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cPredicate.seq.Insert @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TPredicate.seq.size_4,((cHOL.eq @ (cNat.size_class.size @ cPredicate.seq.Empty)) @ cNat.zero_nat_inst.zero_nat))
(TPredicate.seq.size_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.seq.seq_size @ V0) @ ((cPredicate.seq.Join @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cPredicate.pred.pred_size @ V0) @ V1)) @ ((cPredicate.seq.seq_size @ V0) @ V2))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TPredicate.seq.size_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.seq.seq_size @ V0) @ ((cPredicate.seq.Insert @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ ((cPredicate.pred.pred_size @ V0) @ V2))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TPredicate.seq.size_1,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.seq.seq_size @ V0) @ cPredicate.seq.Empty)) @ cNat.zero_nat_inst.zero_nat))))
(TPredicate.singleE',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ (cPredicate.single @ V0)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V2)) @ V2)))))))))
(TPredicate.sup_bind,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.bind @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cPredicate.bind @ V0) @ V2)) @ ((cPredicate.bind @ V1) @ V2))))))))))
(TPredicate.sup_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cPredicate.Seq @ V0)) @ (cPredicate.Seq @ V1))) @ (cPredicate.Seq @ (^[V2]: ((((cPredicate.seq.seq_case @ (V1 @ cProduct_Type.Unity)) @ (^[V3]: (^[V4]: ((cPredicate.seq.Insert @ V3) @ ((cLattices.sup_class.sup @ V4) @ (cPredicate.Seq @ V1)))))) @ (^[V3]: (^[V4]: ((cPredicate.adjunct @ (cPredicate.Seq @ V1)) @ ((cPredicate.seq.Join @ V3) @ V4))))) @ (V0 @ cProduct_Type.Unity))))))))))
(TProduct_Type.PairE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TProduct_Type.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TPure.conjunctionD1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPure.conjunction @ V0) @ V1)) @ V0))))))
(TPure.conjunctionD2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPure.conjunction @ V0) @ V1)) @ V1))))))
(TPure.swap_prems_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((c==> @ V0) @ ((c==> @ V1) @ V2))) @ ((c==> @ V1) @ ((c==> @ V0) @ V2))))))))))
(TQuotient.abs_o_rep,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cFun.comp @ V1) @ V2)) @ cFun.id)))))))))
(TQuotient.babs_simp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((((cTransfer.fun_rel @ V0) @ V3) @ ((cQuotient.Babs @ (cLifting.Respects @ V0)) @ V4)) @ ((cQuotient.Babs @ (cLifting.Respects @ V0)) @ V5))) @ ((((cTransfer.fun_rel @ V0) @ V3) @ V4) @ V5))))))))))))))))
(TQuotient.eq_comp_r,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcompp @ cHOL.eq) @ ((cRelation.relcompp @ V0) @ cHOL.eq))) @ V0))))
(TRandom.iterate_def,((c== @ cRandom.iterate) @ (^[V0]: (^[V1]: (^[V2]: (cRandom.iterate_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TRandom.log.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cRandom.log_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cRandom.log_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3)))) @ ((V2 @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom.log_rel_def,((c== @ cRandom.log_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3)))))))))))))))
(TRandom.pick_member,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ (cList.monoid_add_class.listsum @ ((cList.map @ cProduct_Type.fst) @ V1)))) @ ((cSet.member @ ((cRandom.pick @ V1) @ V0)) @ (cList.set @ ((cList.map @ cProduct_Type.snd) @ V1)))))))))
(TRelation.Domain_Id,((cHOL.eq @ (cRelation.Domain @ cRelation.Id)) @ cOrderings.top_class.top))
(TRelation.Field_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Field @ V0)) @ ((cLattices.sup_class.sup @ (cRelation.Domain @ V0)) @ (cRelation.Range @ V0))))))
(TRelation.Id_on_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Id_on @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: ((cSet.insert @ ((cProduct_Type.Pair @ V1) @ V1)) @ cOrderings.bot_class.bot)))))))
(TRelation.Id_on_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.Id_on @ V2)))))))))))
(TRelation.Id_on_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.Id_on @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TRelation.Image_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Image @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V1) @ (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V2)) @ V0)))))))))))
(TRelation.Image_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cRelation.Image @ V1) @ V2))) @ ((cSet.Bex @ V2) @ (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V0)) @ V1)))))))))))
(TRelation.Powp_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cRelation.Powp @ V0)) @ (cRelation.Powp @ V1))))))))
(TRelation.Range_def,((c== @ cRelation.Range) @ (^[V0]: (cSet.Collect @ (^[V1]: ((cRelation.Rangep @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ V1))))))
(TRelation.Range_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cRelation.Range @ V1))) @ (cHOL.Ex @ (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ V1)))))))))
(TRelation.Range_snd,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Range @ V0)) @ ((cSet.image @ cProduct_Type.snd) @ V0)))))
(TRelation.SUP_UN_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (^[V3]: ((cSet.member @ V3) @ (V1 @ V2)))))) @ (^[V2]: ((cSet.member @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))))))))))
(TRelation.converseD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ V2)))))))))
(TRelation.converseE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.converse @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V3))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ V2))))))) @ V2)))))))))
(TRelation.converseI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ (cRelation.converse @ V2))))))))))
(TRelation.refl_onD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)) @ ((cSet.member @ V2) @ V0))))))))))))
(TRelation.refl_onD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)) @ ((cSet.member @ V3) @ V0))))))))))))
(TRelation.reflp_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.reflp @ V0)) @ (cHOL.All @ (^[V1]: ((V0 @ V1) @ V1)))))))
(TRelation.reflp_inf,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ (cRelation.reflp @ V1)) @ (cRelation.reflp @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TRelation.reflp_sup,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ (cRelation.reflp @ V1)) @ (cRelation.reflp @ ((cLattices.sup_class.sup @ V0) @ V1)))))))))
(TRelation.relcomppE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRelation.relcompp @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((V0 @ V2) @ V5)) @ ((c==> @ ((V1 @ V5) @ V3)) @ V4))))) @ V4)))))))))))))
(TRelation.relcomppI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V3 @ V2) @ V4)) @ ((((cRelation.relcompp @ V0) @ V3) @ V1) @ V4))))))))))))))
(TRelation.sup_Un_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1)))) @ (^[V2]: ((cSet.member @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))))
(TRelation.sym_INTER,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cRelation.sym @ (V1 @ V2))))) @ (cRelation.sym @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1))))))))
(TRelation.sym_Id_on,(call @ (^[V0]: (cRelation.sym @ (cRelation.Id_on @ V0)))))
(TRelation.sym_UNION,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cRelation.sym @ (V1 @ V2))))) @ (cRelation.sym @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))))))))
(TRelation.trans_Int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.trans @ V0)) @ ((c==> @ (cRelation.trans @ V1)) @ (cRelation.trans @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TRelation.trans_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.trans @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V0)))))))))))))
(TSMT.pattern.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cSMT.pattern.Pattern)) @ (V0 @ V1)))))))
(TSMT.pattern.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cSMT.pattern.pattern_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cSMT.pattern.Pattern)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TSMT.pattern.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cSMT.pattern.pattern_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cSMT.pattern.Pattern)) @ (V0 @ V1))))))))))
(TSMT.term_false_def,((cHOL.eq @ cSMT.term_false) @ cHOL.False))
(TSet.Collect_imp_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cLattices.sup_class.sup @ (cGroups.uminus_class.uminus @ (cSet.Collect @ (^[V2]: (V0 @ V2))))) @ (cSet.Collect @ (^[V2]: (V1 @ V2))))))))))
(TSet.Collect_mem_eq,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: ((cSet.member @ V1) @ V0)))) @ V0))))
(TSet.Collect_neg_eq,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: (cHOL.Not @ (V0 @ V1))))) @ (cGroups.uminus_class.uminus @ (cSet.Collect @ (^[V1]: (V0 @ V1))))))))
(TSet.Compl_disjoint,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ cOrderings.bot_class.bot))))
(TSet.Compl_empty_eq,((cHOL.eq @ (cGroups.uminus_class.uminus @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top))
(TSet.Compr_image_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cSet.Collect @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ ((cSet.image @ V0) @ V1))) @ (V2 @ V3))))) @ ((cSet.image @ V0) @ (cSet.Collect @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V1)) @ (V2 @ (V0 @ V3))))))))))))))
(TSet.Diff_partition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ V1)))))))
(TSet.Int_UNIV_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ cOrderings.top_class.top)) @ V0))))
(TSet.Int_Un_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TSet.Int_empty_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TSet.Int_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet.UNIV_not_empty,(cHOL.Not @ ((cHOL.eq @ cOrderings.top_class.top) @ cOrderings.bot_class.bot)))
(TSet.Un_Diff_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TSet.Un_Int_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TSet.Un_empty_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ cOrderings.bot_class.bot)) @ V0))))
(TSet.Un_insert_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ V1)) @ V2)) @ ((cSet.insert @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TSet.Un_left_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TSet.arity_type_set,(cHOL.type_class @ cTYPE))
(TSet.bex_one_point1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V3) @ V1)) @ (V2 @ V3))))) @ ((cHOL.conj @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1))))))))))
(TSet.bex_one_point2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ (V2 @ V3))))) @ ((cHOL.conj @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1))))))))))
(TSet.bool_contrapos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.Not @ (V0 @ cHOL.False))) @ (V0 @ cHOL.True))))))))
(TSet.contra_subsetD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V1))) @ (cHOL.Not @ ((cSet.member @ V2) @ V0)))))))))))
(TSet.empty_is_image,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet.image @ V0) @ V1))) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TSet.empty_not_UNIV,(cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ cOrderings.top_class.top)))
(TSet.eqelem_imp_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.member @ V0) @ V2)) @ ((cSet.member @ V1) @ V2))))))))))
(TSet.image_Pow_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ (cSet.image @ V0)) @ (cSet.Pow @ V1))) @ (cSet.Pow @ V2))))))))))
(TSet.image_Pow_surj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ ((cSet.image @ (cSet.image @ V0)) @ (cSet.Pow @ V1))) @ (cSet.Pow @ V2))))))))))
(TSet.image_constant,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.image @ (^[V3]: V2)) @ V1)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))))))))
(TSet.image_is_empty,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TSet.insert_Collect,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ (cSet.Collect @ V1))) @ (cSet.Collect @ (^[V2]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V0))) @ (V1 @ V2))))))))))
(TSet.insert_Diff_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cSet.insert @ V0) @ V1)) @ V2)) @ (((cHOL.If @ ((cSet.member @ V0) @ V2)) @ ((cGroups.minus_class.minus @ V1) @ V2)) @ ((cSet.insert @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2)))))))))))
(TSet.insert_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ ((cSet.insert @ V0) @ V1))) @ ((cSet.insert @ V0) @ V1)))))))
(TSet.insert_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.insert @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cSet.insert @ V1) @ ((cSet.insert @ V0) @ V2))))))))))
(TSet.mem_Collect_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cSet.Collect @ V1))) @ (V1 @ V0)))))))
(TSet.singleton_conv,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: ((cHOL.eq @ V1) @ V0)))) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TSet.subset_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TSet.subset_insertI,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.insert @ V1) @ V0)))))))
(TSet.uminus_set_def,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cSet.Collect @ (cGroups.uminus_class.uminus @ (^[V1]: ((cSet.member @ V1) @ V0))))))))
(TSet.vimage_Collect,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V0 @ (V1 @ V3))) @ (V2 @ V3))))) @ ((cHOL.eq @ ((cSet.vimage @ V1) @ (cSet.Collect @ V0))) @ (cSet.Collect @ V2))))))))))
(TString.STR_inject',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cString.STR @ V0)) @ (cString.STR @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.UNIV_nibble,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cString.nibble.Nibble0) @ ((cSet.insert @ cString.nibble.Nibble1) @ ((cSet.insert @ cString.nibble.Nibble2) @ ((cSet.insert @ cString.nibble.Nibble3) @ ((cSet.insert @ cString.nibble.Nibble4) @ ((cSet.insert @ cString.nibble.Nibble5) @ ((cSet.insert @ cString.nibble.Nibble6) @ ((cSet.insert @ cString.nibble.Nibble7) @ ((cSet.insert @ cString.nibble.Nibble8) @ ((cSet.insert @ cString.nibble.Nibble9) @ ((cSet.insert @ cString.nibble.NibbleA) @ ((cSet.insert @ cString.nibble.NibbleB) @ ((cSet.insert @ cString.nibble.NibbleC) @ ((cSet.insert @ cString.nibble.NibbleD) @ ((cSet.insert @ cString.nibble.NibbleE) @ ((cSet.insert @ cString.nibble.NibbleF) @ cOrderings.bot_class.bot))))))))))))))))))
(TString.char.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cString.char.Char @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TString.char.inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cString.char.Char @ V0) @ V1)) @ ((cString.char.Char @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TString.char.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cString.char.char_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cString.char.Char @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TString.char.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cString.char.char_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cString.char.Char @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TString.nibble.recs_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleF)) @ V15))))))))))))))))))))))))))))))))))
(TString.nibble.recs_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleE)) @ V14))))))))))))))))))))))))))))))))))
(TString.nibble.recs_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleD)) @ V13))))))))))))))))))))))))))))))))))
(TString.nibble.recs_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleC)) @ V12))))))))))))))))))))))))))))))))))
(TString.nibble.recs_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleB)) @ V11))))))))))))))))))))))))))))))))))
(TString.nibble.recs_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleA)) @ V10))))))))))))))))))))))))))))))))))
(TString.nibble.recs_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble9)) @ V9))))))))))))))))))))))))))))))))))
(TString.nibble.recs_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble8)) @ V8))))))))))))))))))))))))))))))))))
(TString.nibble.recs_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble7)) @ V7))))))))))))))))))))))))))))))))))
(TString.nibble.recs_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble6)) @ V6))))))))))))))))))))))))))))))))))
(TString.nibble.recs_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble5)) @ V5))))))))))))))))))))))))))))))))))
(TString.nibble.recs_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble4)) @ V4))))))))))))))))))))))))))))))))))
(TString.nibble.recs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble3)) @ V3))))))))))))))))))))))))))))))))))
(TString.nibble.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble2)) @ V2))))))))))))))))))))))))))))))))))
(TString.nibble.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble1)) @ V1))))))))))))))))))))))))))))))))))
(TString.nibble.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble0)) @ V0))))))))))))))))))))))))))))))))))
(TString.nibble.size_32,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.NibbleF)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_31,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.NibbleE)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_30,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.NibbleD)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_29,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.NibbleC)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_28,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.NibbleB)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_27,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.NibbleA)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_26,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble9)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_25,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble8)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_24,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble7)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_23,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble6)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_22,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble5)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_21,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble4)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_20,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble3)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_19,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble2)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_18,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble1)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_17,((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ cString.nibble.Nibble0)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_16,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.NibbleF)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_15,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.NibbleE)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_14,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.NibbleD)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_13,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.NibbleC)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_12,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.NibbleB)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_11,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.NibbleA)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_10,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble9)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_9,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble8)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_8,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble7)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_7,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble6)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_6,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble5)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_5,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble4)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_4,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble3)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_3,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble2)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_2,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble1)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble.size_1,((cHOL.eq @ (cString.nibble.nibble_size @ cString.nibble.Nibble0)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble_size,(call @ (^[V0]: ((cHOL.eq @ (cString.nibble.nibble_size @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TString.size_nibble,(call @ (^[V0]: ((cHOL.eq @ (cString.nibble.size_nibble_inst.size_nibble @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TSum_Type.Projl_def,((c== @ cSum_Type.Projl) @ (^[V0]: (((cSum_Type.sum.sum_rec @ (^[V1]: V1)) @ cHOL.undefined) @ V0))))
(TSum_Type.Projr_def,((c== @ cSum_Type.Projr) @ (^[V0]: (((cSum_Type.sum.sum_rec @ cHOL.undefined) @ (^[V1]: V1)) @ V0))))
(TSum_Type.sum.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_case @ V0) @ V1) @ (cSum_Type.Inr @ V2))) @ (V1 @ V2)))))))))
(TSum_Type.sum.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_case @ V0) @ V1) @ (cSum_Type.Inl @ V2))) @ (V0 @ V2)))))))))
(TSum_Type.sum.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_rec @ V0) @ V1) @ (cSum_Type.Inr @ V2))) @ (V1 @ V2)))))))))
(TSum_Type.sum.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_rec @ V0) @ V1) @ (cSum_Type.Inl @ V2))) @ (V0 @ V2)))))))))
(TSum_Type.sum.simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_case @ V0) @ V1) @ (cSum_Type.Inr @ V2))) @ (V1 @ V2)))))))))
(TSum_Type.sum.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum.sum_case @ V0) @ V1) @ (cSum_Type.Inl @ V2))) @ (V0 @ V2)))))))))
(TSum_Type.sum.simps_4,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inl @ V1))))))))
(TSum_Type.sum.simps_3,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inr @ V1))))))))
(TSum_Type.sum.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inr @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inl @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cSum_Type.sum.sum_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cSum_Type.Inl @ V4))) @ (V0 @ (V1 @ V4)))))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cSum_Type.Inr @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TTransfer.fun_relD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cTransfer.fun_rel @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V4)) @ ((V1 @ (V2 @ V4)) @ (V3 @ V4)))))))))))))))
(TWellfounded.wfE_pf,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cRelation.Image @ V0) @ V1))) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))))))
(TWellfounded.wfI_pf,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cRelation.Image @ V0) @ V1))) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))) @ (cWellfounded.wf @ V0)))))
(TWellfounded.wf_def,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wf @ V0)) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V2)) @ V0)) @ (V1 @ V3))))) @ (V1 @ V2))))) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(TWellfounded.wf_exp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ ((cNat.compow @ V0) @ V1))) @ (cWellfounded.wf @ V1)))))))
(TATP.fTrue_ne_fFalse,(cHOL.Not @ ((cHOL.eq @ cATP.fFalse) @ cATP.fTrue)))
(TDatatype.In0_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cDatatype.In0 @ V0)) @ (cDatatype.In0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.In1_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cDatatype.In1 @ V0)) @ (cDatatype.In1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.Lim_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cDatatype.Lim @ V0)) @ (cDatatype.Lim @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.Scons_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cDatatype.Scons @ V0) @ V2)) @ ((cDatatype.Scons @ V1) @ V3)))))))))))))
(TDatatype.dprod_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cDatatype.dprod @ V0) @ V2)) @ ((cDatatype.dprod @ V1) @ V3)))))))))))))
(TDatatype.dsum_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cOrderings.ord_class.less_eq @ ((cDatatype.dsum @ ((cProduct_Type.Sigma @ V0) @ (^[V4]: V1))) @ ((cProduct_Type.Sigma @ V2) @ (^[V4]: V3)))) @ ((cProduct_Type.Sigma @ ((cDatatype.usum @ V0) @ V2)) @ (^[V4]: ((cDatatype.usum @ V1) @ V3)))))))))))))
(TDatatype.ndepth_def,(call @ (^[V0]: ((c== @ (cDatatype.ndepth @ V0)) @ ((cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (cOrderings.ord_class.Least @ (^[V3]: ((cHOL.eq @ (V1 @ V3)) @ (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat))))))) @ (cDatatype.Rep_Node @ V0))))))
(TDatatype.ntrunc_In0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ (cNat.Suc @ V0))) @ (cDatatype.In0 @ V1))) @ (cDatatype.In0 @ ((cDatatype.ntrunc @ (cNat.Suc @ V0)) @ V1))))))))
(TDatatype.ntrunc_In1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ (cNat.Suc @ V0))) @ (cDatatype.In1 @ V1))) @ (cDatatype.In1 @ ((cDatatype.ntrunc @ (cNat.Suc @ V0)) @ V1))))))))
(TDatatype.ntrunc_UN1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.ntrunc @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: (V1 @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: ((cDatatype.ntrunc @ V0) @ (V1 @ V2))))))))))
(TDatatype.ntrunc_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cDatatype.ntrunc @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ (cDatatype.ndepth @ V2)) @ V0))))))))))
(TDatatype.uprod_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cDatatype.uprod @ V0) @ V2)) @ ((cDatatype.uprod @ V1) @ V3)))))))))))))
(TDivides.div_add1_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V2)) @ ((cDivides.div_nat_inst.div_nat @ V1) @ V2))) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V2)) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V2))) @ V2))))))))))
(TDivides.div_int_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ (cProduct_Type.fst @ ((cDivides.divmod_int @ V0) @ V1))))))))
(TDivides.div_le_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V2)) @ ((cDivides.div_nat_inst.div_nat @ V1) @ V2))))))))))
(TDivides.div_nat_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ (cProduct_Type.fst @ ((cDivides.divmod_nat @ V0) @ V1))))))))
(TDivides.div_neg_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ (cProduct_Type.fst @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.posDivAlg @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1))))))))))))
(TDivides.div_neg_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ (cProduct_Type.fst @ ((cDivides.negDivAlg @ V0) @ V1))))))))))
(TDivides.div_pos_geq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V1) @ V0)) @ ((cInt.plus_int_inst.plus_int @ ((cDivides.div_int_inst.div_int @ ((cInt.minus_int_inst.minus_int @ V1) @ V0)) @ V0)) @ cInt.one_int_inst.one_int)))))))))
(TDivides.div_pos_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ (cProduct_Type.fst @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.negDivAlg @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1))))))))))))
(TDivides.div_pos_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ (cProduct_Type.fst @ ((cDivides.posDivAlg @ V0) @ V1))))))))))
(TDivides.mod_int_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ (cProduct_Type.snd @ ((cDivides.divmod_int @ V0) @ V1))))))))
(TDivides.mod_nat_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ (cProduct_Type.snd @ ((cDivides.divmod_nat @ V0) @ V1))))))))
(TDivides.mod_neg_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ (cProduct_Type.snd @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.posDivAlg @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1))))))))))))
(TDivides.mod_neg_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ (cProduct_Type.snd @ ((cDivides.negDivAlg @ V0) @ V1))))))))))
(TDivides.mod_pos_geq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)) @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ V1) @ V0)) @ V0)))))))))
(TDivides.mod_pos_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ (cProduct_Type.snd @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.negDivAlg @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1))))))))))))
(TDivides.mod_pos_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ (cProduct_Type.snd @ ((cDivides.posDivAlg @ V0) @ V1))))))))))
(TDivides.posDivAlg_0,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.posDivAlg @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)))))
(TDivides.q_neg_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V2)) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int)))))))))))
(TDivides.q_pos_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V2))) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V2) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)))))))))))
(TDivides.zadd1_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((c==> @ (((cDivides.divmod_int_rel @ V4) @ V1) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cDivides.divmod_int_rel @ ((cInt.plus_int_inst.plus_int @ V0) @ V4)) @ V1) @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ ((cInt.plus_int_inst.plus_int @ V2) @ V5)) @ ((cDivides.div_int_inst.div_int @ ((cInt.plus_int_inst.plus_int @ V3) @ V6)) @ V1))) @ ((cDivides.div_int_inst.mod_int @ ((cInt.plus_int_inst.plus_int @ V3) @ V6)) @ V1))))))))))))))))))))
(TDivides.zminus_zmod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cInt.uminus_int_inst.uminus_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))) @ V1)) @ ((cDivides.div_int_inst.mod_int @ (cInt.uminus_int_inst.uminus_int @ V0)) @ V1)))))))
(TDivides.zmod_minus1,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)) @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int))))))
(TEnum.arity_enum_fun,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_set,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_sum,(cEnum.enum_class @ cTYPE))
(TEnum.class.enum_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.conj @ ((cHOL.eq @ cOrderings.top_class.top) @ (cList.set @ V0))) @ (cList.distinct @ V0))) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.eq @ (V1 @ V3)) @ ((cSet.Ball @ cOrderings.top_class.top) @ V3))))) @ (cHOL.All @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ ((cSet.Bex @ cOrderings.top_class.top) @ V3))))))))))))))
(TEnum.enum.UNIV_enum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.eq @ cOrderings.top_class.top) @ (cList.set @ V0))))))))))
(TEnum.enum.enum_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cList.set @ V0)) @ cOrderings.top_class.top)))))))))
(TEnum.enum.enum_eq_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((cSet.member @ V4) @ (cList.set @ V3))))) @ ((cHOL.eq @ (cList.set @ V0)) @ (cList.set @ V3)))))))))))))
(TEnum.enum_class_def,((c== @ (cEnum.enum_class @ cTYPE)) @ ((cPure.conjunction @ (cHOL.type_class @ cTYPE)) @ (((cEnum.class.enum @ cEnum.enum_class.enum) @ cEnum.enum_class.enum_all) @ cEnum.enum_class.enum_ex))))
(TEnum.ex_n_lists_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.ex_n_lists @ V0) @ V1)) @ ((cSet.Bex @ (cList.set @ ((cList.n_lists @ V1) @ cEnum.enum_class.enum))) @ (^[V2]: (V0 @ V2)))))))))
(TEnum.finite_1.cases,(call @ (^[V0]: ((cHOL.eq @ ((cEnum.finite_1.finite_1_case @ V0) @ cEnum.finite_1.a\<__caret__sub>1)) @ V0))))
(TEnum.finite_1.simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cEnum.finite_1.finite_1_rec @ V0) @ cEnum.finite_1.a\<__caret__sub>1)) @ V0))))
(TEnum.finite_1.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cEnum.finite_1.finite_1_case @ V0) @ cEnum.finite_1.a\<__caret__sub>1)) @ V0))))
(TEnum.finite_1.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cEnum.finite_1.finite_1_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cEnum.finite_1.a\<__caret__sub>1)) @ (V0 @ V1))))))))))
(TEnum.finite_2.cases_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_case @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>2)) @ V1))))))
(TEnum.finite_2.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_case @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>1)) @ V0))))))
(TEnum.finite_2.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_rec @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>2)) @ V1))))))
(TEnum.finite_2.simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_rec @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>1)) @ V0))))))
(TEnum.finite_2.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_case @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>2)) @ V1))))))
(TEnum.finite_2.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cEnum.finite_2.finite_2_case @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>1)) @ V0))))))
(TEnum.finite_2.simps_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_2.a\<__caret__sub>2) @ cEnum.finite_2.a\<__caret__sub>1)))
(TEnum.finite_2.simps_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_2.a\<__caret__sub>1) @ cEnum.finite_2.a\<__caret__sub>2)))
(TEnum.finite_2.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cEnum.finite_2.finite_2_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>2)) @ (V0 @ V2)))))))))))))
(TEnum.finite_3.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>3)) @ V2))))))))
(TEnum.finite_3.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>2)) @ V1))))))))
(TEnum.finite_3.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>1)) @ V0))))))))
(TEnum.finite_3.simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_rec @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>3)) @ V2))))))))
(TEnum.finite_3.simps_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_rec @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>2)) @ V1))))))))
(TEnum.finite_3.simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_rec @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>1)) @ V0))))))))
(TEnum.finite_3.simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>3)) @ V2))))))))
(TEnum.finite_3.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>2)) @ V1))))))))
(TEnum.finite_3.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>1)) @ V0))))))))
(TEnum.finite_3.simps_6,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>3) @ cEnum.finite_3.a\<__caret__sub>2)))
(TEnum.finite_3.simps_5,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>2) @ cEnum.finite_3.a\<__caret__sub>3)))
(TEnum.finite_3.simps_4,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>3) @ cEnum.finite_3.a\<__caret__sub>1)))
(TEnum.finite_3.simps_3,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>1) @ cEnum.finite_3.a\<__caret__sub>3)))
(TEnum.finite_3.simps_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>2) @ cEnum.finite_3.a\<__caret__sub>1)))
(TEnum.finite_3.simps_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>1) @ cEnum.finite_3.a\<__caret__sub>2)))
(TEnum.finite_3.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cEnum.finite_3.finite_3_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>2)) @ (V0 @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>3)) @ (V0 @ V3))))))))))))))))
(TEnum.finite_4.cases_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>4)) @ V3))))))))))
(TEnum.finite_4.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>3)) @ V2))))))))))
(TEnum.finite_4.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>2)) @ V1))))))))))
(TEnum.finite_4.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>1)) @ V0))))))))))
(TEnum.finite_4.simps_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>4)) @ V3))))))))))
(TEnum.finite_4.simps_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>3)) @ V2))))))))))
(TEnum.finite_4.simps_18,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>2)) @ V1))))))))))
(TEnum.finite_4.simps_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>1)) @ V0))))))))))
(TEnum.finite_4.simps_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>4)) @ V3))))))))))
(TEnum.finite_4.simps_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>3)) @ V2))))))))))
(TEnum.finite_4.simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>2)) @ V1))))))))))
(TEnum.finite_4.simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>1)) @ V0))))))))))
(TEnum.finite_4.simps_12,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>3)))
(TEnum.finite_4.simps_11,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>4)))
(TEnum.finite_4.simps_10,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>2)))
(TEnum.finite_4.simps_9,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>4)))
(TEnum.finite_4.simps_8,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>2)))
(TEnum.finite_4.simps_7,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>3)))
(TEnum.finite_4.simps_6,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>1)))
(TEnum.finite_4.simps_5,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>4)))
(TEnum.finite_4.simps_4,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>1)))
(TEnum.finite_4.simps_3,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>3)))
(TEnum.finite_4.simps_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>1)))
(TEnum.finite_4.simps_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>2)))
(TEnum.finite_4.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (V0 @ (((((cEnum.finite_4.finite_4_case @ V1) @ V2) @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>2)) @ (V0 @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>3)) @ (V0 @ V3))) @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>4)) @ (V0 @ V4)))))))))))))))))))
(TEnum.finite_5.cases_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>5)) @ V4))))))))))))
(TEnum.finite_5.cases_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>4)) @ V3))))))))))))
(TEnum.finite_5.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>3)) @ V2))))))))))))
(TEnum.finite_5.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>2)) @ V1))))))))))))
(TEnum.finite_5.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>1)) @ V0))))))))))))
(TEnum.finite_5.simps_30,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>5)) @ V4))))))))))))
(TEnum.finite_5.simps_29,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>4)) @ V3))))))))))))
(TEnum.finite_5.simps_28,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>3)) @ V2))))))))))))
(TEnum.finite_5.simps_27,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>2)) @ V1))))))))))))
(TEnum.finite_5.simps_26,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>1)) @ V0))))))))))))
(TEnum.finite_5.simps_25,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>5)) @ V4))))))))))))
(TEnum.finite_5.simps_24,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>4)) @ V3))))))))))))
(TEnum.finite_5.simps_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>3)) @ V2))))))))))))
(TEnum.finite_5.simps_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>2)) @ V1))))))))))))
(TEnum.finite_5.simps_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>1)) @ V0))))))))))))
(TEnum.finite_5.simps_20,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.simps_19,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.simps_18,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.simps_17,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.simps_16,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.simps_15,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.simps_14,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.simps_13,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.simps_12,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.simps_11,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.simps_10,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.simps_9,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.simps_8,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.simps_7,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.simps_6,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.simps_5,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.simps_4,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.simps_3,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.simps_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.simps_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (V0 @ ((((((cEnum.finite_5.finite_5_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>2)) @ (V0 @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>3)) @ (V0 @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>4)) @ (V0 @ V4))) @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>5)) @ (V0 @ V5))))))))))))))))))))))
(TEnum.tranclp_unfold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cTransitive_Closure.trancl @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4)))))))))))))))
(TFinite_Set.Bex_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cSet.Bex @ V0) @ V1)) @ (((cFinite_Set.fold @ (^[V2]: (^[V3]: ((cHOL.disj @ V3) @ (V1 @ V2))))) @ cHOL.False) @ V0))))))))
(TFinite_Set.Pow_fold,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cSet.Pow @ V0)) @ (((cFinite_Set.fold @ (^[V1]: (^[V2]: ((cLattices.sup_class.sup @ V2) @ ((cSet.image @ (cSet.insert @ V1)) @ V2))))) @ ((cSet.insert @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot)) @ V0))))))
(TFinite_Set.card_Pow,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ (cSet.Pow @ V0))) @ ((cPower.power_class.power @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cFinite_Set.card @ V0)))))))
(TFinite_Set.card_def,((cHOL.eq @ cFinite_Set.card) @ ((cFinite_Set.folding.F @ (^[V0]: cNat.Suc)) @ cNat.zero_nat_inst.zero_nat)))
(TFinite_Set.fold_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V1) @ V2)) @ (((cHOL.If @ (cFinite_Set.finite @ V2)) @ (cHOL.The @ (^[V3]: ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)))) @ V1)))))))))
(TFun.Cantors_paradox,(call @ (^[V0]: (cHOL.Not @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ ((cSet.image @ V1) @ V0)) @ (cSet.Pow @ V0))))))))
(TFun.bij_betw_empty1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.bot_class.bot) @ V1)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TFun.bij_betw_empty2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TFun.bij_betw_id_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cFun.bij_betw @ cFun.id) @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TFun.bij_betw_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ V3)) @ V4)) @ (((cFun.bij_betw @ V0) @ V3) @ V4)))))))))))))))
(TFun.comp_inj_on_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cFun.inj_on @ V2) @ ((cSet.image @ V0) @ V1))) @ ((cFun.inj_on @ ((cFun.comp @ V2) @ V0)) @ V1))))))))))
(TFun.inj_img_insertE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((c==> @ ((cHOL.eq @ ((cSet.insert @ V2) @ V3)) @ ((cSet.image @ V0) @ V1))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cSet.member @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cSet.insert @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ (V0 @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ ((cSet.image @ V0) @ V6))) @ V4))))))))) @ V4)))))))))))))))
(TFun.inj_on_fun_updI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ ((cSet.image @ V0) @ V1)))) @ ((cFun.inj_on @ (((cFun.fun_upd @ V0) @ V3) @ V2)) @ V1))))))))))))
(TFun.inj_on_inverseI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ (V2 @ V3))) @ V3))))) @ ((cFun.inj_on @ V2) @ V0)))))))))
(TFun.inj_on_swap_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ ((cFun.inj_on @ (((cFun.swap @ V0) @ V2) @ V3)) @ V1)) @ ((cFun.inj_on @ V3) @ V1)))))))))))))
(TFun.override_on_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.override_on @ V0) @ V1) @ V2)) @ (^[V3]: (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ (V1 @ V3)) @ (V0 @ V3)))))))))))
(TFunDef.max_weak_def,((cHOL.eq @ cFunDef.max_weak) @ ((cLattices.sup_class.sup @ (cWellfounded.max_ext @ cFunDef.pair_leq)) @ ((cSet.insert @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TFunDef.measure_size,(cFunDef.is_measure @ cNat.size_class.size))
(TFunDef.min_weak_def,((cHOL.eq @ cFunDef.min_weak) @ ((cLattices.sup_class.sup @ (cWellfounded.min_ext @ cFunDef.pair_leq)) @ ((cSet.insert @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TFunDef.pair_leq_def,((cHOL.eq @ cFunDef.pair_leq) @ ((cLattices.sup_class.sup @ cFunDef.pair_less) @ cRelation.Id)))
(TFunDef.smax_insertI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ cFunDef.pair_less)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V1)) @ cFunDef.max_strict)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cSet.insert @ V2) @ V3)) @ V1)) @ cFunDef.max_strict)))))))))))))
(TFunDef.smin_insertI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ cFunDef.pair_less)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ cFunDef.min_strict)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ ((cSet.insert @ V2) @ V3))) @ cFunDef.min_strict)))))))))))))
(TFunDef.wf_pair_less,(cWellfounded.wf @ cFunDef.pair_less))
(TFunDef.wmax_insertI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ cFunDef.pair_leq)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V1)) @ cFunDef.max_weak)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cSet.insert @ V2) @ V3)) @ V1)) @ cFunDef.max_weak)))))))))))))
(TFunDef.wmin_insertI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ cFunDef.pair_leq)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ cFunDef.min_weak)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ ((cSet.insert @ V2) @ V3))) @ cFunDef.min_weak)))))))))))))
(TGroups.monoid.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.semigroup @ V0)) @ ((c==> @ ((cGroups.monoid_axioms @ V0) @ V1)) @ ((cGroups.monoid @ V0) @ V1))))))))
(TGroups.one_reorient,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ V0)) @ ((cHOL.eq @ V0) @ cGroups.one_class.one)))))
(THOL.arity_type_bool,(cHOL.type_class @ cTYPE))
(THOL.class.equal_def,(call @ (^[V0]: ((c== @ (cHOL.class.equal @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((cHOL.eq @ V1) @ V2))))))))))
(THOL.eq_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cHOL.eq @ V1) @ V2))) @ ((cHOL.eq @ V1) @ ((cHOL.eq @ V0) @ V2))))))))))
(THOL.equal_class_def,((c== @ (cHOL.equal_class @ cTYPE)) @ ((cPure.conjunction @ (cHOL.type_class @ cTYPE)) @ (cHOL.class.equal @ cHOL.equal_class.equal))))
(THOL.eta_contract_eq,(call @ (^[V0]: ((cHOL.eq @ (^[V1]: (V0 @ V1))) @ V0))))
(THOL.ex_disj_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(THOL.excluded_middle,(call @ (^[V0]: ((cHOL.disj @ (cHOL.Not @ V0)) @ V0))))
(THOL.if_bool_eq_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ V2))))))))))
(THOL.if_bool_eq_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ V2))))))))))
(THOL.induct_atomize'_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPure.conjunction @ V0) @ V1)) @ ((cHOL.induct_conj @ V0) @ V1)))))))
(THOL.induct_atomize'_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c==> @ V0) @ V1)) @ ((cHOL.induct_implies @ V0) @ V1)))))))
(THOL.induct_atomize'_1,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (cHOL.induct_forall @ (^[V1]: (V0 @ V1)))))))
(THOL.induct_conj_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_conj @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V1)))))))
(THOL.induct_equal_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c== @ V0) @ V1)) @ ((cHOL.induct_equal @ V0) @ V1)))))))
(THOL.induct_true_def,((c== @ cHOL.True) @ cHOL.True))
(TInductive.coinduct3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V0 @ (cInductive.complete_lattice_class.lfp @ (^[V3]: ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ (V0 @ V3)) @ V2)) @ (cInductive.complete_lattice_class.gfp @ V0))))))) @ ((cSet.member @ V1) @ (cInductive.complete_lattice_class.gfp @ V0))))))))))))
(TInductive.gfp_least,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V0 @ V2))) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.gfp @ V0)) @ V1)))))))
(TInductive.lfp_const,(call @ (^[V0]: ((cHOL.eq @ (cInductive.complete_lattice_class.lfp @ (^[V1]: V0))) @ V0))))
(TInt.Ints_odd_less_0,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ V0)) @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero))))))
(TInt.Let_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.Let @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V1)) @ (V1 @ (cNum.neg_numeral_class.neg_numeral @ V0))))))))
(TInt.arity_equal_int,(cHOL.equal_class @ cTYPE))
(TInt.divide_Numeral1,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ (cNum.numeral_class.numeral @ cNum.num.One))) @ V0))))
(TInt.double_eq_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TInt.even_less_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TInt.int.right_total,(cTransfer.right_total @ cInt.cr_int))
(TInt.int_arith_rules_24,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cInt.times_int_inst.times_int @ V0) @ V1))) @ ((cGroups.times_class.times @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))))))))
(TInt.int_arith_rules_23,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))))))))
(TInt.int_arith_rules_22,((cHOL.eq @ (cInt.ring_1_class.of_int @ cInt.one_int_inst.one_int)) @ cGroups.one_class.one))
(TInt.int_arith_rules_21,((cHOL.eq @ (cInt.ring_1_class.of_int @ cInt.zero_int_inst.zero_int)) @ cGroups.zero_class.zero))
(TInt.int_arith_rules_20,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TInt.int_arith_rules_19,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TInt.int_arith_rules_18,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V0))) @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNat.semiring_1_class.of_nat @ V0))))))
(TInt.int_arith_rules_17,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ cNat.one_nat_inst.one_nat)) @ cGroups.one_class.one))
(TInt.int_arith_rules_16,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ cNat.zero_nat_inst.zero_nat)) @ cGroups.zero_class.zero))
(TInt.int_arith_rules_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TInt.int_arith_rules_14,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cGroups.uminus_class.uminus @ V0))) @ V0))))
(TInt.int_arith_rules_13,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.plus_class.plus @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TInt.int_arith_rules_12,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cGroups.times_class.times @ V0) @ V1))))))))
(TInt.int_arith_rules_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ (cGroups.uminus_class.uminus @ ((cGroups.times_class.times @ V0) @ V1))))))))
(TInt.int_arith_rules_10,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.one_class.one)) @ V0))))
(TInt.int_arith_rules_9,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.one_class.one) @ V0)) @ V0))))
(TInt.int_arith_rules_8,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TInt.int_arith_rules_7,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TInt.int_arith_rules_6,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ cGroups.zero_class.zero))))
(TInt.int_arith_rules_5,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ cGroups.zero_class.zero))))
(TInt.int_arith_rules_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TInt.int_arith_rules_3,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TInt.int_arith_rules_2,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ cGroups.one_class.one))
(TInt.int_arith_rules_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TInt.int_less_0_conv,(call @ (^[V0]: (cHOL.Not @ ((cInt.ord_int_inst.less_int @ (cNat.semiring_1_class.of_nat @ V0)) @ cInt.zero_int_inst.zero_int)))))
(TInt.int_less_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((c==> @ (V2 @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ V3) @ V1)) @ ((c==> @ (V2 @ V3)) @ (V2 @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))))))) @ (V2 @ V0)))))))))))
(TInt.less_eq_int.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ ((cTransfer.fun_rel @ cInt.intrel) @ cHOL.eq)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TInt.less_eq_int_def,((c== @ cInt.ord_int_inst.less_eq_int) @ (((cFun.map_fun @ cInt.Rep_Integ) @ ((cFun.map_fun @ cInt.Rep_Integ) @ cFun.id)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1)))))))))))
(TInt.less_int.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.Abs_Integ @ V0)) @ (cInt.Abs_Integ @ V1))) @ (((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V5)) @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V3)))))))) @ V0) @ V1)))))))
(TInt.less_int.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ (((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V5)) @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V3)))))))) @ (cInt.Rep_Integ @ V0)) @ (cInt.Rep_Integ @ V1))))))))
(TInt.nat_add_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ (cInt.nat @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))))))))))
(TInt.nat_neg_numeral,(call @ (^[V0]: ((cHOL.eq @ (cInt.nat @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TInt.one_less_nat_eq,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ (cInt.nat @ V0))) @ ((cInt.ord_int_inst.less_int @ cInt.one_int_inst.one_int) @ V0)))))
(TInt.plus_int.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cInt.Abs_Integ @ V0)) @ (cInt.Abs_Integ @ V1))) @ (cInt.Abs_Integ @ (((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V4)) @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V5)))))))) @ V0) @ V1))))))))
(TInt.ring_1.Ints_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cSet.member @ V6) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((c==> @ ((cSet.member @ V7) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((cSet.member @ ((V2 @ V6) @ V7)) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))))))))))))))))))))))
(TInt.ring_1.Ints_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4)) @ ((cSet.image @ ((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4)) @ cOrderings.top_class.top))))))))))))))))
(TInt.ring_1.of_int_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ cInt.zero_int_inst.zero_int)) @ V3)))))))))))))))
(TInt.ring_1.of_int_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ cInt.one_int_inst.one_int)) @ V0)))))))))))))))
(TInt.uminus_int_code_3,(call @ (^[V0]: ((cHOL.eq @ (cInt.uminus_int_inst.uminus_int @ (cInt.Neg @ V0))) @ (cInt.Pos @ V0)))))
(TInt.uminus_int_code_2,(call @ (^[V0]: ((cHOL.eq @ (cInt.uminus_int_inst.uminus_int @ (cInt.Pos @ V0))) @ (cInt.Neg @ V0)))))
(TInt.uminus_int_code_1,((cHOL.eq @ (cInt.uminus_int_inst.uminus_int @ cInt.zero_int_inst.zero_int)) @ cInt.zero_int_inst.zero_int))
(TInt.zero_int.abs_eq,((cHOL.eq @ cInt.zero_int_inst.zero_int) @ (cInt.Abs_Integ @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat))))
(TLattices.sup_boolI1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((cLattices.sup_bool_inst.sup_bool @ V0) @ V1)))))))
(TLattices.sup_boolI2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((cLattices.sup_bool_inst.sup_bool @ V1) @ V0)))))))
(TLifting.apply_rsp'',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cTransfer.fun_rel @ V0) @ V4) @ V5) @ V5)) @ ((V4 @ (V5 @ (V2 @ V6))) @ (V5 @ (V2 @ V6))))))))))))))))))))
(TLifting.in_respects,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cLifting.Respects @ V1))) @ ((V1 @ V0) @ V0)))))))
(TLifting.left_totalE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_total @ V0)) @ ((c==> @ ((c==> @ (call @ (^[V2]: (cHOL.Ex @ (^[V3]: ((V0 @ V2) @ V3)))))) @ V1)) @ V1)))))))
(TLifting.left_totalI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cLifting.left_total @ V0)))))
(TLifting.pcr_Domainp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((cHOL.eq @ (cRelation.Domainp @ ((cRelation.relcompp @ V2) @ V0))) @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V2 @ V3) @ V4)) @ (V1 @ V4))))))))))))))
(TList.ListMem.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.ListMem @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ V3) @ ((cList.list.Cons @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cList.ListMem @ V3) @ V4)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ V3) @ ((cList.list.Cons @ V5) @ V4))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.ListMem.insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.ListMem @ V0) @ V1)) @ ((cList.ListMem @ V0) @ ((cList.list.Cons @ V2) @ V1))))))))))
(TList.ListMem.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.ListMem @ V0) @ V1)) @ ((cList.ListMem @ V0) @ ((cList.list.Cons @ V2) @ V1))))))))))
(TList.ListMem.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((cList.ListMem @ V0) @ ((cList.list.Cons @ V0) @ V1)))))))
(TList.Nil2_notin_lex,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil)) @ (cList.lex @ V1))))))))
(TList.append_same_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ ((cList.append @ V2) @ V1))) @ ((cHOL.eq @ V0) @ V2)))))))))
(TList.butlast_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.butlast @ ((cList.append @ V0) @ V1))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ (cList.butlast @ V0)) @ ((cList.append @ V0) @ (cList.butlast @ V1)))))))))
(TList.can_select_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.can_select @ V0) @ V1)) @ (cHOL.Ex1 @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V1)) @ (V0 @ V2))))))))))
(TList.distinct.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.distinct @ ((cList.list.Cons @ V0) @ V1))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ (cList.distinct @ V1))))))))
(TList.distinct.simps_1,((cHOL.eq @ (cList.distinct @ cList.list.Nil)) @ cHOL.True))
(TList.distinct_zipI1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.zip @ V0) @ V1))))))))
(TList.distinct_zipI2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.zip @ V1) @ V0))))))))
(TList.drop.drop_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cNat.nat.nat_case @ ((cList.list.Cons @ V1) @ V2)) @ (^[V3]: ((cList.drop @ V3) @ V2))) @ V0)))))))))
(TList.dropWhile_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V0))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cList.dropWhile @ V2) @ V0)) @ ((cList.dropWhile @ V3) @ V1)))))))))))))
(TList.dropWhile_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.dropWhile @ V0) @ ((cList.dropWhile @ V0) @ V1))) @ ((cList.dropWhile @ V0) @ V1)))))))
(TList.dropWhile_last,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ (cHOL.Not @ (V2 @ V0))) @ ((cHOL.eq @ (cList.last @ ((cList.dropWhile @ V2) @ V1))) @ (cList.last @ V1)))))))))))
(TList.drop_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ V0) @ ((cList.replicate @ V1) @ V2))) @ ((cList.replicate @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)))))))))
(TList.embed_list_def,(call @ (^[V0]: ((cHOL.eq @ (cList.embed_list @ V0)) @ ((cList.map @ cNat.semiring_1_class.of_nat) @ V0)))))
(TList.eq_Nil_appendI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ ((cList.append @ cList.list.Nil) @ V1))))))))
(TList.equal_Nil_null_2,((cHOL.eq @ (cHOL.equal_class.equal @ cList.list.Nil)) @ cList.null))
(TList.equal_Nil_null_1,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ cList.list.Nil)) @ (cList.null @ V0)))))
(TList.equal_list_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TList.ex_nat_less_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V2) @ V0)) @ (V1 @ V2))))) @ ((cSet.Bex @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (^[V2]: (V1 @ V2)))))))))
(TList.filter_id_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.filter @ V0) @ V1)) @ V1)) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: (V0 @ V2)))))))))
(TList.filter_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.filter @ V0) @ ((cList.remove1 @ V1) @ V2))) @ ((cList.remove1 @ V1) @ ((cList.filter @ V0) @ V2))))))))))
(TList.find_dropWhile,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.find @ V0) @ V1)) @ (((cList.list.list_case @ cOption.option.None) @ (^[V2]: (^[V3]: (cOption.option.Some @ V2)))) @ ((cList.dropWhile @ ((cFun.comp @ cHOL.Not) @ V0)) @ V1))))))))
(TList.fold.fold_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.fold @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cFun.comp @ ((cList.fold @ V0) @ V2)) @ (V0 @ V1))))))))))
(TList.fold_invariant,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ (cList.set @ V0))) @ (V1 @ V5))))) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (V1 @ V5)) @ ((c==> @ (V2 @ V6)) @ (V2 @ ((V4 @ V5) @ V6))))))))) @ (V2 @ (((cList.fold @ V4) @ V0) @ V3))))))))))))))))
(TList.fold_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.fold @ V0) @ ((cList.replicate @ V1) @ V2))) @ ((cNat.compow @ V1) @ (V0 @ V2))))))))))
(TList.foldl_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ V0))) @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ V0))) @ cList.foldl) @ cList.foldl))))))
(TList.foldr_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ V1))) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ V1) @ V1))) @ cList.foldr) @ cList.foldr))))))
(TList.gen_length_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.gen_length @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ (cNat.size_class.size @ V1))))))))
(TList.in_set_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ ((cList.remove1 @ V1) @ V2)))) @ ((cSet.member @ V0) @ (cList.set @ V2)))))))))))
(TList.inj_map_eq_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TList.inj_split_Cons,(call @ (^[V0]: ((cFun.inj_on @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cList.list.Cons @ V2) @ V1))))) @ V0))))
(TList.insert_remdups,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.insert @ V0) @ (cList.remdups @ V1))) @ (cList.remdups @ ((cList.insert @ V0) @ V1))))))))
(TList.last_replicate,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ (cList.last @ ((cList.replicate @ V0) @ V1))) @ V1)))))))
(TList.length_butlast,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.butlast @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat)))))
(TList.length_n_lists,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.n_lists @ V0) @ V1))) @ ((cPower.power_class.power @ (cNat.size_class.size @ V1)) @ V0)))))))
(TList.length_product,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.product @ V0) @ V1))) @ ((cNat.times_nat_inst.times_nat @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))
(TList.length_remove1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.remove1 @ V0) @ V1))) @ (((cHOL.If @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V1)) @ cNat.one_nat_inst.one_nat)) @ (cNat.size_class.size @ V1))))))))
(TList.length_rotate1,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.rotate1 @ V0))) @ (cNat.size_class.size @ V0)))))
(TList.length_sublist,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.sublist @ V0) @ V1))) @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cSet.member @ V2) @ V1)))))))))))
(TList.list.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V6) @ V7))) @ ((cHOL.eq @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))) @ ((cHOL.eq @ (((cList.list.list_case @ V2) @ V4) @ V0)) @ (((cList.list.list_case @ V3) @ V5) @ V1))))))))))))))))))
(TList.list.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cList.list.list_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ (cHOL.Not @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))))
(TList.list_all2_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ ((cList.list.Cons @ V1) @ V2)) @ ((cList.list.Cons @ V3) @ V4))) @ ((cHOL.conj @ ((V0 @ V1) @ V3)) @ (((cList.list_all2 @ V0) @ V2) @ V4))))))))))))))
(TList.list_all2_Nil2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ V1) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.list_all2_map1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ ((cList.map @ V1) @ V2)) @ V3)) @ (((cList.list_all2 @ (^[V4]: (^[V5]: ((V0 @ (V1 @ V4)) @ V5)))) @ V2) @ V3)))))))))))
(TList.list_all2_map2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ V1) @ ((cList.map @ V2) @ V3))) @ (((cList.list_all2 @ (^[V4]: (^[V5]: ((V0 @ V4) @ (V2 @ V5))))) @ V1) @ V3)))))))))))
(TList.list_all2_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V3 @ V4) @ V5))))))) @ (((cList.list_all2 @ V3) @ V1) @ V2))))))))))))
(TList.list_all2_nthD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V1))) @ ((V0 @ ((cList.nth @ V1) @ V3)) @ ((cList.nth @ V2) @ V3)))))))))))))
(TList.list_all2_refl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((V0 @ V2) @ V2)))) @ (((cList.list_all2 @ V0) @ V1) @ V1)))))))
(TList.list_all2_rev1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ (cList.rev @ V1)) @ V2)) @ (((cList.list_all2 @ V0) @ V1) @ (cList.rev @ V2))))))))))
(TList.list_all_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cList.list_all @ V0) @ cList.list.Nil)) @ cHOL.True))))
(TList.list_all_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_all @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cHOL.conj @ (V0 @ V1)) @ ((cList.list_all @ V0) @ V2))))))))))
(TList.list_ex1_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_ex1 @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ (V0 @ V1)) @ ((cList.list_all @ (^[V3]: ((cHOL.disj @ (cHOL.Not @ (V0 @ V3))) @ ((cHOL.eq @ V1) @ V3)))) @ V2)) @ ((cList.list_ex1 @ V0) @ V2))))))))))
(TList.list_ex1_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.list_ex1 @ V0) @ cList.list.Nil)) @ cHOL.False))))
(TList.list_ex_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_ex @ V0) @ ((cList.append @ V1) @ V2))) @ ((cHOL.disj @ ((cList.list_ex @ V0) @ V1)) @ ((cList.list_ex @ V0) @ V2))))))))))
(TList.list_ex_length,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list_ex @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V1))) @ (V0 @ ((cList.nth @ V1) @ V2)))))))))))
(TList.list_update_id,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list_update @ V0) @ V1) @ ((cList.nth @ V0) @ V1))) @ V0))))))
(TList.listrel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((c==> @ ((V3 @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ (cList.listrel @ V2))) @ ((c==> @ ((V3 @ V6) @ V7)) @ ((V3 @ ((cList.list.Cons @ V4) @ V6)) @ ((cList.list.Cons @ V5) @ V7)))))))))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TList.listrel.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (cList.listrel @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V3)) @ ((cList.list.Cons @ V1) @ V4))) @ (cList.listrel @ V2)))))))))))))))
(TList.listrel.intros_1,(call @ (^[V0]: ((cSet.member @ ((cProduct_Type.Pair @ cList.list.Nil) @ cList.list.Nil)) @ (cList.listrel @ V0)))))
(TList.listrel_eq_len,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))))
(TList.listrel_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V2]: V1)))) @ ((cOrderings.ord_class.less_eq @ (cList.listrel @ V0)) @ ((cProduct_Type.Sigma @ (cList.lists @ V1)) @ (^[V2]: (cList.lists @ V1))))))))))
(TList.listrelp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.listrelp @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ V3))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V5) @ V7))) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ (((cList.listrelp @ V0) @ V6) @ V7)) @ V3))))))))))))) @ V3))))))))))))
(TList.listrelp.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.listrelp @ V0) @ V1) @ V2)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((cHOL.eq @ V2) @ cList.list.Nil))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ V6))) @ ((cHOL.conj @ ((V0 @ V3) @ V4)) @ (((cList.listrelp @ V0) @ V5) @ V6)))))))))))))))))))))
(TList.lists_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ (cList.list_all2 @ V0))) @ cList.lists) @ cList.lists))))
(TList.listsp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.listsp @ V0) @ V1)) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V3)) @ ((c==> @ ((cList.listsp @ V0) @ V4)) @ ((c==> @ (V2 @ V4)) @ (V2 @ ((cList.list.Cons @ V3) @ V4)))))))))) @ (V2 @ V1)))))))))))
(TList.listsp_conj_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.listsp @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V2))))) @ (^[V2]: ((cHOL.conj @ ((cList.listsp @ V0) @ V2)) @ ((cList.listsp @ V1) @ V2)))))))))
(TList.map_filter_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map_filter @ V0) @ V1)) @ ((cList.map @ ((cFun.comp @ cOption.the) @ V0)) @ ((cList.filter @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (V0 @ V2)) @ cOption.option.None)))) @ V1))))))))
(TList.minus_set_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ (cList.set @ V1))) @ (((cList.fold @ cSet.remove) @ V1) @ V0)))))))
(TList.not_Cons_self2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ V1)))))))
(TList.nth_take_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.size_class.size @ V2))) @ ((c==> @ (call @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ ((cHOL.eq @ ((cList.nth @ V1) @ V3)) @ ((cList.nth @ V2) @ V3)))))) @ ((cHOL.eq @ ((cList.take @ V0) @ V1)) @ ((cList.take @ V0) @ V2))))))))))))
(TList.remdups_filter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.remdups @ ((cList.filter @ V0) @ V1))) @ ((cList.filter @ V0) @ (cList.remdups @ V1))))))))
(TList.remove1_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.remove1 @ V0) @ ((cList.append @ V1) @ V2))) @ (((cHOL.If @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cList.append @ ((cList.remove1 @ V0) @ V1)) @ V2)) @ ((cList.append @ V1) @ ((cList.remove1 @ V0) @ V2)))))))))))
(TList.same_append_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ ((cList.append @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2)))))))))
(TList.set_dropWhileD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ ((cList.dropWhile @ V1) @ V2)))) @ ((cSet.member @ V0) @ (cList.set @ V2))))))))))
(TList.set_remove1_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ (cList.set @ ((cList.remove1 @ V1) @ V0))) @ ((cGroups.minus_class.minus @ (cList.set @ V0)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))
(TList.set_takeWhileD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ ((cList.takeWhile @ V1) @ V2)))) @ ((cHOL.conj @ ((cSet.member @ V0) @ (cList.set @ V2))) @ (V1 @ V0))))))))))
(TList.set_zip_rightD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.set @ ((cList.zip @ V2) @ V3)))) @ ((cSet.member @ V1) @ (cList.set @ V3))))))))))))
(TList.splice.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V3))) @ ((V2 @ cList.list.Nil) @ V3))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ cList.list.Nil))) @ ((V2 @ ((cList.list.Cons @ V3) @ V4)) @ cList.list.Nil))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cList.splice_rel) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6)))) @ ((c==> @ ((V2 @ V4) @ V6)) @ ((V2 @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6))))))))))))) @ ((V2 @ V0) @ V1))))))))))))
(TList.splice_rel_def,((c== @ cList.splice_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V6))) @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6))))))))))))))))))
(TList.sublist_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.sublist @ ((cList.append @ V0) @ V1)) @ V2)) @ ((cList.append @ ((cList.sublist @ V0) @ V2)) @ ((cList.sublist @ V1) @ (cSet.Collect @ (^[V3]: ((cSet.member @ ((cNat.plus_nat_inst.plus_nat @ V3) @ (cNat.size_class.size @ V0))) @ V2)))))))))))))
(TList.sublists.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.sublists @ ((cList.list.Cons @ V0) @ V1))) @ ((cHOL.Let @ (cList.sublists @ V1)) @ (^[V2]: ((cList.append @ ((cList.map @ (cList.list.Cons @ V0)) @ V2)) @ V2)))))))))
(TList.sublists.simps_1,((cHOL.eq @ (cList.sublists @ cList.list.Nil)) @ ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil)))
(TList.take.take_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cNat.nat.nat_case @ cList.list.Nil) @ (^[V3]: ((cList.list.Cons @ V1) @ ((cList.take @ V3) @ V2)))) @ V0)))))))))
(TList.takeWhile_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V0))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cList.takeWhile @ V2) @ V0)) @ ((cList.takeWhile @ V3) @ V1)))))))))))))
(TList.takeWhile_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.takeWhile @ V0) @ ((cList.takeWhile @ V0) @ V1))) @ ((cList.takeWhile @ V0) @ V1)))))))
(TList.takeWhile_tail,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ (V0 @ V1))) @ ((cHOL.eq @ ((cList.takeWhile @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V1) @ V3)))) @ ((cList.takeWhile @ V0) @ V2))))))))))))
(TList.take_equalityI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((cList.take @ V2) @ V0)) @ ((cList.take @ V2) @ V1))))) @ ((cHOL.eq @ V0) @ V1)))))))
(TList.take_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ V0) @ ((cList.replicate @ V1) @ V2))) @ ((cList.replicate @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)))))))))
(TList.union_set_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cList.set @ V0)) @ V1)) @ (((cList.fold @ cSet.insert) @ V0) @ V1)))))))
(TList.upt_Suc_append,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cList.upt @ V0) @ (cNat.Suc @ V1))) @ ((cList.append @ ((cList.upt @ V0) @ V1)) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))))))
(TList.upto_graph_def,((c== @ cList.upto_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.list.Cons @ V4) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)))) @ cList.list.Nil))) @ ((cHOL.induct_implies @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((V0 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))))))))))))))))))
(TList.upto_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)) @ V2)))))))) @ V2)))))))))
(TList.upto_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V2) @ cInt.one_int_inst.one_int)) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cInt.ord_int_inst.less_eq_int @ V2) @ V3)))))))))))))
(TMap.dom_override_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cMap.dom @ (((cFun.override_on @ V0) @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cGroups.minus_class.minus @ (cMap.dom @ V0)) @ (cSet.Collect @ (^[V3]: ((cSet.member @ V3) @ ((cGroups.minus_class.minus @ V2) @ (cMap.dom @ V1))))))) @ (cSet.Collect @ (^[V3]: ((cSet.member @ V3) @ ((cLattices.inf_class.inf @ V2) @ (cMap.dom @ V1))))))))))))))
(TMap.map_add_le_mapE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cMap.map_le @ ((cMap.map_add @ V0) @ V1)) @ V2)) @ ((cMap.map_le @ V1) @ V2)))))))))
(TMap.map_add_le_mapI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cMap.map_le @ V0) @ V1)) @ ((c==> @ ((cMap.map_le @ V2) @ V1)) @ ((cMap.map_le @ ((cMap.map_add @ V0) @ V2)) @ V1))))))))))
(TMap.map_of_is_SomeD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cMap.map_of @ V0) @ V1)) @ (cOption.option.Some @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.set @ V0))))))))))
(TMap.map_of_is_SomeI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.distinct @ ((cList.map @ cProduct_Type.fst) @ V0))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cMap.map_of @ V0) @ V1)) @ (cOption.option.Some @ V2)))))))))))
(TMap.map_of_map_keys,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cList.set @ V0)) @ (cMap.dom @ V1))) @ ((cHOL.eq @ (cMap.map_of @ ((cList.map @ (^[V2]: ((cProduct_Type.Pair @ V2) @ (cOption.the @ (V1 @ V2))))) @ V0))) @ V1)))))))
(TMap.upd_None_map_le,(call @ (^[V0]: (call @ (^[V1]: ((cMap.map_le @ (((cFun.fun_upd @ V0) @ V1) @ cOption.option.None)) @ V0))))))
(TMeson.disj_forward2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.disj @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ V2)) @ ((c==> @ ((c==> @ V1) @ ((c==> @ ((c==> @ V2) @ cHOL.False)) @ V3))) @ ((cHOL.disj @ V2) @ V3)))))))))))))
(TMeson.make_neg_goal,(call @ (^[V0]: ((c==> @ (cHOL.Not @ V0)) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V0)) @ cHOL.False)))))
(TMeson.make_neg_rule,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V0)) @ V1)))))))
(TMeson.make_pos_goal,(call @ (^[V0]: ((c==> @ V0) @ ((c==> @ ((c==> @ V0) @ (cHOL.Not @ V0))) @ cHOL.False)))))
(TMeson.make_pos_rule,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ V0) @ V1)) @ ((c==> @ ((c==> @ V0) @ (cHOL.Not @ V0))) @ V1)))))))
(TMetis.select_FalseI,((c==> @ cHOL.False) @ (cMetis.select @ cHOL.False)))
(TNat.Suc_Rep_inject',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Suc_Rep @ V0)) @ (cNat.Suc_Rep @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.add_diff_assoc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2)) @ V0))))))))))
(TNat.arity_equal_nat,(cHOL.equal_class @ cTYPE))
(TNat.def_nat_rec_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c== @ (V0 @ V4)) @ (((cNat.nat.nat_rec @ V1) @ V2) @ V4))))) @ ((cHOL.eq @ (V0 @ (cNat.Suc @ V3))) @ ((V2 @ V3) @ (V0 @ V3)))))))))))))
(TNat.diff_add_assoc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2)) @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2))))))))))
(TNat.diff_diff_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V2) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0)) @ V1))))))))))
(TNat.diff_less_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V1)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V0)))))))))))
(TNat.dvd.less_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.dvd.less_irrefl,(call @ (^[V0]: (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V0)))))))
(TNat.dvd.order.trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TNat.dvd.order_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TNat.dvd_mult_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))
(TNat.ex_least_nat_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (V0 @ cNat.zero_nat_inst.zero_nat))) @ ((c==> @ (V0 @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V2)) @ (cHOL.Not @ (V0 @ V3)))))) @ (V0 @ V2))))))))))))
(TNat.full_nat_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V3)) @ V2)) @ (V0 @ V3))))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TNat.funpow_code_def,((cHOL.eq @ cNat.funpow) @ cNat.compow))
(TNat.gr0_implies_Suc,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNat.Suc @ V1))))))))
(TNat.gr_implies_not0,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TNat.inj_on_diff_nat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)))) @ ((cFun.inj_on @ (^[V2]: ((cNat.minus_nat_inst.minus_nat @ V2) @ V1))) @ V0)))))))
(TNat.le_imp_less_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))))))))
(TNat.less_Suc_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ V3) @ (cNat.Suc @ V3))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V4)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V4) @ V5)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((c==> @ ((V2 @ V4) @ V5)) @ ((V2 @ V3) @ V5)))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TNat.less_diff_conv2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0)))))))))))
(TNat.less_eq_nat_def,((c== @ cNat.ord_nat_inst.less_eq_nat) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: cHOL.True)) @ (^[V1]: (^[V2]: (^[V3]: (((cNat.nat.nat_case @ cHOL.False) @ (^[V4]: (V2 @ V4))) @ V3))))) @ V0))))
(TNat.less_imp_le_nat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.less_irrefl_nat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V0)) @ V1))))))
(TNat.lfp_Kleene_iter,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cHOL.eq @ (((cNat.compow @ (cNat.Suc @ V1)) @ V0) @ cOrderings.bot_class.bot)) @ (((cNat.compow @ V1) @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ (((cNat.compow @ V1) @ V0) @ cOrderings.bot_class.bot)))))))))
(TNat.minus_nat.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.Suc @ V1))) @ (((cNat.nat.nat_case @ cNat.zero_nat_inst.zero_nat) @ (^[V2]: V2)) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))))))))
(TNat.minus_nat.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V0))))
(TNat.mono_iff_le_Suc,(call @ (^[V0]: ((cHOL.eq @ (cOrderings.order_class.mono @ V0)) @ (cHOL.All @ (^[V1]: ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ (cNat.Suc @ V1)))))))))
(TNat.mult_le_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2))))))))))
(TNat.mult_le_cancel2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V2) @ V1))) @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2))))))))))
(TNat.mult_less_mono1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)))))))))))
(TNat.mult_less_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V0)) @ ((cNat.times_nat_inst.times_nat @ V2) @ V1)))))))))))
(TNat.n_less_m_mult_n,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V0)))))))))
(TNat.n_less_n_mult_m,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)))))))))
(TNat.nat.nat_rec_def,((c== @ cNat.nat.nat_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cNat.nat.nat_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TNat.nat_add_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V0)))))))
(TNat.nat_dvd_1_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ V0) @ cNat.one_nat_inst.one_nat)))))
(TNat.nat_less_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V2)) @ (V0 @ V3))))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TNat.one_eq_mult_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TNat.one_le_mult_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V1))))))))
(TNat.times_nat.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))))))))
(TNat.times_nat.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TNat.trans_less_add1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TNat.trans_less_add2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TNat_Transfer.ex_nat,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ (cInt.nat @ V1)))))))))
(TNitpick.int_gcd_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.int_gcd @ V0) @ V1)) @ (cNat.semiring_1_class.of_nat @ ((cNitpick.nat_gcd @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V0))) @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V1))))))))))
(TNitpick.int_lcm_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.int_lcm @ V0) @ V1)) @ (cNat.semiring_1_class.of_nat @ ((cNitpick.nat_lcm @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V0))) @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V1))))))))))
(TNitpick.nat_gcd_def,((c== @ cNitpick.nat_gcd) @ (^[V0]: (^[V1]: (cNitpick.nat_gcd_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TNitpick.nat_lcm_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.nat_lcm @ V0) @ V1)) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNitpick.nat_gcd @ V0) @ V1))))))))
(TNitpick.of_frac_def,(call @ (^[V0]: ((c== @ (cNitpick.of_frac @ V0)) @ ((cFields.inverse_class.divide @ (cInt.ring_1_class.of_int @ (cNitpick.num @ V0))) @ (cInt.ring_1_class.of_int @ (cNitpick.denom @ V0)))))))
(TNitpick.setsum'_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cNitpick.setsum' @ V0) @ V1)) @ (((cHOL.If @ (cFinite_Set.finite @ V1)) @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ (cHilbert_Choice.Eps @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (cList.set @ V2)) @ V1)) @ (cList.distinct @ V2))))))) @ cGroups.zero_class.zero)))))))
(TNitpick.word.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cNitpick.word.Word @ V2))))) @ (V0 @ V1)))))))
(TNitpick.word.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNitpick.word.Word @ V0)) @ (cNitpick.word.Word @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.word.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.word.word_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cNitpick.word.Word @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TNitpick.word.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.word.word_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cNitpick.word.Word @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TNum.add_One_commute,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0)) @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One)))))
(TNum.arity_equal_num,(cHOL.equal_class @ cTYPE))
(TNum.arity_times_num,(cGroups.times_class @ cTYPE))
(TNum.less_eq_num_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V1))))))))
(TNum.max_Suc_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNat.Suc @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNat.Suc @ ((cOrderings.ord_class.max @ V0) @ (cNum.pred_numeral @ V1)))))))))
(TNum.max_numeral_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNum.numeral_class.numeral @ V0)) @ (cNat.Suc @ V1))) @ (cNat.Suc @ ((cOrderings.ord_class.max @ (cNum.pred_numeral @ V0)) @ V1))))))))
(TNum.min_Suc_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNat.Suc @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNat.Suc @ ((cOrderings.ord_class.min @ V0) @ (cNum.pred_numeral @ V1)))))))))
(TNum.min_numeral_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ (cNum.numeral_class.numeral @ V0)) @ (cNat.Suc @ V1))) @ (cNat.Suc @ ((cOrderings.ord_class.min @ (cNum.pred_numeral @ V0)) @ V1))))))))
(TNum.nat_of_num_code_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.nat_of_num @ (cNum.num.Bit1 @ V0))) @ ((cHOL.Let @ (cNum.nat_of_num @ V0)) @ (^[V1]: (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V1))))))))
(TNum.nat_of_num_code_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.nat_of_num @ (cNum.num.Bit0 @ V0))) @ ((cHOL.Let @ (cNum.nat_of_num @ V0)) @ (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ V1)))))))
(TNum.nat_of_num_code_1,((cHOL.eq @ (cNum.nat_of_num @ cNum.num.One)) @ cNat.one_nat_inst.one_nat))
(TNum.nat_of_num_mult,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNum.nat_of_num @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ ((cNat.times_nat_inst.times_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V1))))))))
(TNum.nat_rec_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ (cNum.numeral_class.numeral @ V2))) @ ((cHOL.Let @ (cNum.pred_numeral @ V2)) @ (^[V3]: ((V1 @ V3) @ (((cNat.nat.nat_rec @ V0) @ V1) @ V3))))))))))))
(TNum.num.num_rec_def,((c== @ cNum.num.num_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cHOL.The @ (^[V4]: (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)))))))))
(TNum.ring_1.iszero_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cNum.ring_1.iszero @ V3) @ V3)))))))))))))))
(TOption.is_none_code_2,(call @ (^[V0]: ((cHOL.eq @ (cOption.is_none @ (cOption.option.Some @ V0))) @ cHOL.False))))
(TOption.is_none_code_1,((cHOL.eq @ (cOption.is_none @ cOption.option.None)) @ cHOL.True))
(TOption.map.identity,((cHOL.eq @ (cOption.map @ (^[V0]: V0))) @ cFun.id))
(TOption.option.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cOption.option.option_case @ V0) @ V1) @ (cOption.option.Some @ V2))) @ (V1 @ V2)))))))))
(TOption.option.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cOption.option.option_case @ V0) @ V1) @ cOption.option.None)) @ V0))))))
(TOption.option.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cOption.option.option_rec @ V0) @ V1) @ (cOption.option.Some @ V2))) @ (V1 @ V2)))))))))
(TOption.option.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cOption.option.option_rec @ V0) @ V1) @ cOption.option.None)) @ V0))))))
(TOption.option.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cOption.option.option_case @ V0) @ V1) @ (cOption.option.Some @ V2))) @ (V1 @ V2)))))))))
(TOption.option.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cOption.option.option_case @ V0) @ V1) @ cOption.option.None)) @ V0))))))
(TOption.option.simps_3,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cOption.option.Some @ V0)) @ cOption.option.None)))))
(TOption.option.simps_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOption.option.None) @ (cOption.option.Some @ V0))))))
(TOption.option.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cOption.option.Some @ V0)) @ (cOption.option.Some @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TOption.option.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cOption.option.option_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cOption.option.None)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cOption.option.Some @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TOption.option_caseE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOption.option.option_case @ V0) @ (^[V4]: (V1 @ V4))) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cOption.option.None)) @ ((c==> @ V0) @ V3))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V2) @ (cOption.option.Some @ V4))) @ ((c==> @ (V1 @ V4)) @ V3))))) @ V3))))))))))))
(TOption.set_empty_eq,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cOption.set @ V0)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOption.option.None)))))
(TOrderings.bot_apply,(call @ (^[V0]: ((cHOL.eq @ (cOrderings.bot_class.bot @ V0)) @ cOrderings.bot_class.bot))))
(TOrderings.bot_boolE,(call @ (^[V0]: ((c==> @ cOrderings.bot_bool_inst.bot_bool) @ V0))))
(TOrderings.le_boolI',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((cOrderings.ord_bool_inst.less_eq_bool @ V0) @ V1)))))))
(TOrderings.top_apply,(call @ (^[V0]: ((cHOL.eq @ (cOrderings.top_class.top @ V0)) @ cOrderings.top_class.top))))
(TOrderings.top_boolI,cOrderings.top_bool_inst.top_bool)
(TPower.power_inverse,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFields.inverse_class.inverse @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ (cFields.inverse_class.inverse @ V0)) @ V1)))))))
(TPredicate.Pred_eval,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.pred.Pred @ (cPredicate.eval @ V0))) @ V0))))
(TPredicate.apply_def,((c== @ cPredicate.apply) @ (^[V0]: (^[V1]: (((((cPredicate.seq.seq_rec @ (^[V2]: cPredicate.seq.Empty)) @ (^[V2]: (^[V3]: (^[V4]: ((cPredicate.seq.Join @ (V4 @ V2)) @ ((cPredicate.seq.Join @ ((cPredicate.bind @ V3) @ V4)) @ cPredicate.seq.Empty)))))) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((cPredicate.seq.Join @ ((cPredicate.bind @ V2) @ V5)) @ (V4 @ V5))))))) @ V1) @ V0)))))
(TPredicate.bind_bind,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.bind @ ((cPredicate.bind @ V0) @ V1)) @ V2)) @ ((cPredicate.bind @ V0) @ (^[V3]: ((cPredicate.bind @ (V1 @ V3)) @ V2)))))))))))
(TPredicate.bind_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.bind @ (cPredicate.Seq @ V0)) @ V1)) @ (cPredicate.Seq @ (^[V2]: ((cPredicate.apply @ V1) @ (V0 @ cProduct_Type.Unity))))))))))
(TPredicate.eq.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ V3) @ V3)))) @ ((V2 @ V0) @ V1))))))))))
(TPredicate.eq.intros,(call @ (^[V0]: ((cPredicate.eq @ V0) @ V0))))
(TPredicate.eval_INFI,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.eval @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ ((cFun.comp @ cPredicate.eval) @ V1))))))))
(TPredicate.eval_SUPR,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.eval @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ ((cFun.comp @ cPredicate.eval) @ V1))))))))
(TPredicate.eval_bind,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.eval @ ((cPredicate.bind @ V0) @ V1))) @ (cPredicate.eval @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V2]: ((cPredicate.eval @ V0) @ V2)))) @ V1))))))))
(TPredicate.eval_code,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.eval @ (cPredicate.Seq @ V0))) @ (cPredicate.member @ (V0 @ cProduct_Type.Unity))))))
(TPredicate.not_predE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ (cPredicate.not_pred @ (cPredicate.pred.Pred @ (^[V3]: V0)))) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V0)) @ V2)) @ V2)))))))))
(TPredicate.not_predI,(call @ (^[V0]: ((c==> @ (cHOL.Not @ V0)) @ ((cPredicate.eval @ (cPredicate.not_pred @ (cPredicate.pred.Pred @ (^[V1]: V0)))) @ cProduct_Type.Unity)))))
(TPredicate.pred.recs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.pred.pred_rec @ V0) @ (cPredicate.pred.Pred @ V1))) @ (V0 @ V1)))))))
(TPredicate.pred.size_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cPredicate.pred.Pred @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TPredicate.pred.size_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.pred.pred_size @ V0) @ (cPredicate.pred.Pred @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TPredicate.pred_iffI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ V0) @ V2)) @ ((cPredicate.eval @ V1) @ V2))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ V1) @ V2)) @ ((cPredicate.eval @ V0) @ V2))))) @ ((cHOL.eq @ V0) @ V1))))))))
(TPredicate.seq.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V0) @ V1) @ V2) @ ((cPredicate.seq.Join @ V3) @ V4))) @ ((V2 @ V3) @ V4)))))))))))))
(TPredicate.seq.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V0) @ V1) @ V2) @ ((cPredicate.seq.Insert @ V3) @ V4))) @ ((V1 @ V3) @ V4)))))))))))))
(TPredicate.seq.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V0) @ V1) @ V2) @ cPredicate.seq.Empty)) @ V0))))))))
(TPredicate.seq.simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ ((cPredicate.seq.Join @ V3) @ V4))) @ (((V2 @ V3) @ V4) @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ V4))))))))))))))
(TPredicate.seq.simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ ((cPredicate.seq.Insert @ V3) @ V4))) @ ((V1 @ V3) @ V4)))))))))))))
(TPredicate.seq.simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cPredicate.seq.seq_rec @ V0) @ V1) @ V2) @ cPredicate.seq.Empty)) @ V0))))))))
(TPredicate.seq.simps_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V0) @ V1) @ V2) @ ((cPredicate.seq.Join @ V3) @ V4))) @ ((V2 @ V3) @ V4)))))))))))))
(TPredicate.seq.simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V0) @ V1) @ V2) @ ((cPredicate.seq.Insert @ V3) @ V4))) @ ((V1 @ V3) @ V4)))))))))))))
(TPredicate.seq.simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V0) @ V1) @ V2) @ cPredicate.seq.Empty)) @ V0))))))))
(TPredicate.seq.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Join @ V0) @ V1)) @ ((cPredicate.seq.Insert @ V2) @ V3))))))))))))
(TPredicate.seq.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Insert @ V0) @ V1)) @ ((cPredicate.seq.Join @ V2) @ V3))))))))))))
(TPredicate.seq.simps_6,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Join @ V0) @ V1)) @ cPredicate.seq.Empty)))))))
(TPredicate.seq.simps_5,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cPredicate.seq.Empty) @ ((cPredicate.seq.Join @ V0) @ V1))))))))
(TPredicate.seq.simps_4,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Insert @ V0) @ V1)) @ cPredicate.seq.Empty)))))))
(TPredicate.seq.simps_3,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ V0) @ V1))))))))
(TPredicate.seq.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cPredicate.seq.Join @ V0) @ V1)) @ ((cPredicate.seq.Join @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TPredicate.seq.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cPredicate.seq.Insert @ V0) @ V1)) @ ((cPredicate.seq.Insert @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TPredicate.seq.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cPredicate.seq.seq_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cPredicate.seq.Empty)) @ (V0 @ V1))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Insert @ V5) @ V6))) @ (V0 @ ((V2 @ V5) @ V6)))))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Join @ V5) @ V6))) @ (V0 @ ((V3 @ V5) @ V6)))))))))))))))))))))
(TProduct_Type.SigmaE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cProduct_Type.Sigma @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((c==> @ ((cSet.member @ V5) @ (V2 @ V4))) @ ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3)))))))) @ V3)))))))))))
(TProduct_Type.SigmaI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (V3 @ V0))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ ((cProduct_Type.Sigma @ V1) @ V3)))))))))))))
(TProduct_Type.curryD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cProduct_Type.curry @ V0) @ V1) @ V2)) @ (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TProduct_Type.curryE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cProduct_Type.curry @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ (V0 @ ((cProduct_Type.Pair @ V1) @ V2))) @ V3)) @ V3)))))))))))
(TProduct_Type.curryI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ ((cProduct_Type.Pair @ V1) @ V2))) @ (((cProduct_Type.curry @ V0) @ V1) @ V2)))))))))
(TProduct_Type.splitD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.splitE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cProduct_Type.prod.prod_case @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((V0 @ V3) @ V4)) @ V2))))))) @ V2)))))))))
(TProduct_Type.splitI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TQuotient.Quotient3I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V0 @ (V1 @ V3))) @ V3)))) @ ((c==> @ (call @ (^[V3]: ((V2 @ (V1 @ V3)) @ (V1 @ V3))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((V2 @ V3) @ V4)) @ ((cHOL.conj @ ((V2 @ V3) @ V3)) @ ((cHOL.conj @ ((V2 @ V4) @ V4)) @ ((cHOL.eq @ (V0 @ V3)) @ (V0 @ V4)))))))))) @ (((cQuotient.Quotient3 @ V2) @ V0) @ V1)))))))))))
(TQuotient.equals_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((V0 @ V5) @ V6)) @ ((cHOL.eq @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TQuotient.lambda_prs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cFun.map_fun @ V2) @ V4) @ (^[V7]: (V5 @ (V6 @ (V1 @ V7)))))) @ (^[V7]: (V6 @ V7))))))))))))))))))))
(TRandom.log_sumC_def,((c== @ cRandom.log_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cRandom.log_graph @ V0) @ V1))))))
(TRandom_Pred.map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Pred.map @ V0) @ V1)) @ ((cRandom_Pred.bind @ V1) @ ((cFun.comp @ cRandom_Pred.single) @ V0))))))))
(TRecord.o_eq_id_dest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ ((cFun.comp @ cFun.id) @ V2))) @ ((cHOL.eq @ (V0 @ (V1 @ V3))) @ (V2 @ V3))))))))))))
(TRecord.refl_conj_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.conj @ V2) @ V0)) @ ((cHOL.conj @ V2) @ V1))))))))))
(TRelation.Domain_def,((c== @ cRelation.Domain) @ (^[V0]: (cSet.Collect @ (^[V1]: ((cRelation.Domainp @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ V1))))))
(TRelation.Domain_fst,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ V0)) @ ((cSet.image @ cProduct_Type.fst) @ V0)))))
(TRelation.Domain_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cRelation.Domain @ V1))) @ (cHOL.Ex @ (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ V1)))))))))
(TRelation.INF_INT_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (^[V3]: ((cSet.member @ V3) @ (V1 @ V2)))))) @ (^[V2]: ((cSet.member @ V2) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))))))))))
(TRelation.INF_Int_eq,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V1]: (^[V2]: ((cSet.member @ V2) @ V1))))) @ (^[V1]: ((cSet.member @ V1) @ (cComplete_Lattices.Inf_class.Inf @ V0)))))))
(TRelation.Id_on_def',(call @ (^[V0]: ((cHOL.eq @ (cRelation.Id_on @ (cSet.Collect @ (^[V1]: (V0 @ V1))))) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ (V0 @ V1))))))))))
(TRelation.Id_on_fold,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cRelation.Id_on @ V0)) @ (((cFinite_Set.fold @ (^[V1]: (cSet.insert @ ((cProduct_Type.Pair @ V1) @ V1)))) @ cOrderings.bot_class.bot) @ V0))))))
(TRelation.Image_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cRelation.Image @ V0) @ V1)) @ (((cFinite_Set.fold @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (^[V4]: (((cHOL.If @ ((cSet.member @ V2) @ V1)) @ ((cSet.insert @ V3) @ V4)) @ V4)))))) @ cOrderings.bot_class.bot) @ V0))))))))
(TRelation.Image_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V0) @ V2)) @ ((cRelation.Image @ V1) @ V3)))))))))))))
(TRelation.Inf_INT_eq,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (^[V1]: ((cSet.member @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ cSet.Collect)))))))
(TRelation.Range_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cRelation.Range @ V0)) @ (cRelation.Range @ V1))))))))
(TRelation.Rangep_def,((c== @ cRelation.Rangep) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((V0 @ V3) @ V4))))))))))))
(TRelation.SUP_Sup_eq,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: (^[V2]: ((cSet.member @ V2) @ V1))))) @ (^[V1]: ((cSet.member @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))
(TRelation.SUP_UN_eq2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (V1 @ V2))))))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V1 @ V4))))))))))))
(TRelation.Sup_SUP_eq,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V1]: ((cSet.member @ V1) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ cSet.Collect)))))))
(TRelation.antisym_Id,(cRelation.antisym @ cRelation.Id))
(TRelation.conversepD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRelation.conversep @ V0) @ V1) @ V2)) @ ((V0 @ V2) @ V1)))))))))
(TRelation.conversepE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cRelation.conversep @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ V4)) @ ((c==> @ ((V0 @ V4) @ V5)) @ V3)))))))) @ V3)))))))))))
(TRelation.conversepI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cRelation.conversep @ V0) @ V2) @ V1)))))))))
(TRelation.inf_Int_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1)))) @ (^[V2]: ((cSet.member @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TRelation.irrefl_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.irrefl @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ V0))))))))
(TRelation.mono_Field,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cRelation.Field @ V0)) @ (cRelation.Field @ V1))))))))
(TRelation.refl_on_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((c==> @ ((cRelation.refl_on @ V2) @ V3)) @ ((cRelation.refl_on @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V3)))))))))))))
(TRelation.rev_ImageI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ V3)) @ ((cSet.member @ V2) @ ((cRelation.Image @ V3) @ V1)))))))))))))
(TRelation.sup_Un_eq2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cLattices.sup_class.sup @ V0) @ V1))))))))))
(TRelation.trans_join,(call @ (^[V0]: ((cHOL.eq @ (cRelation.trans @ V0)) @ ((cSet.Ball @ V0) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cSet.Ball @ V0) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V4)) @ V0))))))))))))))
(TRelation.transp_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.transp @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V1) @ V2)) @ ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((V0 @ V1) @ V3)))))))))))))
(TRelation.transp_inf,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.transp @ V0)) @ ((c==> @ (cRelation.transp @ V1)) @ (cRelation.transp @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TRings.dvd_class_def,((c== @ (cRings.dvd_class @ cTYPE)) @ (cGroups.times_class @ cTYPE)))
(TRings.ring_distribs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TRings.ring_distribs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TRings.ring_distribs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TRings.ring_distribs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TSMT.pattern.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TSMT.pattern.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cSMT.pattern.Pattern)) @ V1)) @ V1))))))
(TSMT.pattern.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cSMT.pattern.Pattern)) @ (V0 @ V1)))))))
(TSet.Collect_conj_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cLattices.inf_class.inf @ (cSet.Collect @ (^[V2]: (V0 @ V2)))) @ (cSet.Collect @ (^[V2]: (V1 @ V2))))))))))
(TSet.Collect_conv_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V0)) @ (V1 @ V2))))) @ (((cHOL.If @ (V1 @ V0)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot)))))))
(TSet.Collect_disj_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cLattices.sup_class.sup @ (cSet.Collect @ (^[V2]: (V0 @ V2)))) @ (cSet.Collect @ (^[V2]: (V1 @ V2))))))))))
(TSet.Compl_anti_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TSet.Compl_disjoint2,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ cOrderings.bot_class.bot))))
(TSet.Compl_partition,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ cOrderings.top_class.top))))
(TSet.Int_Un_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TSet.Int_empty_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TSet.Int_insert_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet.insert @ V0) @ V1)) @ V2)) @ (((cHOL.If @ ((cSet.member @ V0) @ V2)) @ ((cSet.insert @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TSet.Int_left_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TSet.Un_Diff_cancel2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TSet.Un_Int_assoc_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2)))) @ ((cOrderings.ord_class.less_eq @ V2) @ V0)))))))))
(TSet.Un_Int_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TSet.Un_insert_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cSet.insert @ V1) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TSet.Un_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ V1) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TSet.all_not_in_conv,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (cHOL.Not @ ((cSet.member @ V1) @ V0))))) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TSet.arity_equal_set,(cHOL.equal_class @ cTYPE))
(TSet.ball_one_point1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V3) @ V1)) @ (V2 @ V3))))) @ ((cHOL.implies @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1))))))))))
(TSet.ball_one_point2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V1) @ V3)) @ (V2 @ V3))))) @ ((cHOL.implies @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1))))))))))
(TSet.disjoint_insert_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cLattices.inf_class.inf @ V0) @ ((cSet.insert @ V1) @ V2)))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cLattices.inf_class.inf @ V0) @ V2)))))))))))
(TSet.disjoint_insert_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cSet.insert @ V1) @ V2))) @ cOrderings.bot_class.bot)) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V2)) @ cOrderings.bot_class.bot))))))))))
(TSet.image_vimage_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ V0) @ ((cSet.vimage @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V1) @ ((cSet.image @ V0) @ cOrderings.top_class.top))))))))
(TSet.insert_disjoint_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cLattices.inf_class.inf @ ((cSet.insert @ V0) @ V1)) @ V2))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V0) @ V2))) @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cLattices.inf_class.inf @ V1) @ V2)))))))))))
(TSet.insert_disjoint_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet.insert @ V0) @ V1)) @ V2)) @ cOrderings.bot_class.bot)) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V0) @ V2))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ V2)) @ cOrderings.bot_class.bot))))))))))
(TSet.less_eq_set_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1)))))))))
(TSet.singleton_conv2,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: ((cHOL.eq @ V0) @ V1)))) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TSet.strong_bex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cSet.Bex @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TSet.subset_insertI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.insert @ V2) @ V1))))))))))
(TSet.vimage_image_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cSet.image @ V0) @ V1))) @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V1) @ (^[V3]: ((cHOL.eq @ (V0 @ V3)) @ (V0 @ V2))))))))))))
(TString.char.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TString.char.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cString.char.Char @ V2) @ V3))) @ V1)))))) @ V1))))))
(TString.char.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cString.char.Char @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TString.nibble.cases_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleF)) @ V15))))))))))))))))))))))))))))))))))
(TString.nibble.cases_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleE)) @ V14))))))))))))))))))))))))))))))))))
(TString.nibble.cases_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleD)) @ V13))))))))))))))))))))))))))))))))))
(TString.nibble.cases_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleC)) @ V12))))))))))))))))))))))))))))))))))
(TString.nibble.cases_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleB)) @ V11))))))))))))))))))))))))))))))))))
(TString.nibble.cases_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleA)) @ V10))))))))))))))))))))))))))))))))))
(TString.nibble.cases_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble9)) @ V9))))))))))))))))))))))))))))))))))
(TString.nibble.cases_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble8)) @ V8))))))))))))))))))))))))))))))))))
(TString.nibble.cases_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble7)) @ V7))))))))))))))))))))))))))))))))))
(TString.nibble.cases_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble6)) @ V6))))))))))))))))))))))))))))))))))
(TString.nibble.cases_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble5)) @ V5))))))))))))))))))))))))))))))))))
(TString.nibble.cases_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble4)) @ V4))))))))))))))))))))))))))))))))))
(TString.nibble.cases_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble3)) @ V3))))))))))))))))))))))))))))))))))
(TString.nibble.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble2)) @ V2))))))))))))))))))))))))))))))))))
(TString.nibble.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble1)) @ V1))))))))))))))))))))))))))))))))))
(TString.nibble.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble0)) @ V0))))))))))))))))))))))))))))))))))
(TString.nibble.simps_272,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleF)) @ V15))))))))))))))))))))))))))))))))))
(TString.nibble.simps_271,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleE)) @ V14))))))))))))))))))))))))))))))))))
(TString.nibble.simps_270,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleD)) @ V13))))))))))))))))))))))))))))))))))
(TString.nibble.simps_269,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleC)) @ V12))))))))))))))))))))))))))))))))))
(TString.nibble.simps_268,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleB)) @ V11))))))))))))))))))))))))))))))))))
(TString.nibble.simps_267,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleA)) @ V10))))))))))))))))))))))))))))))))))
(TString.nibble.simps_266,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble9)) @ V9))))))))))))))))))))))))))))))))))
(TString.nibble.simps_265,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble8)) @ V8))))))))))))))))))))))))))))))))))
(TString.nibble.simps_264,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble7)) @ V7))))))))))))))))))))))))))))))))))
(TString.nibble.simps_263,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble6)) @ V6))))))))))))))))))))))))))))))))))
(TString.nibble.simps_262,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble5)) @ V5))))))))))))))))))))))))))))))))))
(TString.nibble.simps_261,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble4)) @ V4))))))))))))))))))))))))))))))))))
(TString.nibble.simps_260,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble3)) @ V3))))))))))))))))))))))))))))))))))
(TString.nibble.simps_259,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble2)) @ V2))))))))))))))))))))))))))))))))))
(TString.nibble.simps_258,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble1)) @ V1))))))))))))))))))))))))))))))))))
(TString.nibble.simps_257,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble0)) @ V0))))))))))))))))))))))))))))))))))
(TString.nibble.simps_256,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleF)) @ V15))))))))))))))))))))))))))))))))))
(TString.nibble.simps_255,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleE)) @ V14))))))))))))))))))))))))))))))))))
(TString.nibble.simps_254,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleD)) @ V13))))))))))))))))))))))))))))))))))
(TString.nibble.simps_253,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleC)) @ V12))))))))))))))))))))))))))))))))))
(TString.nibble.simps_252,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleB)) @ V11))))))))))))))))))))))))))))))))))
(TString.nibble.simps_251,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleA)) @ V10))))))))))))))))))))))))))))))))))
(TString.nibble.simps_250,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble9)) @ V9))))))))))))))))))))))))))))))))))
(TString.nibble.simps_249,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble8)) @ V8))))))))))))))))))))))))))))))))))
(TString.nibble.simps_248,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble7)) @ V7))))))))))))))))))))))))))))))))))
(TString.nibble.simps_247,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble6)) @ V6))))))))))))))))))))))))))))))))))
(TString.nibble.simps_246,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble5)) @ V5))))))))))))))))))))))))))))))))))
(TString.nibble.simps_245,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble4)) @ V4))))))))))))))))))))))))))))))))))
(TString.nibble.simps_244,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble3)) @ V3))))))))))))))))))))))))))))))))))
(TString.nibble.simps_243,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble2)) @ V2))))))))))))))))))))))))))))))))))
(TString.nibble.simps_242,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble1)) @ V1))))))))))))))))))))))))))))))))))
(TString.nibble.simps_241,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble0)) @ V0))))))))))))))))))))))))))))))))))
(TString.nibble.simps_240,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleE)))
(TString.nibble.simps_239,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleF)))
(TString.nibble.simps_238,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleD)))
(TString.nibble.simps_237,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleF)))
(TString.nibble.simps_236,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleD)))
(TString.nibble.simps_235,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleE)))
(TString.nibble.simps_234,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleC)))
(TString.nibble.simps_233,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleF)))
(TString.nibble.simps_232,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleC)))
(TString.nibble.simps_231,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleE)))
(TString.nibble.simps_230,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleC)))
(TString.nibble.simps_229,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleD)))
(TString.nibble.simps_228,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleB)))
(TString.nibble.simps_227,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleF)))
(TString.nibble.simps_226,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleB)))
(TString.nibble.simps_225,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleE)))
(TString.nibble.simps_224,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleB)))
(TString.nibble.simps_223,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleD)))
(TString.nibble.simps_222,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleB)))
(TString.nibble.simps_221,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleC)))
(TString.nibble.simps_220,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleA)))
(TString.nibble.simps_219,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleF)))
(TString.nibble.simps_218,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleA)))
(TString.nibble.simps_217,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleE)))
(TString.nibble.simps_216,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleA)))
(TString.nibble.simps_215,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleD)))
(TString.nibble.simps_214,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleA)))
(TString.nibble.simps_213,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleC)))
(TString.nibble.simps_212,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleA)))
(TString.nibble.simps_211,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleB)))
(TString.nibble.simps_210,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble9)))
(TString.nibble.simps_209,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleF)))
(TString.nibble.simps_208,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble9)))
(TString.nibble.simps_207,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleE)))
(TString.nibble.simps_206,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble9)))
(TString.nibble.simps_205,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleD)))
(TString.nibble.simps_204,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble9)))
(TString.nibble.simps_203,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleC)))
(TString.nibble.simps_202,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble9)))
(TString.nibble.simps_201,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleB)))
(TString.nibble.simps_200,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble9)))
(TString.nibble.simps_199,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleA)))
(TString.nibble.simps_198,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble8)))
(TString.nibble.simps_197,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleF)))
(TString.nibble.simps_196,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble8)))
(TString.nibble.simps_195,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleE)))
(TString.nibble.simps_194,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble8)))
(TString.nibble.simps_193,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleD)))
(TString.nibble.simps_192,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble8)))
(TString.nibble.simps_191,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleC)))
(TString.nibble.simps_190,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble8)))
(TString.nibble.simps_189,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleB)))
(TString.nibble.simps_188,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble8)))
(TString.nibble.simps_187,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleA)))
(TString.nibble.simps_186,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble8)))
(TString.nibble.simps_185,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble9)))
(TString.nibble.simps_184,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble7)))
(TString.nibble.simps_183,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleF)))
(TString.nibble.simps_182,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble7)))
(TString.nibble.simps_181,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleE)))
(TString.nibble.simps_180,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble7)))
(TString.nibble.simps_179,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleD)))
(TString.nibble.simps_178,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble7)))
(TString.nibble.simps_177,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleC)))
(TString.nibble.simps_176,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble7)))
(TString.nibble.simps_175,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleB)))
(TString.nibble.simps_174,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble7)))
(TString.nibble.simps_173,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)))
(TString.nibble.simps_172,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble7)))
(TString.nibble.simps_171,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)))
(TString.nibble.simps_170,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble7)))
(TString.nibble.simps_169,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)))
(TString.nibble.simps_168,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble6)))
(TString.nibble.simps_167,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)))
(TString.nibble.simps_166,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble6)))
(TString.nibble.simps_165,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)))
(TString.nibble.simps_164,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble6)))
(TString.nibble.simps_163,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)))
(TString.nibble.simps_162,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble6)))
(TString.nibble.simps_161,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)))
(TString.nibble.simps_160,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble6)))
(TString.nibble.simps_159,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)))
(TString.nibble.simps_158,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble6)))
(TString.nibble.simps_157,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleA)))
(TString.nibble.simps_156,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble6)))
(TString.nibble.simps_155,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)))
(TString.nibble.simps_154,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble6)))
(TString.nibble.simps_153,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)))
(TString.nibble.simps_152,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)))
(TString.nibble.simps_151,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)))
(TString.nibble.simps_150,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble5)))
(TString.nibble.simps_149,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)))
(TString.nibble.simps_148,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble5)))
(TString.nibble.simps_147,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)))
(TString.nibble.simps_146,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble5)))
(TString.nibble.simps_145,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleD)))
(TString.nibble.simps_144,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble5)))
(TString.nibble.simps_143,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)))
(TString.nibble.simps_142,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble5)))
(TString.nibble.simps_141,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleB)))
(TString.nibble.simps_140,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble5)))
(TString.nibble.simps_139,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleA)))
(TString.nibble.simps_138,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble5)))
(TString.nibble.simps_137,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble9)))
(TString.nibble.simps_136,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble5)))
(TString.nibble.simps_135,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble8)))
(TString.nibble.simps_134,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)))
(TString.nibble.simps_133,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)))
(TString.nibble.simps_132,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)))
(TString.nibble.simps_131,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)))
(TString.nibble.simps_130,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble4)))
(TString.nibble.simps_129,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)))
(TString.nibble.simps_128,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble4)))
(TString.nibble.simps_127,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)))
(TString.nibble.simps_126,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble4)))
(TString.nibble.simps_125,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)))
(TString.nibble.simps_124,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble4)))
(TString.nibble.simps_123,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)))
(TString.nibble.simps_122,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble4)))
(TString.nibble.simps_121,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)))
(TString.nibble.simps_120,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble4)))
(TString.nibble.simps_119,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleA)))
(TString.nibble.simps_118,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble4)))
(TString.nibble.simps_117,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)))
(TString.nibble.simps_116,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble4)))
(TString.nibble.simps_115,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)))
(TString.nibble.simps_114,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)))
(TString.nibble.simps_113,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble7)))
(TString.nibble.simps_112,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)))
(TString.nibble.simps_111,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)))
(TString.nibble.simps_110,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)))
(TString.nibble.simps_109,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)))
(TString.nibble.simps_108,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble3)))
(TString.nibble.simps_107,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleF)))
(TString.nibble.simps_106,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble3)))
(TString.nibble.simps_105,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)))
(TString.nibble.simps_104,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble3)))
(TString.nibble.simps_103,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleD)))
(TString.nibble.simps_102,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble3)))
(TString.nibble.simps_101,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)))
(TString.nibble.simps_100,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble3)))
(TString.nibble.simps_99,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleB)))
(TString.nibble.simps_98,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble3)))
(TString.nibble.simps_97,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleA)))
(TString.nibble.simps_96,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble3)))
(TString.nibble.simps_95,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)))
(TString.nibble.simps_94,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble3)))
(TString.nibble.simps_93,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)))
(TString.nibble.simps_92,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)))
(TString.nibble.simps_91,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)))
(TString.nibble.simps_90,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)))
(TString.nibble.simps_89,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)))
(TString.nibble.simps_88,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)))
(TString.nibble.simps_87,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)))
(TString.nibble.simps_86,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)))
(TString.nibble.simps_85,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)))
(TString.nibble.simps_84,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble2)))
(TString.nibble.simps_83,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleF)))
(TString.nibble.simps_82,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble2)))
(TString.nibble.simps_81,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)))
(TString.nibble.simps_80,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble2)))
(TString.nibble.simps_79,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleD)))
(TString.nibble.simps_78,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble2)))
(TString.nibble.simps_77,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleC)))
(TString.nibble.simps_76,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble2)))
(TString.nibble.simps_75,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleB)))
(TString.nibble.simps_74,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble2)))
(TString.nibble.simps_73,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleA)))
(TString.nibble.simps_72,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble2)))
(TString.nibble.simps_71,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble9)))
(TString.nibble.simps_70,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble2)))
(TString.nibble.simps_69,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble8)))
(TString.nibble.simps_68,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)))
(TString.nibble.simps_67,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble7)))
(TString.nibble.simps_66,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)))
(TString.nibble.simps_65,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble6)))
(TString.nibble.simps_64,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)))
(TString.nibble.simps_63,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble5)))
(TString.nibble.simps_62,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)))
(TString.nibble.simps_61,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble4)))
(TString.nibble.simps_60,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)))
(TString.nibble.simps_59,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble3)))
(TString.nibble.simps_58,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble1)))
(TString.nibble.simps_57,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleF)))
(TString.nibble.simps_56,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble1)))
(TString.nibble.simps_55,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleE)))
(TString.nibble.simps_54,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble1)))
(TString.nibble.simps_53,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleD)))
(TString.nibble.simps_52,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble1)))
(TString.nibble.simps_51,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleC)))
(TString.nibble.simps_50,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble1)))
(TString.nibble.simps_49,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleB)))
(TString.nibble.simps_48,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble1)))
(TString.nibble.simps_47,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleA)))
(TString.nibble.simps_46,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble1)))
(TString.nibble.simps_45,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble9)))
(TString.nibble.simps_44,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble1)))
(TString.nibble.simps_43,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble8)))
(TString.nibble.simps_42,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)))
(TString.nibble.simps_41,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble7)))
(TString.nibble.simps_40,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)))
(TString.nibble.simps_39,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble6)))
(TString.nibble.simps_38,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)))
(TString.nibble.simps_37,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble5)))
(TString.nibble.simps_36,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)))
(TString.nibble.simps_35,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble4)))
(TString.nibble.simps_34,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)))
(TString.nibble.simps_33,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble3)))
(TString.nibble.simps_32,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble1)))
(TString.nibble.simps_31,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble2)))
(TString.nibble.simps_30,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble0)))
(TString.nibble.simps_29,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleF)))
(TString.nibble.simps_28,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble0)))
(TString.nibble.simps_27,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleE)))
(TString.nibble.simps_26,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble0)))
(TString.nibble.simps_25,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleD)))
(TString.nibble.simps_24,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble0)))
(TString.nibble.simps_23,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleC)))
(TString.nibble.simps_22,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble0)))
(TString.nibble.simps_21,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleB)))
(TString.nibble.simps_20,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble0)))
(TString.nibble.simps_19,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleA)))
(TString.nibble.simps_18,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble0)))
(TString.nibble.simps_17,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble9)))
(TString.nibble.simps_16,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble0)))
(TString.nibble.simps_15,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble8)))
(TString.nibble.simps_14,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)))
(TString.nibble.simps_13,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble7)))
(TString.nibble.simps_12,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble0)))
(TString.nibble.simps_11,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble6)))
(TString.nibble.simps_10,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)))
(TString.nibble.simps_9,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble5)))
(TString.nibble.simps_8,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble0)))
(TString.nibble.simps_7,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble4)))
(TString.nibble.simps_6,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)))
(TString.nibble.simps_5,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble3)))
(TString.nibble.simps_4,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble0)))
(TString.nibble.simps_3,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble2)))
(TString.nibble.simps_2,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble0)))
(TString.nibble.simps_1,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble1)))
(TString.nibble.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: ((cHOL.eq @ (V0 @ (((((((((((((((((cString.nibble.nibble_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble0)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble1)) @ (V0 @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble2)) @ (V0 @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble3)) @ (V0 @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble4)) @ (V0 @ V5))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble5)) @ (V0 @ V6))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble6)) @ (V0 @ V7))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble7)) @ (V0 @ V8))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble8)) @ (V0 @ V9))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble9)) @ (V0 @ V10))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleA)) @ (V0 @ V11))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleB)) @ (V0 @ V12))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleC)) @ (V0 @ V13))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleD)) @ (V0 @ V14))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleE)) @ (V0 @ V15))) @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleF)) @ (V0 @ V16)))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TSum_Type.Inl_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inl @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.Inr_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inr @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.Suml.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSum_Type.Suml @ V0) @ (cSum_Type.Inl @ V1))) @ (V0 @ V1)))))))
(TSum_Type.Sumr.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSum_Type.Sumr @ V0) @ (cSum_Type.Inr @ V1))) @ (V0 @ V1)))))))
(TSum_Type.sum.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cSum_Type.Inl @ V2))))) @ ((c==> @ (call @ (^[V2]: (V0 @ (cSum_Type.Inr @ V2))))) @ (V0 @ V1))))))))
(TSum_Type.sum.inject_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inr @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.inject_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inl @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cSum_Type.sum.sum_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cSum_Type.Inl @ V4))) @ (cHOL.Not @ (V0 @ (V1 @ V4))))))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cSum_Type.Inr @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TSum_Type.sum.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cSum_Type.sum.sum_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cSum_Type.Inl @ V4))) @ (V0 @ (V1 @ V4)))))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cSum_Type.Inr @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TSum_Type.sum_map.id,((cHOL.eq @ ((cSum_Type.sum_map @ cFun.id) @ cFun.id)) @ cFun.id))
(TTransfer.fun_rel_eq,((cHOL.eq @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cHOL.eq))
(TWellfounded.acc_def,((c== @ cWellfounded.acc) @ (^[V0]: (cSet.Collect @ (^[V1]: ((cWellfounded.accp @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ V1))))))
(TWellfounded.acc_wfD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((cSet.member @ V1) @ (cWellfounded.acc @ V0))))))))
(TWellfounded.acc_wfI,(call @ (^[V0]: ((c==> @ (cHOL.All @ (^[V1]: ((cSet.member @ V1) @ (cWellfounded.acc @ V0))))) @ (cWellfounded.wf @ V0)))))
(TWellfounded.less_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ cWellfounded.pred_nat))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TWellfounded.wfE_min,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V4)) @ V0)) @ (cHOL.Not @ ((cSet.member @ V5) @ V2)))))) @ V3))))) @ V3))))))))))))
(TWellfounded.wfI_min,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V1) @ V2)) @ ((cSet.Bex @ V2) @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)) @ (cHOL.Not @ ((cSet.member @ V4) @ V2))))))))))))) @ (cWellfounded.wf @ V0)))))
(TWellfounded.wfP_SUP,(call @ (^[V0]: ((c==> @ (cHOL.All @ (^[V1]: (cWellfounded.wfP @ (V0 @ V1))))) @ ((c==> @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2)))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cRelation.Domainp @ (V0 @ V1))) @ (cRelation.Rangep @ (V0 @ V2)))) @ cOrderings.bot_class.bot))))))) @ (cWellfounded.wfP @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ V0)))))))
(TWellfounded.wfP_def,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wfP @ V0)) @ (cWellfounded.wf @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2))))))))))
(TWellfounded.wfUNIVI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))) @ (cWellfounded.wf @ V0)))))
(TWellfounded.wf_Int1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ ((cLattices.inf_class.inf @ V0) @ V1))))))))
(TWellfounded.wf_Int2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ ((cLattices.inf_class.inf @ V1) @ V0))))))))
(TWellfounded.wf_asym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0))) @ V3)) @ V3))))))))))))
(TWellfounded.wf_less,(cWellfounded.wf @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TWellfounded.wf_mlex,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ ((cWellfounded.mlex_prod @ V1) @ V0))))))))
(TCode_Generator.holds,cCode_Generator.holds)
(TCode_Numeral.Nat.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cInt.nat) @ cInt.nat))
(TCode_Numeral.Nat_def,((c== @ cCode_Numeral.Nat) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.natural_of_nat) @ cInt.nat)))
(TCode_Numeral.Neg_def,((cHOL.eq @ cCode_Numeral.Neg) @ cNum.neg_numeral_class.neg_numeral))
(TCode_Numeral.Pos_def,((cHOL.eq @ cCode_Numeral.Pos) @ cNum.numeral_class.numeral))
(TCode_Numeral.Suc.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cNat.Suc) @ cNat.Suc))
(TCode_Numeral.Suc_def,((c== @ cCode_Numeral.Suc) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.natural_of_nat) @ cNat.Suc)))
(TCode_Numeral.dup.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ (^[V0]: ((cInt.plus_int_inst.plus_int @ V0) @ V0))) @ (^[V0]: ((cInt.plus_int_inst.plus_int @ V0) @ V0))))
(TCode_Numeral.dup_def,((c== @ cCode_Numeral.dup) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int) @ (^[V0]: ((cInt.plus_int_inst.plus_int @ V0) @ V0)))))
(TCode_Numeral.sub.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ (^[V0]: (^[V1]: ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))) @ (^[V0]: (^[V1]: ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))
(TCode_Numeral.sub_def,((c== @ cCode_Numeral.sub) @ (((cFun.map_fun @ cFun.id) @ ((cFun.map_fun @ cFun.id) @ cCode_Numeral.integer_of_int)) @ (^[V0]: (^[V1]: ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TDatatype.Atom_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cDatatype.Atom @ V0)) @ (cDatatype.Atom @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.In0_not_In1,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cDatatype.In0 @ V0)) @ (cDatatype.In1 @ V1))))))))
(TDatatype.In1_not_In0,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cDatatype.In1 @ V0)) @ (cDatatype.In0 @ V1))))))))
(TDatatype.Leaf_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cDatatype.Leaf @ V0)) @ (cDatatype.Leaf @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.Node_Push_I,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cDatatype.Node)) @ ((cSet.member @ ((cProduct_Type.apfst @ (cDatatype.Push @ V1)) @ V0)) @ cDatatype.Node)))))))
(TDatatype.Numb_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cDatatype.Numb @ V0)) @ (cDatatype.Numb @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.Push_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cDatatype.Push @ V0) @ V1)) @ ((cDatatype.Push @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ V4))) @ V4)))))))))))))
(TDatatype.Push_neq_K0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cDatatype.Push @ (cSum_Type.Inr @ (cNat.Suc @ V0))) @ V1)) @ (^[V3]: (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat)))) @ V2))))))))
(TDatatype.Scons_UN1_x,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.Scons @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: (V0 @ V2)))) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: ((cDatatype.Scons @ (V0 @ V2)) @ V1)))))))))
(TDatatype.Scons_UN1_y,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.Scons @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: (V1 @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: ((cDatatype.Scons @ V0) @ (V1 @ V2))))))))))
(TDatatype.apfst_convE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.apfst @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (V1 @ V4)) @ V5))) @ V3))))))) @ V3)))))))))))
(TDatatype.dprod_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cOrderings.ord_class.less_eq @ ((cDatatype.dprod @ ((cProduct_Type.Sigma @ V0) @ (^[V4]: V1))) @ ((cProduct_Type.Sigma @ V2) @ (^[V4]: V3)))) @ ((cProduct_Type.Sigma @ ((cDatatype.uprod @ V0) @ V2)) @ (^[V4]: ((cDatatype.uprod @ V1) @ V3)))))))))))))
(TDatatype.ntrunc_Atom,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ V0)) @ (cDatatype.Atom @ V1))) @ (cDatatype.Atom @ V1)))))))
(TDatatype.ntrunc_Leaf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ V0)) @ (cDatatype.Leaf @ V1))) @ (cDatatype.Leaf @ V1)))))))
(TDatatype.ntrunc_Numb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ V0)) @ (cDatatype.Numb @ V1))) @ (cDatatype.Numb @ V1)))))))
(TDivides.div2_Suc_Suc,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ (cNat.Suc @ (cNat.Suc @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cNat.Suc @ ((cDivides.div_nat_inst.div_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TDivides.div_le_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cDivides.div_nat_inst.div_nat @ V2) @ V1)) @ ((cDivides.div_nat_inst.div_nat @ V2) @ V0)))))))))))
(TDivides.div_mult1_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cDivides.div_nat_inst.div_nat @ V1) @ V2))) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V2))) @ V2))))))))))
(TDivides.div_mult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))) @ ((cDivides.div_nat_inst.div_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ V2)))))))))
(TDivides.div_positive,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cDivides.div_nat_inst.div_nat @ V1) @ V0)))))))))
(TDivides.mod2_Suc_Suc,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ (cNat.Suc @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TDivides.mod_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TDivides.mod_induct_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ ((cHOL.implies @ (V1 @ V3)) @ (V1 @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ V3)) @ V0))))))) @ ((c==> @ (V1 @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ V0)) @ (V1 @ cNat.zero_nat_inst.zero_nat)))))))))))
(TDivides.mod_mult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ ((cDivides.div_nat_inst.mod_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ V2))) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))))))))))
(TDivides.neg_mod_conj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ V0) @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)))))))))
(TDivides.neg_mod_sign,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)) @ cInt.zero_int_inst.zero_int)))))))
(TDivides.pos_mod_conj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.mod_int @ V1) @ V0))) @ ((cInt.ord_int_inst.less_int @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)) @ V0))))))))
(TDivides.pos_mod_sign,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.mod_int @ V1) @ V0))))))))
(TDivides.zmult1_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (((cDivides.divmod_int_rel @ ((cInt.times_int_inst.times_int @ V4) @ V0)) @ V1) @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V4) @ V2)) @ ((cDivides.div_int_inst.div_int @ ((cInt.times_int_inst.times_int @ V4) @ V3)) @ V1))) @ ((cDivides.div_int_inst.mod_int @ ((cInt.times_int_inst.times_int @ V4) @ V3)) @ V1)))))))))))))))
(TDivides.zmult2_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V4)) @ (((cDivides.divmod_int_rel @ V0) @ ((cInt.times_int_inst.times_int @ V1) @ V4)) @ ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V2) @ V4)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ ((cDivides.div_int_inst.mod_int @ V2) @ V4))) @ V3))))))))))))))))
(TEnum.all_n_lists_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.all_n_lists @ V0) @ V1)) @ ((cSet.Ball @ (cList.set @ ((cList.n_lists @ V1) @ cEnum.enum_class.enum))) @ (^[V2]: (V0 @ V2)))))))))
(TEnum.arity_enum_bool,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_prod,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_unit,(cEnum.enum_class @ cTYPE))
(TEnum.arity_equal_fun,(cHOL.equal_class @ cTYPE))
(TEnum.enum_ex_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_ex @ V0)) @ ((cEnum.ex_n_lists @ (^[V1]: (V0 @ ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ cEnum.enum_class.enum) @ V1)))))) @ (cNat.size_class.size @ cEnum.enum_class.enum))))))
(TEnum.enum_ex_set_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_ex @ V0)) @ ((cSet.Bex @ (cList.set @ cEnum.enum_class.enum)) @ (^[V1]: (V0 @ V1)))))))
(TEnum.enum_ex_sum_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_ex @ V0)) @ ((cHOL.disj @ (cEnum.enum_class.enum_ex @ (^[V1]: (V0 @ (cSum_Type.Inl @ V1))))) @ (cEnum.enum_class.enum_ex @ (^[V1]: (V0 @ (cSum_Type.Inr @ V1)))))))))
(TEnum.enum_option_def,((cHOL.eq @ cEnum.enum_class.enum) @ ((cList.list.Cons @ cOption.option.None) @ ((cList.map @ cOption.option.Some) @ cEnum.enum_class.enum))))
(TEnum.finite_1.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_1.a\<__caret__sub>1)) @ (V0 @ V1)))))))
(TEnum.finite_1.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cEnum.finite_1.finite_1_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cEnum.finite_1.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TEnum.finite_1.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cEnum.finite_1.finite_1_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cEnum.finite_1.a\<__caret__sub>1)) @ (V0 @ V1))))))))))
(TEnum.finite_2.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_2.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_2.a\<__caret__sub>2)) @ (V0 @ V1))))))))
(TEnum.finite_2.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cEnum.finite_2.finite_2_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))))))))))))))
(TEnum.finite_2.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cEnum.finite_2.finite_2_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>2)) @ (V0 @ V2)))))))))))))
(TEnum.finite_3.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_3.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_3.a\<__caret__sub>2)) @ ((c==> @ (V0 @ cEnum.finite_3.a\<__caret__sub>3)) @ (V0 @ V1)))))))))
(TEnum.finite_3.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cEnum.finite_3.finite_3_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>3)) @ (cHOL.Not @ (V0 @ V3))))))))))))))))))
(TEnum.finite_3.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cEnum.finite_3.finite_3_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>2)) @ (V0 @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>3)) @ (V0 @ V3))))))))))))))))
(TEnum.finite_4.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>2)) @ ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>3)) @ ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>4)) @ (V0 @ V1))))))))))
(TEnum.finite_4.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (V0 @ (((((cEnum.finite_4.finite_4_case @ V1) @ V2) @ V3) @ V4) @ V5))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>3)) @ (cHOL.Not @ (V0 @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>4)) @ (cHOL.Not @ (V0 @ V4)))))))))))))))))))))
(TEnum.finite_4.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (V0 @ (((((cEnum.finite_4.finite_4_case @ V1) @ V2) @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>2)) @ (V0 @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>3)) @ (V0 @ V3))) @ ((cHOL.implies @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>4)) @ (V0 @ V4)))))))))))))))))))
(TEnum.finite_5.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>2)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>3)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>4)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>5)) @ (V0 @ V1)))))))))))
(TEnum.finite_5.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (V0 @ ((((((cEnum.finite_5.finite_5_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>3)) @ (cHOL.Not @ (V0 @ V3)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>4)) @ (cHOL.Not @ (V0 @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>5)) @ (cHOL.Not @ (V0 @ V5))))))))))))))))))))))))
(TEnum.finite_5.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (V0 @ ((((((cEnum.finite_5.finite_5_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>1)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>2)) @ (V0 @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>3)) @ (V0 @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>4)) @ (V0 @ V4))) @ ((cHOL.implies @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>5)) @ (V0 @ V5))))))))))))))))))))))
(TFinite_Set.Ball_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cSet.Ball @ V0) @ V1)) @ (((cFinite_Set.fold @ (^[V2]: (^[V3]: ((cHOL.conj @ V3) @ (V1 @ V2))))) @ cHOL.True) @ V0))))))))
(TFinite_Set.card_0_eq,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))))))
(TFinite_Set.card_Plus,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSum_Type.Plus @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))))))))))
(TFinite_Set.card_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V0)))))))))
(TFinite_Set.finite_UN,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.finite @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ (V1 @ V2)))))))))))
(TFinite_Set.finite_Un,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.finite @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cHOL.conj @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.fold_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.comp_fun_commute @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V2)) @ ((cHOL.eq @ (V0 @ V6)) @ (V1 @ V6)))))) @ ((c==> @ ((cHOL.eq @ V3) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V5)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V3) @ V2)) @ (((cFinite_Set.fold @ V1) @ V4) @ V5)))))))))))))))))))))
(TFinite_Set.inj_graph,((cFun.inj_on @ (^[V0]: (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.eq @ V2) @ (V0 @ V1)))))))) @ cOrderings.top_class.top))
(TFun.bij_betw_combine,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((c==> @ (((cFun.bij_betw @ V0) @ V3) @ V4)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V4)) @ cOrderings.bot_class.bot)) @ (((cFun.bij_betw @ V0) @ ((cLattices.sup_class.sup @ V1) @ V3)) @ ((cLattices.sup_class.sup @ V2) @ V4))))))))))))))))
(TFun.f_the_inv_into_f,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ ((cSet.image @ V0) @ V1))) @ ((cHOL.eq @ (V0 @ (((cFun.the_inv_into @ V1) @ V0) @ V2))) @ V2))))))))))
(TFun.fun_upd_idem_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (((cFun.fun_upd @ V0) @ V1) @ V2)) @ V0)) @ ((cHOL.eq @ (V0 @ V1)) @ V2)))))))))
(TFun.inj_image_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TFun.inj_on_image_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cLattices.inf_class.inf @ V2) @ V3))) @ ((cLattices.inf_class.inf @ ((cSet.image @ V0) @ V2)) @ ((cSet.image @ V0) @ V3)))))))))))))))
(TFun.inj_on_image_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ V0) @ (^[V4]: ((cHOL.eq @ ((cHOL.eq @ (V1 @ (V2 @ V3))) @ (V1 @ (V2 @ V4)))) @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V4)))))))) @ ((c==> @ ((cFun.inj_on @ V2) @ V0)) @ ((cHOL.eq @ ((cFun.inj_on @ V1) @ ((cSet.image @ V2) @ V0))) @ ((cFun.inj_on @ V1) @ V0)))))))))))
(TFun.map_fun.identity,((cHOL.eq @ ((cFun.map_fun @ (^[V0]: V0)) @ (^[V0]: V0))) @ cFun.id))
(TFun.the_inv_into_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cFun.the_inv_into @ V0) @ V1)) @ (^[V2]: (cHOL.The @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ V3)) @ V2)))))))))))
(TFun.the_inv_into_f_f,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ (((cFun.the_inv_into @ V1) @ V0) @ (V0 @ V2))) @ V2))))))))))
(TFun.vimage_subset_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet.vimage @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cSet.image @ V0) @ V2)))))))))))
(TFunDef.THE_defaultI',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2)))) @ (V0 @ ((cFunDef.THE_default @ V1) @ V0))))))))
(TFunDef.less_by_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TFunDef.max_rpair_set,(cFunDef.reduction_pair @ ((cProduct_Type.Pair @ cFunDef.max_strict) @ cFunDef.max_weak)))
(TFunDef.min_rpair_set,(cFunDef.reduction_pair @ ((cProduct_Type.Pair @ cFunDef.min_strict) @ cFunDef.min_weak)))
(TFunDef.pair_less_def,((cHOL.eq @ cFunDef.pair_less) @ ((cWellfounded.lex_prod @ cWellfounded.less_than) @ cWellfounded.less_than)))
(TGroups.abs_class_def,((c== @ (cGroups.abs_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.abs_if.abs_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.abs_if @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V0 @ V4)) @ (((cHOL.If @ ((V3 @ V4) @ V2)) @ (V1 @ V4)) @ V4))))))))))))))
(TGroups.monoid.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.monoid @ V0) @ V1)) @ ((cGroups.monoid_axioms @ V0) @ V1)))))))
(TGroups.monoid.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.monoid @ V0) @ V1)) @ (cGroups.semigroup @ V0)))))))
(TGroups.one_class_def,((c== @ (cGroups.one_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.semigroup_def,(call @ (^[V0]: ((c== @ (cGroups.semigroup @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TGroups.sgn_class_def,((c== @ (cGroups.sgn_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.sgn_if.sgn_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cGroups.class.sgn_if @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ (V1 @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ V3)) @ V3) @ (((cHOL.If @ ((V4 @ V3) @ V5)) @ V0) @ (V2 @ V0))))))))))))))))))
(TGroups.zero_reorient,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(THOL.all_conj_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(THOL.conj_left_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.conj @ V0) @ V1)))))))
(THOL.disj_left_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.disj @ V0) @ V1)))))))
(THOL.equal.equal_refl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.class.equal @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V1)) @ cHOL.True)))))))
(THOL.equal_alias_cert,((c== @ (cHOL.equal_class @ cTYPE)) @ ((c== @ cHOL.eq) @ cHOL.equal_class.equal)))
(THOL.equal_itself_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(THOL.induct_equal_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(THOL.induct_false_def,((c== @ cHOL.False) @ cHOL.False))
(THOL.induct_forall_eq,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (cHOL.induct_forall @ (^[V1]: (V0 @ V1)))))))
(THOL.simp_implies_def,((c== @ c==>) @ c==>))
(THilbert_Choice.someI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ (V0 @ (cHilbert_Choice.Eps @ V0))))))))
(TInductive.gfp_lemma2,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.gfp @ V0)) @ (V0 @ (cInductive.complete_lattice_class.gfp @ V0)))))))
(TInductive.gfp_lemma3,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ (V0 @ (cInductive.complete_lattice_class.gfp @ V0))) @ (cInductive.complete_lattice_class.gfp @ V0))))))
(TInductive.gfp_unfold,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cHOL.eq @ (cInductive.complete_lattice_class.gfp @ V0)) @ (V0 @ (cInductive.complete_lattice_class.gfp @ V0)))))))
(TInductive.lfp_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ ((cLattices.inf_class.inf @ (cInductive.complete_lattice_class.lfp @ V0)) @ V1))) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ V1))))))))
(TInductive.lfp_lemma2,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ (V0 @ (cInductive.complete_lattice_class.lfp @ V0))) @ (cInductive.complete_lattice_class.lfp @ V0))))))
(TInductive.lfp_lemma3,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ (V0 @ (cInductive.complete_lattice_class.lfp @ V0)))))))
(TInductive.lfp_unfold,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cHOL.eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ (V0 @ (cInductive.complete_lattice_class.lfp @ V0)))))))
(TInt.Ints_odd_nonzero,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ (cHOL.Not @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ V0)) @ V0)) @ cGroups.zero_class.zero))))))
(TInt.arity_no_bot_int,(cOrderings.no_bot_class @ cTYPE))
(TInt.arity_no_top_int,(cOrderings.no_top_class @ cTYPE))
(TInt.diff_nat_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TInt.half_gt_zero_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TInt.int.right_unique,(cTransfer.right_unique @ cInt.cr_int))
(TInt.less_eq_int_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cInt.Neg @ V0)) @ (cInt.Neg @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V1) @ V0)))))))
(TInt.less_eq_int_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cInt.Neg @ V0)) @ (cInt.Pos @ V1))) @ cHOL.True))))))
(TInt.less_eq_int_code_7,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cInt.Neg @ V0)) @ cInt.zero_int_inst.zero_int)) @ cHOL.True))))
(TInt.less_eq_int_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cInt.Pos @ V0)) @ (cInt.Neg @ V1))) @ cHOL.False))))))
(TInt.less_eq_int_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cInt.Pos @ V0)) @ (cInt.Pos @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TInt.less_eq_int_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cInt.Pos @ V0)) @ cInt.zero_int_inst.zero_int)) @ cHOL.False))))
(TInt.less_eq_int_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cInt.Neg @ V0))) @ cHOL.False))))
(TInt.less_eq_int_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cInt.Pos @ V0))) @ cHOL.True))))
(TInt.less_eq_int_code_1,((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)) @ cHOL.True))
(TInt.less_minus_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cGroups.uminus_class.uminus @ V0))) @ ((cOrderings.ord_class.less @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))))))
(TInt.minus_int.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.minus_int_inst.minus_int @ (cInt.Abs_Integ @ V0)) @ (cInt.Abs_Integ @ V1))) @ (cInt.Abs_Integ @ (((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V5)) @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V4)))))))) @ V0) @ V1))))))))
(TInt.minus_less_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)))))
(TInt.nat_diff_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cHOL.eq @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ V1) @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ (cInt.nat @ V1)) @ (cInt.nat @ V0))))))))))
(TInt.nat_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ (cInt.nat @ ((cInt.times_int_inst.times_int @ V0) @ V1))) @ ((cNat.times_nat_inst.times_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1)))))))))
(TInt.negative_zless_0,(call @ (^[V0]: ((cInt.ord_int_inst.less_int @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V0)))) @ cInt.zero_int_inst.zero_int))))
(TInt.nonneg_int_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V2))) @ V1)))) @ V1)))))))
(TInt.one_int.transfer,((cInt.cr_int @ ((cProduct_Type.Pair @ cNat.one_nat_inst.one_nat) @ cNat.zero_nat_inst.zero_nat)) @ cInt.one_int_inst.one_int))
(TInt.ring_1.Ints_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cSet.member @ V6) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((c==> @ ((cSet.member @ V7) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((cSet.member @ ((V4 @ V6) @ V7)) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))))))))))))))))))))))
(TInt.ring_1.Ints_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cSet.member @ V6) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((c==> @ ((cSet.member @ V7) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((cSet.member @ ((V1 @ V6) @ V7)) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))))))))))))))))))))))
(TInt.times_int.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cInt.Abs_Integ @ V0)) @ (cInt.Abs_Integ @ V1))) @ (cInt.Abs_Integ @ (((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V4)) @ ((cNat.times_nat_inst.times_nat @ V3) @ V5))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V5)) @ ((cNat.times_nat_inst.times_nat @ V3) @ V4))))))))) @ V0) @ V1))))))))
(TInt.zdvd_antisym_abs,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ V0)) @ (cInt.abs_int_inst.abs_int @ V1)))))))))
(TInt.zdvd_mult_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ ((cInt.times_int_inst.times_int @ V0) @ V2))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))
(TInt.zero_less_nat_eq,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cInt.nat @ V0))) @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)))))
(TLattices.inf_fun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V2]: ((cLattices.inf_class.inf @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TLattices.minus_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cGroups.minus_class.minus @ V0) @ V1) @ V2)) @ ((cGroups.minus_class.minus @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TLattices.sup_fun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V2]: ((cLattices.sup_class.sup @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TLifting.NEG_pcr_rule,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cLifting.NEG @ ((cRelation.relcompp @ V0) @ V1)) @ V2)) @ ((cLifting.NEG @ ((cRelation.relcompp @ V0) @ ((cRelation.relcompp @ V1) @ V3))) @ ((cRelation.relcompp @ V2) @ V3))))))))))))
(TLifting.POS_pcr_rule,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cLifting.POS @ ((cRelation.relcompp @ V0) @ V1)) @ V2)) @ ((cLifting.POS @ ((cRelation.relcompp @ V0) @ ((cRelation.relcompp @ V1) @ V3))) @ ((cRelation.relcompp @ V2) @ V3))))))))))))
(TLifting.Quotient_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((cHOL.eq @ (V1 @ (V2 @ V4))) @ V4)))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((V0 @ (V2 @ V4)) @ (V2 @ V4))))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.conj @ ((V0 @ V5) @ V5)) @ ((cHOL.eq @ (V1 @ V4)) @ (V1 @ V5)))))))))) @ ((cHOL.eq @ V3) @ (^[V4]: (^[V5]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V1 @ V4)) @ V5))))))))))))))))))
(TLifting.Quotient_rel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.conj @ ((V0 @ V5) @ V5)) @ ((cHOL.eq @ (V1 @ V4)) @ (V1 @ V5))))) @ ((V0 @ V4) @ V5))))))))))))))))
(TLifting.Respects_def,(call @ (^[V0]: ((cHOL.eq @ (cLifting.Respects @ V0)) @ (cSet.Collect @ (^[V1]: ((V0 @ V1) @ V1)))))))
(TLifting.bi_total_iff,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_total @ V0)) @ ((cHOL.conj @ (cTransfer.right_total @ V0)) @ (cLifting.left_total @ V0))))))
(TLifting.fun_quotient,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cLifting.Quotient @ V4) @ V5) @ V6) @ V7)) @ ((((cLifting.Quotient @ ((cTransfer.fun_rel @ V0) @ V4)) @ ((cFun.map_fun @ V2) @ V5)) @ ((cFun.map_fun @ V1) @ V6)) @ ((cTransfer.fun_rel @ V3) @ V7)))))))))))))))))))))
(TLifting.left_uniqueD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cLifting.left_unique @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V1) @ V3)))))))))))))
(TLifting.left_uniqueI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V3)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V1) @ V2)))))))))) @ (cLifting.left_unique @ V0)))))
(TLifting_Set.set_relI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cSet.Bex @ V1) @ (^[V4]: ((V2 @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cSet.Bex @ V0) @ (^[V4]: ((V2 @ V4) @ V3))))))) @ (((cLifting_Set.set_rel @ V2) @ V0) @ V1))))))))))
(TList.Bex_set_list_ex,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ (cList.set @ V0)) @ V1)) @ ((cList.list_ex @ V1) @ V0)))))))
(TList.Cons_eq_appendI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ ((c==> @ ((cHOL.eq @ V3) @ ((cList.append @ V1) @ V4))) @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V3)) @ ((cList.append @ V2) @ V4)))))))))))))))
(TList.Cons_eq_filterD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.filter @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.append @ V4) @ ((cList.list.Cons @ V0) @ V5)))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: (cHOL.Not @ (V2 @ V6))))) @ ((cHOL.conj @ (V2 @ V0)) @ ((cHOL.eq @ V1) @ ((cList.filter @ V2) @ V5)))))))))))))))))))
(TList.Cons_listrel1E1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ (cList.listrel1 @ V3))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V5) @ V1))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V5)) @ V3)) @ V4))))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V0) @ V5))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V5)) @ (cList.listrel1 @ V3))) @ V4))))) @ V4))))))))))))))
(TList.Cons_listrel1E2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (cList.listrel1 @ V3))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V5) @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ V3)) @ V4))))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V1) @ V5))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V2)) @ (cList.listrel1 @ V3))) @ V4))))) @ V4))))))))))))))
(TList.ListMem.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.ListMem @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ V3) @ ((cList.list.Cons @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cList.ListMem @ V3) @ V4)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ V3) @ ((cList.list.Cons @ V5) @ V4))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.Nil_is_map_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cList.list.Nil) @ ((cList.map @ V0) @ V1))) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.Nil_is_rev_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cList.list.Nil) @ (cList.rev @ V0))) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.Skolem_list_nth,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V2) @ V0)) @ (cHOL.Ex @ (^[V3]: ((V1 @ V2) @ V3))))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ V0)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ ((V1 @ V3) @ ((cList.nth @ V2) @ V3))))))))))))))
(TList.Suc_length_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Suc @ V0)) @ (cNat.size_class.size @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.eq @ (cNat.size_class.size @ V3)) @ V0))))))))))))
(TList.all_nat_less_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V2) @ V0)) @ (V1 @ V2))))) @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (^[V2]: (V1 @ V2)))))))))
(TList.append1_eq_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ cList.list.Nil)))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TList.append_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.append) @ cList.append))))
(TList.arity_type_list,(cHOL.type_class @ cTYPE))
(TList.concat_map_maps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.concat @ ((cList.map @ V0) @ V1))) @ ((cList.maps @ V0) @ V1)))))))
(TList.concat_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ (cList.list_all2 @ V0))) @ (cList.list_all2 @ V0)) @ cList.concat) @ cList.concat))))
(TList.distinct_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.distinct @ ((cList.append @ V0) @ V1))) @ ((cHOL.conj @ (cList.distinct @ V0)) @ ((cHOL.conj @ (cList.distinct @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cList.set @ V0)) @ (cList.set @ V1))) @ cOrderings.bot_class.bot)))))))))
(TList.distinct_concat,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ ((c==> @ (call @ (^[V1]: ((c==> @ ((cSet.member @ V1) @ (cList.set @ V0))) @ (cList.distinct @ V1))))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V1) @ (cList.set @ V0))) @ ((c==> @ ((cSet.member @ V2) @ (cList.set @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cList.set @ V1)) @ (cList.set @ V2))) @ cOrderings.bot_class.bot))))))))) @ (cList.distinct @ (cList.concat @ V0))))))))
(TList.distinct_filter,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.filter @ V1) @ V0))))))))
(TList.distinct_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.insert @ V1) @ V0))))))))
(TList.distinct_rotate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.distinct @ ((cList.rotate @ V0) @ V1))) @ (cList.distinct @ V1)))))))
(TList.dropWhile.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.dropWhile @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ (V0 @ V1)) @ ((cList.dropWhile @ V0) @ V2)) @ ((cList.list.Cons @ V1) @ V2))))))))))
(TList.dropWhile.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.dropWhile @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.empty_replicate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cList.list.Nil) @ ((cList.replicate @ V0) @ V1))) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))))
(TList.enumerate_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.enumerate @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cList.enumerate @ (cNat.Suc @ V0)) @ V2))))))))))
(TList.enumerate_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.enumerate @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.filter_eq_ConsD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.filter @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V4) @ ((cList.list.Cons @ V2) @ V5)))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: (cHOL.Not @ (V0 @ V6))))) @ ((cHOL.conj @ (V0 @ V2)) @ ((cHOL.eq @ V3) @ ((cList.filter @ V0) @ V5)))))))))))))))))))
(TList.filter_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.filter) @ cList.filter))))
(TList.foldl.foldl_Nil,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ cList.list.Nil)) @ V1))))))
(TList.foldl_conv_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ V2)) @ (((cList.fold @ (^[V3]: (^[V4]: ((V0 @ V4) @ V3)))) @ V2) @ V1)))))))))
(TList.foldr.foldr_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.foldr @ V0) @ cList.list.Nil)) @ cFun.id))))
(TList.foldr_conv_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.foldr @ V0) @ V1)) @ ((cList.fold @ V0) @ (cList.rev @ V1))))))))
(TList.foldr_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.foldr @ V0) @ ((cList.replicate @ V1) @ V2))) @ ((cNat.compow @ V1) @ (V0 @ V2))))))))))
(TList.gen_length_code_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.gen_length @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.gen_length @ (cNat.Suc @ V0)) @ V2)))))))))
(TList.gen_length_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.gen_length @ V0) @ cList.list.Nil)) @ V0))))
(TList.impossible_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V1))) @ cHOL.False)))))))))
(TList.in_set_butlastD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ (cList.butlast @ V1)))) @ ((cSet.member @ V0) @ (cList.set @ V1))))))))
(TList.in_set_conv_nth,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.nth @ V1) @ V2)) @ V0))))))))))
(TList.in_set_sublistD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ ((cList.sublist @ V1) @ V2)))) @ ((cSet.member @ V0) @ (cList.set @ V1))))))))))
(TList.insert_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.insert) @ cList.insert)))))
(TList.length_Suc_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.Suc @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.eq @ (cNat.size_class.size @ V3)) @ V1))))))))))))
(TList.length_sublists,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.sublists @ V0))) @ ((cPower.power_class.power @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNat.size_class.size @ V0))))))
(TList.length_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ cHOL.eq) @ cNat.size_class.size) @ cNat.size_class.size))))
(TList.lexord_Nil_left,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ cList.list.Nil) @ V0)) @ (cList.lexord @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V3))))))))))))
(TList.list_all2_Cons1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ ((cList.list.Cons @ V1) @ V2)) @ V3)) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ ((cHOL.conj @ ((V0 @ V1) @ V4)) @ (((cList.list_all2 @ V0) @ V2) @ V5)))))))))))))))))
(TList.list_all2_Cons2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V5))) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ (((cList.list_all2 @ V0) @ V5) @ V3)))))))))))))))))
(TList.list_all2_dropI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ (((cList.list_all2 @ V0) @ ((cList.drop @ V3) @ V1)) @ ((cList.drop @ V3) @ V2))))))))))))
(TList.list_all2_mono',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V1))))))))
(TList.list_all2_nthD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V2))) @ ((V0 @ ((cList.nth @ V1) @ V3)) @ ((cList.nth @ V2) @ V3)))))))))))))
(TList.list_all2_takeI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ (((cList.list_all2 @ V0) @ ((cList.take @ V3) @ V1)) @ ((cList.take @ V3) @ V2))))))))))))
(TList.list_all2_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((V0 @ V6) @ V7)) @ ((c==> @ ((V1 @ V7) @ V8)) @ ((V2 @ V6) @ V8)))))))))) @ ((c==> @ (((cList.list_all2 @ V0) @ V3) @ V4)) @ ((c==> @ (((cList.list_all2 @ V1) @ V4) @ V5)) @ (((cList.list_all2 @ V2) @ V3) @ V5)))))))))))))))))
(TList.list_all_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_all @ V0) @ ((cList.append @ V1) @ V2))) @ ((cHOL.conj @ ((cList.list_all @ V0) @ V1)) @ ((cList.list_all @ V0) @ V2))))))))))
(TList.list_all_length,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list_all @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V1))) @ (V0 @ ((cList.nth @ V1) @ V2)))))))))))
(TList.list_update_def,((c== @ cList.list_update) @ (^[V0]: (((cList.list.list_rec @ (^[V1]: (^[V2]: cList.list.Nil))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cNat.nat.nat_case @ ((cList.list.Cons @ V5) @ V2)) @ (^[V6]: ((cList.list.Cons @ V1) @ ((V3 @ V6) @ V5)))) @ V4))))))) @ V0))))
(TList.listrel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((c==> @ ((V3 @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ (cList.listrel @ V2))) @ ((c==> @ ((V3 @ V6) @ V7)) @ ((V3 @ ((cList.list.Cons @ V4) @ V6)) @ ((cList.list.Cons @ V5) @ V7)))))))))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TList.listrel1_eq_len,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel1 @ V2))) @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))))
(TList.listrel_iff_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V0))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.nth @ V0) @ V3)) @ ((cList.nth @ V1) @ V3))) @ V2)))))))))))))
(TList.listrel_iff_zip,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cSet.Ball @ (cList.set @ ((cList.zip @ V0) @ V1))) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V2))))))))))))))
(TList.listrel_refl_on,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((cRelation.refl_on @ (cList.lists @ V0)) @ (cList.listrel @ V1))))))))
(TList.listrelp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.listrelp @ V0) @ V1) @ V2)) @ ((c==> @ ((V3 @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ (((cList.listrelp @ V0) @ V6) @ V7)) @ ((c==> @ ((V3 @ V6) @ V7)) @ ((V3 @ ((cList.list.Cons @ V4) @ V6)) @ ((cList.list.Cons @ V5) @ V7)))))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TList.listrelp.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ (((cList.listrelp @ V0) @ V3) @ V4)) @ (((cList.listrelp @ V0) @ ((cList.list.Cons @ V1) @ V3)) @ ((cList.list.Cons @ V2) @ V4)))))))))))))))
(TList.listrelp.intros_1,(call @ (^[V0]: (((cList.listrelp @ V0) @ cList.list.Nil) @ cList.list.Nil))))
(TList.listsp_lists_eq,(call @ (^[V0]: ((cHOL.eq @ (cList.listsp @ (^[V1]: ((cSet.member @ V1) @ V0)))) @ (^[V1]: ((cSet.member @ V1) @ (cList.lists @ V0)))))))
(TList.map_is_Nil_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.map_project_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map_project @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V1) @ (^[V3]: ((cHOL.eq @ (V0 @ V3)) @ (cOption.option.Some @ V2))))))))))))
(TList.map_tailrec_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map_tailrec @ V0) @ V1)) @ (cList.rev @ (((cList.map_tailrec_rev @ V0) @ V1) @ cList.list.Nil))))))))
(TList.map_tailrec_rev,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.map_tailrec_rev @ V0) @ V1) @ V2)) @ ((cList.append @ (cList.rev @ ((cList.map @ V0) @ V1))) @ V2)))))))))
(TList.measures_lesseq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (V0 @ V1)) @ (V0 @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.measures @ V3))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.measures @ ((cList.list.Cons @ V0) @ V3))))))))))))))
(TList.nth_list_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.nth @ (((cList.list_update @ V1) @ V0) @ V2)) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V3)) @ V2) @ ((cList.nth @ V1) @ V3)))))))))))))
(TList.partition.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.partition @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cHOL.Let @ ((cList.partition @ V0) @ V2)) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (((cHOL.If @ (V0 @ V1)) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V1) @ V3)) @ V4)) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V1) @ V4)))))))))))))))
(TList.partition.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.partition @ V0) @ cList.list.Nil)) @ ((cProduct_Type.Pair @ cList.list.Nil) @ cList.list.Nil)))))
(TList.reflp_list_all2,(call @ (^[V0]: ((c==> @ (cRelation.reflp @ V0)) @ (cRelation.reflp @ (cList.list_all2 @ V0))))))
(TList.remdups_adj_def,((c== @ cList.remdups_adj) @ (^[V0]: (cList.remdups_adj_sumC @ V0))))
(TList.remdups_adj_rev,(call @ (^[V0]: ((cHOL.eq @ (cList.remdups_adj @ (cList.rev @ V0))) @ (cList.rev @ (cList.remdups_adj @ V0))))))
(TList.remdups_adj_set,(call @ (^[V0]: ((cHOL.eq @ (cList.set @ (cList.remdups_adj @ V0))) @ (cList.set @ V0)))))
(TList.remdups_remdups,(call @ (^[V0]: ((cHOL.eq @ (cList.remdups @ (cList.remdups @ V0))) @ (cList.remdups @ V0)))))
(TList.remove1_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.remove1 @ V0) @ ((cList.remove1 @ V1) @ V2))) @ ((cList.remove1 @ V1) @ ((cList.remove1 @ V0) @ V2))))))))))
(TList.remove1_remdups,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ ((cList.remove1 @ V1) @ (cList.remdups @ V0))) @ (cList.remdups @ ((cList.remove1 @ V1) @ V0)))))))))
(TList.removeAll.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.removeAll @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V1)) @ ((cList.removeAll @ V0) @ V2)) @ ((cList.list.Cons @ V1) @ ((cList.removeAll @ V0) @ V2)))))))))))
(TList.removeAll.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.removeAll @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.replicate.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.replicate @ (cNat.Suc @ V0)) @ V1)) @ ((cList.list.Cons @ V1) @ ((cList.replicate @ V0) @ V1))))))))
(TList.replicate.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.replicate @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cList.list.Nil))))
(TList.replicate_empty,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.replicate @ V0) @ V1)) @ cList.list.Nil)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))))
(TList.return_list_def,(call @ (^[V0]: ((cHOL.eq @ (cList.return_list @ V0)) @ ((cList.map @ cInt.nat) @ V0)))))
(TList.rev_eq_Cons_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (cList.rev @ V0)) @ ((cList.list.Cons @ V1) @ V2))) @ ((cHOL.eq @ V0) @ ((cList.append @ (cList.rev @ V2)) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))))))))
(TList.rev_is_Nil_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.rev @ V0)) @ cList.list.Nil)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.rev_is_rev_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cList.rev @ V0)) @ (cList.rev @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TList.rotate_conv_mod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.rotate @ V0) @ V1)) @ ((cList.rotate @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.size_class.size @ V1))) @ V1)))))))
(TList.rotate_length01,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ ((cList.rotate @ V1) @ V0)) @ V0)))))))
(TList.rotate_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.rotate) @ cList.rotate))))
(TList.set_drop_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cList.set @ ((cList.drop @ V0) @ V1))) @ (cList.set @ V1)))))))
(TList.set_subset_Cons,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cList.set @ V0)) @ (cList.set @ ((cList.list.Cons @ V1) @ V0))))))))
(TList.set_take_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cList.set @ ((cList.take @ V0) @ V1))) @ (cList.set @ V1)))))))
(TList.set_update_memI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cSet.member @ V2) @ (cList.set @ (((cList.list_update @ V1) @ V0) @ V2)))))))))))
(TList.sorted_find_Min,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ ((c==> @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cHOL.eq @ ((cList.find @ V1) @ V0)) @ (cOption.option.Some @ (cBig_Operators.linorder_class.Min @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ (cList.set @ V0))) @ (V1 @ V2))))))))))))))
(TList.splice_sumC_def,((c== @ cList.splice_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cList.splice_graph @ V0) @ V1))))))
(TList.splice_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.splice) @ cList.splice))))
(TList.split_list_last,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V2) @ ((cList.list.Cons @ V0) @ V3)))) @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V3))))))))))))))
(TList.split_list_prop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ (V1 @ V3))))))))))))))
(TList.sublists_powset,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cList.set) @ (cList.set @ (cList.sublists @ V0)))) @ (cSet.Pow @ (cList.set @ V0))))))
(TList.takeWhile.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.takeWhile @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ (V0 @ V1)) @ ((cList.list.Cons @ V1) @ ((cList.takeWhile @ V0) @ V2))) @ cList.list.Nil)))))))))
(TList.takeWhile.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.takeWhile @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.transpose.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ cList.list.Nil) @ V2))) @ V1)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ ((cList.list.Cons @ V2) @ V3)) @ V4))) @ V1)))))))) @ V1))))))))
(TList.transpose.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cList.transpose @ V0)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ V2))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ cList.list.Nil) @ V3))) @ ((c==> @ ((cHOL.eq @ V1) @ (cList.transpose @ V3))) @ V2))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V6) @ cList.list.Nil))))) @ V5)))) @ (cList.transpose @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5))))))) @ V2))))))))) @ V2)))))))))))
(TList.transpose.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.transpose @ ((cList.list.Cons @ ((cList.list.Cons @ V0) @ V1)) @ V2))) @ ((cList.list.Cons @ ((cList.list.Cons @ V0) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ V3) @ cList.list.Nil))))) @ V2)))) @ (cList.transpose @ ((cList.list.Cons @ V1) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ V4) @ cList.list.Nil))))) @ V2)))))))))))))
(TList.transpose.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cList.transpose @ ((cList.list.Cons @ cList.list.Nil) @ V0))) @ (cList.transpose @ V0)))))
(TList.transpose.simps_1,((cHOL.eq @ (cList.transpose @ cList.list.Nil)) @ cList.list.Nil))
(TList.transpose_empty,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.transpose @ V0)) @ cList.list.Nil)) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V1]: ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.upt_eq_Nil_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.upt @ V0) @ V1)) @ cList.list.Nil)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V0))))))))
(TList.upt_rec_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upt @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cList.list.Cons @ (cNum.numeral_class.numeral @ V0)) @ ((cList.upt @ (cNat.Suc @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V1)))) @ cList.list.Nil)))))))
(TList.upto_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)) @ ((V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4)) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TList.upto_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cList.upto_rel @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)) @ ((cProduct_Type.Pair @ V0) @ V1))))))))
(TList.wf_listrel1_iff,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wf @ (cList.listrel1 @ V0))) @ (cWellfounded.wf @ V0)))))
(TList.zip_map_fst_snd,(call @ (^[V0]: ((cHOL.eq @ ((cList.zip @ ((cList.map @ cProduct_Type.fst) @ V0)) @ ((cList.map @ cProduct_Type.snd) @ V0))) @ V0))))
(TMap.fun_upd_restrict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cFun.fun_upd @ ((cMap.restrict_map @ V0) @ V1)) @ V2) @ V3)) @ (((cFun.fun_upd @ ((cMap.restrict_map @ V0) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ V2) @ V3)))))))))))
(TMap.map_add_Some_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ (((cMap.map_add @ V0) @ V1) @ V2)) @ (cOption.option.Some @ V3))) @ ((cHOL.disj @ ((cHOL.eq @ (V1 @ V2)) @ (cOption.option.Some @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ cOption.option.None)) @ ((cHOL.eq @ (V0 @ V2)) @ (cOption.option.Some @ V3))))))))))))))
(TMap.map_add_upd_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cMap.dom @ V1)))) @ ((cHOL.eq @ ((cMap.map_add @ (((cFun.fun_upd @ V2) @ V0) @ (cOption.option.Some @ V3))) @ V1)) @ (((cFun.fun_upd @ ((cMap.map_add @ V2) @ V1)) @ V0) @ (cOption.option.Some @ V3)))))))))))))
(TMap.map_of_Cons_code_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cMap.map_of @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V3)) @ (cOption.option.Some @ V1)) @ ((cMap.map_of @ V2) @ V3))))))))))))
(TMap.map_of_Cons_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cMap.map_of @ cList.list.Nil) @ V0)) @ cOption.option.None))))
(TMap.map_of_filter_in,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cMap.map_of @ V0) @ V1)) @ (cOption.option.Some @ V2))) @ ((c==> @ ((V3 @ V1) @ V2)) @ ((cHOL.eq @ ((cMap.map_of @ ((cList.filter @ (cProduct_Type.prod.prod_case @ V3)) @ V0)) @ V1)) @ (cOption.option.Some @ V2)))))))))))))
(TMap.map_upd_nonempty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2))) @ (^[V3]: cOption.option.None))))))))))
(TMap.map_upds_append1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (((cMap.map_upds @ V2) @ ((cList.append @ V0) @ ((cList.list.Cons @ V3) @ cList.list.Nil))) @ V1)) @ (((cFun.fun_upd @ (((cMap.map_upds @ V2) @ V0) @ V1)) @ V3) @ (cOption.option.Some @ ((cList.nth @ V1) @ (cNat.size_class.size @ V0)))))))))))))))
(TMap.restrict_fun_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cMap.restrict_map @ (((cFun.fun_upd @ V0) @ V1) @ V2)) @ V3)) @ (((cHOL.If @ ((cSet.member @ V1) @ V3)) @ (((cFun.fun_upd @ ((cMap.restrict_map @ V0) @ ((cGroups.minus_class.minus @ V3) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ V1) @ V2)) @ ((cMap.restrict_map @ V0) @ V3))))))))))))
(TMap.restrict_map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMap.restrict_map @ V0) @ V1)) @ (^[V2]: (((cHOL.If @ ((cSet.member @ V2) @ V1)) @ (V0 @ V2)) @ cOption.option.None))))))))
(TMap.set_map_of_compr,(call @ (^[V0]: ((c==> @ (cList.distinct @ ((cList.map @ cProduct_Type.fst) @ V0))) @ ((cHOL.eq @ (cList.set @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.eq @ ((cMap.map_of @ V0) @ V1)) @ (cOption.option.Some @ V2)))))))))))
(TMeson.make_neg_rule',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TMeson.make_pos_rule',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ V0)) @ V1)))))))
(TMeson.skolem_COMBK_D,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cMeson.skolem @ ((cMeson.COMBK @ V0) @ V1))) @ V0))))))
(TMeson.skolem_COMBK_I,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ (cMeson.skolem @ ((cMeson.COMBK @ V0) @ V1))))))))
(TNat.Kleene_iter_lpfp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (((cNat.compow @ V2) @ V0) @ cOrderings.bot_class.bot)) @ V1))))))))))
(TNat.Suc_mult_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V2))) @ ((cHOL.eq @ V1) @ V2)))))))))
(TNat.add_diff_inverse,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V1) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))) @ V0)))))))
(TNat.add_eq_self_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V0)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)))))))
(TNat.add_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.arity_no_top_nat,(cOrderings.no_top_class @ cTYPE))
(TNat.diff_add_inverse,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V0)) @ V1))))))
(TNat.diff_diff_cancel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V1) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ V0)))))))
(TNat.diffs0_imp_equal,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.dvd.antisym_conv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.dvd.le_neq_trans,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))))
(TNat.dvd.less_imp_neq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.dvd.less_not_sym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))))))))))
(TNat.dvd.neq_le_trans,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))))
(TNat.dvd.order.irrefl,(call @ (^[V0]: (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V0)))))))
(TNat.dvd.order_axioms,((cOrderings.class.order @ cRings.dvd_class.dvd) @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))
(TNat.dvd.strict_monoD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.order.strict_mono @ (^[V3]: (^[V4]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V3) @ V4)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V4) @ V3)))))) @ V0)) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat.dvd.strict_monoI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2)))))))) @ ((cOrderings.order.strict_mono @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))))) @ V0)))))
(TNat.dvd_mult_cancel1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ V0)) @ ((cHOL.eq @ V1) @ cNat.one_nat_inst.one_nat))))))))
(TNat.dvd_mult_cancel2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cNat.times_nat_inst.times_nat @ V1) @ V0)) @ V0)) @ ((cHOL.eq @ V1) @ cNat.one_nat_inst.one_nat))))))))
(TNat.dvd_plus_eq_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TNat.funpow_Suc_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ (cNat.Suc @ V0)) @ V1)) @ ((cFun.comp @ ((cNat.compow @ V0) @ V1)) @ V1)))))))
(TNat.infinite_descent,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ (cHOL.Not @ (V0 @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V3) @ V2)) @ (cHOL.Not @ (V0 @ V3))))))))) @ (V0 @ V1)))))))
(TNat.le_eq_less_or_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.less_add_eq_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3))) @ ((cNat.ord_nat_inst.less_nat @ V2) @ V3))))))))))))
(TNat.less_iff_Suc_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)))))))))))
(TNat.less_imp_Suc_add,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)))))))))))
(TNat.minus_nat.diff_0,(call @ (^[V0]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V0))))
(TNat.nat.nat_case_def,((c== @ cNat.nat.nat_case) @ (^[V0]: (^[V1]: ((cNat.nat.nat_rec @ V0) @ (^[V2]: (^[V3]: (V1 @ V2))))))))
(TNat.nat.nat_size_def,((c== @ cNat.nat.nat_size) @ ((cNat.nat.nat_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))
(TNat.nat_add_max_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TNat.nat_dvd_not_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))))
(TNat.nat_mult_1_right,(call @ (^[V0]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V0))))
(TNat.nat_mult_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V0)))))))
(TNat.not0_implies_Suc,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNat.Suc @ V1))))))))
(TNat.plus_nat.add_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cNat.Suc @ V0)) @ V1)) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TNat.size_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cNat.size_class @ cTYPE)))
(TNat.size_class.super,((c==> @ (cNat.size_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TNat.times_nat.mult_0,(call @ (^[V0]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TNat_Transfer.all_nat,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ (cInt.nat @ V1)))))))))
(TNat_Transfer.ex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cHOL.eq @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ (V0 @ V3)) @ (V1 @ V3))))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ (V0 @ V3)) @ (V2 @ V3)))))))))))))
(TNat_Transfer.tsub_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cHOL.eq @ ((cNat_Transfer.tsub @ V1) @ V0)) @ ((cInt.minus_int_inst.minus_int @ V1) @ V0))))))))
(TNitpick.fun_box.recs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.fun_box.fun_box_rec @ V0) @ (cNitpick.fun_box.FunBox @ V1))) @ (V0 @ V1)))))))
(TNitpick.fun_box.size_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cNitpick.fun_box.FunBox @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TNitpick.fun_box.size_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNitpick.fun_box.fun_box_size @ V0) @ V1) @ (cNitpick.fun_box.FunBox @ V2))) @ cNat.zero_nat_inst.zero_nat))))))))
(TNitpick.one_frac_def,((c== @ cNitpick.one_frac) @ (cNitpick.Abs_Frac @ ((cProduct_Type.Pair @ cInt.one_int_inst.one_int) @ cInt.one_int_inst.one_int))))
(TNitpick.word.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TNitpick.word.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.word.Word @ V2))) @ V1)))) @ V1))))))
(TNitpick.word.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cNitpick.word.Word @ V2))))) @ (V0 @ V1)))))))
(TNum.add_numeral_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))) @ V2)))))))))
(TNum.diff_Suc_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNum.pred_numeral @ V1))))))))
(TNum.diff_numeral_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNat.Suc @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ (cNum.pred_numeral @ V0)) @ V1)))))))
(TNum.divide_numeral_1,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ (cNum.numeral_class.numeral @ cNum.num.One))) @ V0))))
(TNum.eq_numeral_extra_2,(cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNum.eq_numeral_extra_1,(cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ cGroups.one_class.one)))
(TNum.eval_nat_numeral_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))) @ (cNat.Suc @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0)))))))
(TNum.eval_nat_numeral_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))) @ (cNat.Suc @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0)))))))
(TNum.eval_nat_numeral_1,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))
(TNum.less_Suc_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNum.pred_numeral @ V1))))))))
(TNum.less_numeral_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNat.Suc @ V1))) @ ((cNat.ord_nat_inst.less_nat @ (cNum.pred_numeral @ V0)) @ V1)))))))
(TNum.nat_case_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ (cNum.numeral_class.numeral @ V2))) @ ((cHOL.Let @ (cNum.pred_numeral @ V2)) @ (^[V3]: (V1 @ V3)))))))))))
(TNum.nat_of_num.simps_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.nat_of_num @ (cNum.num.Bit1 @ V0))) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V0)))))))
(TNum.nat_of_num.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.nat_of_num @ (cNum.num.Bit0 @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.nat_of_num @ V0)) @ (cNum.nat_of_num @ V0))))))
(TNum.nat_of_num.simps_1,((cHOL.eq @ (cNum.nat_of_num @ cNum.num.One)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))
(TNum.nat_of_num_neq_0,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.nat_of_num @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TNum.num.num_case_def,((c== @ cNum.num.num_case) @ (^[V0]: (^[V1]: (^[V2]: (((cNum.num.num_rec @ V0) @ (^[V3]: (^[V4]: (V1 @ V3)))) @ (^[V3]: (^[V4]: (V2 @ V3)))))))))
(TNum.num.num_size_def,((c== @ cNum.num.num_size) @ (((cNum.num.num_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))
(TNum.num_of_nat.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.num_of_nat @ (cNat.Suc @ V0))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (cNum.inc @ (cNum.num_of_nat @ V0))) @ cNum.num.One)))))
(TNum.num_of_nat.simps_1,((cHOL.eq @ (cNum.num_of_nat @ cNat.zero_nat_inst.zero_nat)) @ cNum.num.One))
(TNum.pred_numeral_def,(call @ (^[V0]: ((cHOL.eq @ (cNum.pred_numeral @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ cNat.one_nat_inst.one_nat)))))
(TOption.option.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cOption.option.None)) @ ((c==> @ (call @ (^[V2]: (V0 @ (cOption.option.Some @ V2))))) @ (V0 @ V1))))))))
(TOption.option.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cOption.option.Some @ V0)) @ (cOption.option.Some @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TOption.option.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cOption.option.option_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cOption.option.None)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cOption.option.Some @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TOption.option.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cOption.option.option_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cOption.option.None)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cOption.option.Some @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TOrderings.le_fun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TPower.power_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)))))))))
(TPower.power_one_over,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0)) @ V1)))))))
(TPredicate.apply_bind,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.pred_of_seq @ ((cPredicate.apply @ V0) @ V1))) @ ((cPredicate.bind @ (cPredicate.pred_of_seq @ V1)) @ V0)))))))
(TPredicate.eq.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ V3) @ V3)))) @ ((V2 @ V0) @ V1))))))))))
(TPredicate.eval.simps,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.eval @ (cPredicate.pred.Pred @ V0))) @ V0))))
(TPredicate.eval_compl,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.eval @ (cGroups.uminus_class.uminus @ V0))) @ (cGroups.uminus_class.uminus @ (cPredicate.eval @ V0))))))
(TPredicate.eval_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.eval @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cGroups.minus_class.minus @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1))))))))
(TPredicate.if_pred_eq,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.if_pred @ V0)) @ (((cHOL.If @ V0) @ (cPredicate.single @ cProduct_Type.Unity)) @ cOrderings.bot_class.bot)))))
(TPredicate.member_def,((c== @ cPredicate.member) @ (^[V0]: ((((cPredicate.seq.seq_rec @ (^[V1]: cHOL.False)) @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.disj @ ((cHOL.eq @ V3) @ V1)) @ ((cPredicate.eval @ V2) @ V3)))))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cPredicate.eval @ V1) @ V4)) @ (V3 @ V4))))))) @ V0))))
(TPredicate.not_predE',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ (cPredicate.not_pred @ V0)) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cPredicate.eval @ V0) @ V1))) @ V2)) @ V2)))))))))
(TPredicate.not_predI',(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cPredicate.eval @ V0) @ cProduct_Type.Unity))) @ ((cPredicate.eval @ (cPredicate.not_pred @ V0)) @ cProduct_Type.Unity)))))
(TPredicate.null.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.null @ ((cPredicate.seq.Join @ V0) @ V1))) @ ((cHOL.conj @ (cPredicate.is_empty @ V0)) @ (cPredicate.null @ V1))))))))
(TPredicate.null.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.null @ ((cPredicate.seq.Insert @ V0) @ V1))) @ cHOL.False))))))
(TPredicate.null.simps_1,((cHOL.eq @ (cPredicate.null @ cPredicate.seq.Empty)) @ cHOL.True))
(TPredicate.pred.cases,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.pred.pred_case @ V0) @ (cPredicate.pred.Pred @ V1))) @ (V0 @ V1)))))))
(TPredicate.pred.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.pred.pred_rec @ V0) @ (cPredicate.pred.Pred @ V1))) @ (V0 @ V1)))))))
(TPredicate.pred.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.pred.pred_case @ V0) @ (cPredicate.pred.Pred @ V1))) @ (V0 @ V1)))))))
(TPredicate.pred.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cPredicate.pred.Pred @ V0)) @ (cPredicate.pred.Pred @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.pred.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cPredicate.pred.pred_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cPredicate.pred.Pred @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TPredicate.seq.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cPredicate.seq.Empty)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cPredicate.seq.Insert @ V2) @ V3))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cPredicate.seq.Join @ V2) @ V3)))))))) @ (V0 @ V1)))))))))
(TPredicate.seq.inject_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cPredicate.seq.Join @ V0) @ V1)) @ ((cPredicate.seq.Join @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TPredicate.seq.inject_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cPredicate.seq.Insert @ V0) @ V1)) @ ((cPredicate.seq.Insert @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TPredicate.seq.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cPredicate.seq.seq_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cPredicate.seq.Empty)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Insert @ V5) @ V6))) @ (cHOL.Not @ (V0 @ ((V2 @ V5) @ V6))))))))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Join @ V5) @ V6))) @ (cHOL.Not @ (V0 @ ((V3 @ V5) @ V6)))))))))))))))))))))))
(TPredicate.seq.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cPredicate.seq.seq_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cPredicate.seq.Empty)) @ (V0 @ V1))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Insert @ V5) @ V6))) @ (V0 @ ((V2 @ V5) @ V6)))))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Join @ V5) @ V6))) @ (V0 @ ((V3 @ V5) @ V6)))))))))))))))))))))
(TPredicate.single_def,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.single @ V0)) @ (cPredicate.pred.Pred @ (cHOL.eq @ V0))))))
(TPresburger.zdvd_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((c== @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cRings.dvd_class.dvd @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ ((cInt.times_int_inst.times_int @ V0) @ V2)))))))))))
(TProduct_Type.Pair_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TProduct_Type.SigmaD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Sigma @ V2) @ V3))) @ ((cSet.member @ V0) @ V2)))))))))))
(TProduct_Type.SigmaD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Sigma @ V2) @ V3))) @ ((cSet.member @ V1) @ (V3 @ V0))))))))))))
(TProduct_Type.SigmaE2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Sigma @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V2)) @ ((c==> @ ((cSet.member @ V1) @ (V3 @ V0))) @ V4))) @ V4)))))))))))))
(TProduct_Type.fst_def,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.fst @ V0)) @ ((cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: V1))) @ V0)))))
(TProduct_Type.fst_eqD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cProduct_Type.fst @ ((cProduct_Type.Pair @ V0) @ V1))) @ V2)) @ ((cHOL.eq @ V0) @ V2)))))))))
(TProduct_Type.snd_def,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.snd @ V0)) @ ((cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: V2))) @ V0)))))
(TProduct_Type.snd_eqD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cProduct_Type.snd @ ((cProduct_Type.Pair @ V0) @ V1))) @ V2)) @ ((cHOL.eq @ V1) @ V2)))))))))
(TProduct_Type.splitD',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ V3)) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TProduct_Type.splitE',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cProduct_Type.prod.prod_case @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ (((V0 @ V4) @ V5) @ V2)) @ V3))))))) @ V3)))))))))))
(TProduct_Type.splitE2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ (V0 @ ((V1 @ V4) @ V5))) @ V3))))))) @ V3)))))))))))
(TProduct_Type.splitI2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((V1 @ V2) @ V3))))))) @ ((cProduct_Type.prod.prod_case @ V1) @ V0)))))))
(TProduct_Type.unit_eq,(call @ (^[V0]: ((cHOL.eq @ V0) @ cProduct_Type.Unity))))
(TPure.all_conjunction,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (call @ (^[V2]: ((cPure.conjunction @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cPure.conjunction @ (call @ (^[V2]: (V0 @ V2)))) @ (call @ (^[V2]: (V1 @ V2))))))))))
(TPure.conjunction_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPure.conjunction @ V0) @ V1)) @ (call @ (^[V2]: ((c==> @ ((c==> @ V0) @ ((c==> @ V1) @ V2))) @ V2)))))))))
(TPure.conjunction_imp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((c==> @ ((cPure.conjunction @ V0) @ V1)) @ V2)) @ ((c==> @ V0) @ ((c==> @ V1) @ V2))))))))))
(TPure.equal_intr_rule,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ V0)) @ ((c== @ V0) @ V1))))))))
(TPure.imp_conjunction,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((c==> @ V0) @ ((cPure.conjunction @ V1) @ V2))) @ ((cPure.conjunction @ ((c==> @ V0) @ V1)) @ ((c==> @ V0) @ V2))))))))))
(TQuotient.apply_rspQ3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((((cTransfer.fun_rel @ V0) @ V3) @ V4) @ V5)) @ ((c==> @ ((V0 @ V6) @ V7)) @ ((V3 @ (V4 @ V6)) @ (V5 @ V7))))))))))))))))))))))
(TQuotient.bex_ex_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.implies @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((V0 @ V4) @ V3)))))) @ (cHOL.Ex @ (^[V3]: ((cSet.Bex @ V1) @ (^[V4]: ((V2 @ V4) @ V3))))))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((V0 @ V3) @ V4)))))) @ ((cSet.Bex @ V1) @ (^[V3]: (cHOL.Ex @ (^[V4]: ((V2 @ V3) @ V4))))))))))))))
(TQuotient.bex_reg_eqv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((cHOL.eq @ ((cSet.Bex @ (cLifting.Respects @ V0)) @ V1)) @ (cHOL.Ex @ V1))))))))
(TQuotient.lambda_prs1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cFun.map_fun @ V2) @ V4) @ (^[V7]: ((((cFun.map_fun @ V1) @ V5) @ V6) @ V7)))) @ (^[V7]: (V6 @ V7))))))))))))))))))))
(TQuotient.rep_abs_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ (V2 @ (V1 @ V4))))))))))))))))
(TRandom.inc_shift_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom.inc_shift @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V1)) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))))))
(TRandom.iterate.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TRandom.iterate.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cRandom.iterate @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V7)) @ ((cProduct_Type.scomp @ (V6 @ V7)) @ ((cRandom.iterate @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))) @ V4))))))))))) @ V4)))))))))))))
(TRandom.iterate.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRandom.iterate @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V2)) @ ((cProduct_Type.scomp @ (V1 @ V2)) @ ((cRandom.iterate @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)))))))))))
(TRandom.log_graph_def,((c== @ cRandom.log_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))))))))))))))))
(TRandom.log_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.log_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3)))) @ V2)))))))) @ V2)))))))))
(TRandom.log_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom.log_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cCode_Numeral.div_natural_inst.div_natural @ V3) @ V2)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V3) @ V2)))))))))))))))
(TRandom_Pred.bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Pred.bind @ V0) @ V1)) @ (^[V2]: ((cHOL.Let @ (V0 @ V2)) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cHOL.Let @ (cRandom.split_seed @ V4)) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cProduct_Type.Pair @ ((cPredicate.bind @ V3) @ (^[V7]: (cProduct_Type.fst @ ((V1 @ V7) @ V5))))) @ V6))))))))))))))))
(TRandom_Pred.iter_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRandom_Pred.iter @ V0) @ V1) @ V2)) @ ((((cRandom_Pred.iter' @ cTYPE) @ V0) @ V1) @ V2)))))))))
(TRecord.K_record_comp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (^[V2]: V0)) @ V1)) @ (^[V2]: V0)))))))
(TRecord.o_eq_dest_lhs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ (V0 @ (V1 @ V3))) @ (V2 @ V3))))))))))))
(TRelation.Domain_dsum,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.Domain @ ((cDatatype.dsum @ V0) @ V1))) @ ((cDatatype.usum @ (cRelation.Domain @ V0)) @ (cRelation.Domain @ V1))))))))
(TRelation.Domain_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cRelation.Domain @ V0)) @ (cRelation.Domain @ V1))))))))
(TRelation.Domainp_def,((c== @ cRelation.Domainp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V3)) @ ((V0 @ V3) @ V4))))))))))))
(TRelation.Field_Union,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Field @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ cRelation.Field) @ V0))))))
(TRelation.Field_empty,((cHOL.eq @ (cRelation.Field @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TRelation.INF_INT_eq2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (V1 @ V2))))))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V1 @ V4))))))))))))
(TRelation.INF_Int_eq2,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V1]: (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)))))) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cComplete_Lattices.Inf_class.Inf @ V0))))))))
(TRelation.Id_on_empty,((cHOL.eq @ (cRelation.Id_on @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TRelation.Image_Id_on,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Image @ (cRelation.Id_on @ V0)) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TRelation.Image_empty,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.Image @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TRelation.Image_eq_UN,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Image @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: ((cRelation.Image @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))))))))
(TRelation.Inf_INT_eq2,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cSet.image @ cProduct_Type.prod.prod_case) @ V0)) @ cSet.Collect))))))))
(TRelation.Powp_Pow_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Powp @ (^[V1]: ((cSet.member @ V1) @ V0)))) @ (^[V1]: ((cSet.member @ V1) @ (cSet.Pow @ V0)))))))
(TRelation.Range.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Range @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ V2))))))) @ V2)))))))))
(TRelation.Range.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cRelation.Range @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))))))))))
(TRelation.Range_Id_on,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Range @ (cRelation.Id_on @ V0))) @ V0))))
(TRelation.Range_Un_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.Range @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cRelation.Range @ V0)) @ (cRelation.Range @ V1))))))))
(TRelation.Range_Union,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Range @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: (cRelation.Range @ V1)))))))
(TRelation.Range_empty,((cHOL.eq @ (cRelation.Range @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TRelation.SUP_Sup_eq2,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)))))) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cComplete_Lattices.Sup_class.Sup @ V0))))))))
(TRelation.Sup_SUP_eq2,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet.image @ cProduct_Type.prod.prod_case) @ V0)) @ cSet.Collect))))))))
(TRelation.antisym_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.antisym @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0)) @ ((cHOL.eq @ V1) @ V2)))))))))))
(TRelation.converse_Id,((cHOL.eq @ (cRelation.converse @ cRelation.Id)) @ cRelation.Id))
(TRelation.converse_Un,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.converse @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cRelation.converse @ V0)) @ (cRelation.converse @ V1))))))))
(TRelation.inf_Int_eq2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cLattices.inf_class.inf @ V0) @ V1))))))))))
(TRelation.lfp_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cInductive.complete_lattice_class.lfp @ V2))) @ ((c==> @ (cOrderings.order_class.mono @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (V2 @ ((cLattices.inf_class.inf @ (cInductive.complete_lattice_class.lfp @ V2)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: ((V3 @ V6) @ V7))))))))) @ ((V3 @ V4) @ V5))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TRelation.refl_on_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((c==> @ ((cRelation.refl_on @ V2) @ V3)) @ ((cRelation.refl_on @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V3)))))))))))))
(TRelation.refl_on_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.refl_on @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V1) @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V0)))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V2)) @ V1))))))))))
(TRelation.relcomp_def,((c== @ cRelation.relcomp) @ (^[V0]: (^[V1]: (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((((cRelation.relcompp @ (^[V4]: (^[V5]: ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V0)))) @ (^[V4]: (^[V5]: ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1)))) @ V2) @ V3)))))))))
(TRelation.symp_sym_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.symp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (cRelation.sym @ V0)))))
(TRelation.trans_INTER,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cRelation.trans @ (V1 @ V2))))) @ (cRelation.trans @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1))))))))
(TRelation.trans_Id_on,(call @ (^[V0]: (cRelation.trans @ (cRelation.Id_on @ V0)))))
(TRings.class.idom_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cRings.class.no_zero_divisors @ V0) @ V3))))))))))))))))
(TRings.class.ring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.semiring @ V0) @ V4))))))))))))))
(TRings.dvd_class.dvdE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ ((cGroups.times_class.times @ V0) @ V3))) @ V2)))) @ V2)))))))))
(TRings.dvd_class.dvdI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))))
(TRings.idom_class_def,((c== @ (cRings.idom_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_ring_1_class @ cTYPE)) @ (cRings.no_zero_divisors_class @ cTYPE))))
(TRings.ring_class_def,((c== @ (cRings.ring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_group_add_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE))))
(TSMT.pattern.eq.simps,((c== @ ((cHOL.equal_class.equal @ cSMT.pattern.Pattern) @ cSMT.pattern.Pattern)) @ cHOL.True))
(TSMT.pattern.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.eq @ V0) @ cSMT.pattern.Pattern))))
(TSet.Collect_conv_if2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ (V1 @ V2))))) @ (((cHOL.If @ (V1 @ V0)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot)))))))
(TSet.Collect_empty_eq,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cSet.Collect @ V0)) @ cOrderings.bot_class.bot)) @ (cHOL.All @ (^[V1]: (cHOL.Not @ (V0 @ V1))))))))
(TSet.Compl_partition2,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ cOrderings.top_class.top))))
(TSet.Diff_Int_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TSet.Diff_subset_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TSet.Int_Collect_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cHOL.implies @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ (cSet.Collect @ V2))) @ ((cLattices.inf_class.inf @ V1) @ (cSet.Collect @ V3))))))))))))))
(TSet.Int_insert_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cSet.insert @ V1) @ V2))) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ ((cSet.insert @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TSet.Int_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TSet.Un_singleton_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))))
(TSet.bex_disj_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V3]: ((cHOL.disj @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cHOL.disj @ ((cSet.Bex @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cSet.Bex @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.doubleton_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.insert @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet.insert @ V2) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.eq @ V1) @ V2)))))))))))))
(TSet.empty_Collect_eq,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (cSet.Collect @ V0))) @ (cHOL.All @ (^[V1]: (cHOL.Not @ (V0 @ V1))))))))
(TSet.empty_not_insert,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet.insert @ V0) @ V1))))))))
(TSet.full_SetCompr_eq,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (V0 @ V2))))))) @ ((cSet.image @ V0) @ cOrderings.top_class.top)))))
(TSet.if_image_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.image @ (^[V4]: (((cHOL.If @ (V0 @ V4)) @ (V1 @ V4)) @ (V2 @ V4)))) @ V3)) @ ((cLattices.sup_class.sup @ ((cSet.image @ V1) @ ((cLattices.inf_class.inf @ V3) @ (cSet.Collect @ (^[V4]: (V0 @ V4)))))) @ ((cSet.image @ V2) @ ((cLattices.inf_class.inf @ V3) @ (cSet.Collect @ (^[V4]: (cHOL.Not @ (V0 @ V4)))))))))))))))))
(TSet.image_Int_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2))))))))))
(TSet.image_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((cSet.Ball @ V1) @ (^[V3]: ((cSet.member @ (V0 @ V3)) @ V2)))))))))))
(TSet.insert_not_empty,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ cOrderings.bot_class.bot)))))))
(TSet.singleton_Un_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V2) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ V2) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))))))))))
(TSet.singleton_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet.strong_ball_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cSet.Ball @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TSet.subset_image_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.image @ V1) @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((cHOL.eq @ V0) @ ((cSet.image @ V1) @ V3)))))))))))))
(TString.char.Char_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cString.char.Char @ V0) @ V1)) @ (cString.Abs_char @ ((cDatatype.Scons @ (cDatatype.Leaf @ V0)) @ (cDatatype.Leaf @ V1)))))))))
(TString.char.Rep_char,(call @ (^[V0]: ((cSet.member @ (cString.Rep_char @ V0)) @ (cSet.Collect @ cString.char.char_rep_set)))))
(TString.char.eq.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cString.char.Char @ V0) @ V1)) @ ((cString.char.Char @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TString.char.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cString.char.Char @ V1) @ V2)))))))))
(TString.enum_char_def,((cHOL.eq @ cString.enum_char_inst.enum_char) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleF)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TString.nibble.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cString.nibble.Nibble0)) @ ((c==> @ (V0 @ cString.nibble.Nibble1)) @ ((c==> @ (V0 @ cString.nibble.Nibble2)) @ ((c==> @ (V0 @ cString.nibble.Nibble3)) @ ((c==> @ (V0 @ cString.nibble.Nibble4)) @ ((c==> @ (V0 @ cString.nibble.Nibble5)) @ ((c==> @ (V0 @ cString.nibble.Nibble6)) @ ((c==> @ (V0 @ cString.nibble.Nibble7)) @ ((c==> @ (V0 @ cString.nibble.Nibble8)) @ ((c==> @ (V0 @ cString.nibble.Nibble9)) @ ((c==> @ (V0 @ cString.nibble.NibbleA)) @ ((c==> @ (V0 @ cString.nibble.NibbleB)) @ ((c==> @ (V0 @ cString.nibble.NibbleC)) @ ((c==> @ (V0 @ cString.nibble.NibbleD)) @ ((c==> @ (V0 @ cString.nibble.NibbleE)) @ ((c==> @ (V0 @ cString.nibble.NibbleF)) @ (V0 @ V1))))))))))))))))))))))
(TString.nibble.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: ((cHOL.eq @ (V0 @ (((((((((((((((((cString.nibble.nibble_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble0)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble1)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble2)) @ (cHOL.Not @ (V0 @ V3)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble3)) @ (cHOL.Not @ (V0 @ V4)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble4)) @ (cHOL.Not @ (V0 @ V5)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble5)) @ (cHOL.Not @ (V0 @ V6)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble6)) @ (cHOL.Not @ (V0 @ V7)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble7)) @ (cHOL.Not @ (V0 @ V8)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble8)) @ (cHOL.Not @ (V0 @ V9)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble9)) @ (cHOL.Not @ (V0 @ V10)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleA)) @ (cHOL.Not @ (V0 @ V11)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleB)) @ (cHOL.Not @ (V0 @ V12)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleC)) @ (cHOL.Not @ (V0 @ V13)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleD)) @ (cHOL.Not @ (V0 @ V14)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleE)) @ (cHOL.Not @ (V0 @ V15)))) @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleF)) @ (cHOL.Not @ (V0 @ V16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TString.nibble.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: ((cHOL.eq @ (V0 @ (((((((((((((((((cString.nibble.nibble_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble0)) @ (V0 @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble1)) @ (V0 @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble2)) @ (V0 @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble3)) @ (V0 @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble4)) @ (V0 @ V5))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble5)) @ (V0 @ V6))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble6)) @ (V0 @ V7))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble7)) @ (V0 @ V8))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble8)) @ (V0 @ V9))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.Nibble9)) @ (V0 @ V10))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleA)) @ (V0 @ V11))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleB)) @ (V0 @ V12))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleC)) @ (V0 @ V13))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleD)) @ (V0 @ V14))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleE)) @ (V0 @ V15))) @ ((cHOL.implies @ ((cHOL.eq @ V17) @ cString.nibble.NibbleF)) @ (V0 @ V16)))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TSum_Type.Inl_Rep_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cSum_Type.Inl_Rep @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V0)) @ V3)))))))))))
(TSum_Type.Inl_not_Inr,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inr @ V1))))))))
(TSum_Type.Inr_Rep_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cSum_Type.Inr_Rep @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V0)) @ (cHOL.Not @ V3))))))))))))
(TSum_Type.Inr_not_Inl,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inl @ V1))))))))
(TSum_Type.Projl.simps,(call @ (^[V0]: ((cHOL.eq @ (cSum_Type.Projl @ (cSum_Type.Inl @ V0))) @ V0))))
(TSum_Type.Projr.simps,(call @ (^[V0]: ((cHOL.eq @ (cSum_Type.Projr @ (cSum_Type.Inr @ V0))) @ V0))))
(TSum_Type.Suml_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cSum_Type.Suml @ V0)) @ (cSum_Type.Suml @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.Sumr_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cSum_Type.Sumr @ V0)) @ (cSum_Type.Sumr @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.Rep_sum,(call @ (^[V0]: ((cSet.member @ (cSum_Type.Rep_sum @ V0)) @ cSum_Type.sum))))
(TSum_Type.sum.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TSum_Type.sum.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Inl @ V2))) @ V1)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Inr @ V2))) @ V1)))) @ V1)))))))
(TSum_Type.sum.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cSum_Type.Inl @ V2))))) @ ((c==> @ (call @ (^[V2]: (V0 @ (cSum_Type.Inr @ V2))))) @ (V0 @ V1))))))))
(TSum_Type.sum_case_KK,(call @ (^[V0]: ((cHOL.eq @ ((cSum_Type.sum.sum_case @ (^[V1]: V0)) @ (^[V1]: V0))) @ (^[V1]: V0)))))
(TSum_Type.sum_map_def,((c== @ cSum_Type.sum_map) @ (^[V0]: (^[V1]: (^[V2]: (((((cSum_Type.sum.sum_rec @ (^[V3]: (^[V4]: (^[V5]: (cSum_Type.Inl @ (V4 @ V3)))))) @ (^[V3]: (^[V4]: (^[V5]: (cSum_Type.Inr @ (V5 @ V3)))))) @ V2) @ V0) @ V1))))))
(TTransfer.Domainp_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Domainp @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TTransfer.Ex_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ cHOL.Ex) @ cHOL.Ex)))))
(TTransfer.If_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ V0))) @ cHOL.If) @ cHOL.If))))
(TTransfer.Rel_eq_refl,(call @ (^[V0]: (((cTransfer.Rel @ cHOL.eq) @ V0) @ V0))))
(TTransfer.bi_total_OO,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((c==> @ (cTransfer.bi_total @ V1)) @ (cTransfer.bi_total @ ((cRelation.relcompp @ V0) @ V1)))))))))
(TTransfer.bi_total_eq,(cTransfer.bi_total @ cHOL.eq))
(TTransfer.bi_uniqueDl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V1) @ V3)))))))))))))
(TTransfer.bi_uniqueDr,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TTransfer.eq_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ cHOL.eq)))))
(TTransfer.fun_rel_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cTransfer.fun_rel @ V0) @ V1)) @ (^[V2]: (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V0 @ V4) @ V5)) @ ((V1 @ (V2 @ V4)) @ (V3 @ V5)))))))))))))))
(TTransfer.id_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ V0) @ V0) @ cFun.id) @ cFun.id))))
(TTyperep.typerep.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ ((cList.list.Cons @ V3) @ V4))) @ ((((V2 @ V3) @ V4) @ ((((cTyperep.typerep.typerep_rec_1 @ V0) @ V1) @ V2) @ V3)) @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ V4))))))))))))))
(TTyperep.typerep.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ cList.list.Nil)) @ V1))))))))
(TTyperep.typerep.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cTyperep.typerep.typerep_rec_1 @ V0) @ V1) @ V2) @ ((cTyperep.typerep.Typerep @ V3) @ V4))) @ (((V0 @ V3) @ V4) @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ V4))))))))))))))
(TTyperep.typerep.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cTyperep.typerep.size_typerep_inst.size_typerep @ ((cTyperep.typerep.Typerep @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ cTyperep.typerep.size_typerep_inst.size_typerep) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TTyperep.typerep.size_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cTyperep.typerep.typerep_size @ ((cTyperep.typerep.Typerep @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ cTyperep.typerep.typerep_size) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TWellfounded.acc.accI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ V1)) @ ((cSet.member @ V2) @ (cWellfounded.acc @ V1)))))) @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))))))))
(TWellfounded.accp_def,((c== @ cWellfounded.accp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V3)) @ (cHOL.induct_forall @ (^[V4]: ((cHOL.induct_implies @ ((V0 @ V4) @ V3)) @ (V1 @ V4)))))))))))))
(TWellfounded.mlex_leq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (V0 @ V1)) @ (V0 @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cWellfounded.mlex_prod @ V0) @ V3)))))))))))))
(TWellfounded.nat_size,(call @ (^[V0]: ((cHOL.eq @ (cNat.nat.size_nat_inst.size_nat @ V0)) @ V0))))
(TWellfounded.wfPUNIVI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))) @ (cWellfounded.wfP @ V0)))))
(TWellfounded.wf_Union,(call @ (^[V0]: ((c==> @ ((cSet.Ball @ V0) @ (^[V1]: (cWellfounded.wf @ V1)))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cRelation.Domain @ V1)) @ (cRelation.Range @ V2))) @ cOrderings.bot_class.bot))))))) @ (cWellfounded.wf @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))
(TWellfounded.wf_empty,(cWellfounded.wf @ cOrderings.bot_class.bot))
(TCode_Numeral.dup_code_3,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.dup @ (cCode_Numeral.Neg @ V0))) @ (cCode_Numeral.Neg @ (cNum.num.Bit0 @ V0))))))
(TCode_Numeral.dup_code_2,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.dup @ (cCode_Numeral.Pos @ V0))) @ (cCode_Numeral.Pos @ (cNum.num.Bit0 @ V0))))))
(TCode_Numeral.dup_code_1,((cHOL.eq @ (cCode_Numeral.dup @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cCode_Numeral.zero_integer_inst.zero_integer))
(TCode_Numeral.sub_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.dup @ ((cCode_Numeral.sub @ V0) @ V1))) @ cCode_Numeral.one_integer_inst.one_integer)))))))
(TCode_Numeral.sub_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ (cCode_Numeral.dup @ ((cCode_Numeral.sub @ V0) @ V1))) @ cCode_Numeral.one_integer_inst.one_integer)))))))
(TCode_Numeral.sub_code_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cCode_Numeral.dup @ ((cCode_Numeral.sub @ V0) @ V1))))))))
(TCode_Numeral.sub_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cCode_Numeral.dup @ ((cCode_Numeral.sub @ V0) @ V1))))))))
(TCode_Numeral.sub_code_5,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.sub @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cCode_Numeral.Neg @ (cNum.num.Bit0 @ V0))))))
(TCode_Numeral.sub_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.sub @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cCode_Numeral.Neg @ (cNum.BitM @ V0))))))
(TCode_Numeral.sub_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.sub @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cCode_Numeral.Pos @ (cNum.num.Bit0 @ V0))))))
(TCode_Numeral.sub_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.sub @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cCode_Numeral.Pos @ (cNum.BitM @ V0))))))
(TCode_Numeral.sub_code_1,((cHOL.eq @ ((cCode_Numeral.sub @ cNum.num.One) @ cNum.num.One)) @ cCode_Numeral.zero_integer_inst.zero_integer))
(TDatatype.Abs_Node_inj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cDatatype.Abs_Node @ V0)) @ (cDatatype.Abs_Node @ V1))) @ ((c==> @ ((cSet.member @ V0) @ cDatatype.Node)) @ ((c==> @ ((cSet.member @ V1) @ cDatatype.Node)) @ ((cHOL.eq @ V0) @ V1)))))))))
(TDatatype.Atom_Atom_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cDatatype.Atom @ V0)) @ (cDatatype.Atom @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.Push_inject1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDatatype.Push @ V0) @ V1)) @ ((cDatatype.Push @ V2) @ V3))) @ ((cHOL.eq @ V0) @ V2)))))))))))
(TDatatype.Push_inject2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDatatype.Push @ V0) @ V1)) @ ((cDatatype.Push @ V2) @ V3))) @ ((cHOL.eq @ V1) @ V3)))))))))))
(TDatatype.Scons_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cDatatype.Scons @ V0) @ V1)) @ ((cDatatype.Scons @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ V4))) @ V4)))))))))))))
(TDatatype.ntrunc_Scons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ V0)) @ ((cDatatype.Scons @ V1) @ V2))) @ ((cDatatype.Scons @ ((cDatatype.ntrunc @ V0) @ V1)) @ ((cDatatype.ntrunc @ V0) @ V2))))))))))
(TDivides.arity_div_int,(cDivides.div_class @ cTYPE))
(TDivides.div_2_gt_zero,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.one_nat_inst.one_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cDivides.div_nat_inst.div_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TDivides.div_class_def,((c== @ (cDivides.div_class @ cTYPE)) @ (cRings.dvd_class @ cTYPE)))
(TDivides.div_eq_minus1,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))))))
(TDivides.divmod_nat_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_nat @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))) @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.Let @ ((cDivides.divmod_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ (cNat.Suc @ V2)) @ V3))))))))))))
(TDivides.negDivAlg_def,((c== @ cDivides.negDivAlg) @ (^[V0]: (^[V1]: (cDivides.negDivAlg_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TDivides.negDivAlg_eqn,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.negDivAlg @ V1) @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V1) @ V0))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V1) @ V0))) @ ((cDivides.adjust @ V0) @ ((cDivides.negDivAlg @ V1) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)))))))))))
(TDivides.neg_mod_bound,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ V0) @ ((cDivides.div_int_inst.mod_int @ V1) @ V0))))))))
(TDivides.posDivAlg_def,((c== @ cDivides.posDivAlg) @ (^[V0]: (^[V1]: (cDivides.posDivAlg_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TDivides.posDivAlg_eqn,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.posDivAlg @ V1) @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ V0)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cDivides.adjust @ V0) @ ((cDivides.posDivAlg @ V1) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)))))))))))
(TDivides.pos_mod_bound,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_int @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)) @ V0)))))))
(TDivides.zdiv_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.disj @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_int @ V0) @ V1))) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ V1) @ V0))))))))))
(TDivides.zdiv_zadd1_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V1)) @ V2)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.plus_int_inst.plus_int @ ((cDivides.div_int_inst.div_int @ V0) @ V2)) @ ((cDivides.div_int_inst.div_int @ V1) @ V2))) @ ((cDivides.div_int_inst.div_int @ ((cInt.plus_int_inst.plus_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V2)) @ ((cDivides.div_int_inst.mod_int @ V1) @ V2))) @ V2))))))))))
(TDivides.zminus1_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int))) @ (((cDivides.divmod_int_rel @ (cInt.uminus_int_inst.uminus_int @ V0)) @ V1) @ ((cProduct_Type.Pair @ (((cHOL.If @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ (cInt.uminus_int_inst.uminus_int @ V2)) @ ((cInt.minus_int_inst.minus_int @ (cInt.uminus_int_inst.uminus_int @ V2)) @ cInt.one_int_inst.one_int))) @ (((cHOL.If @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ cInt.zero_int_inst.zero_int) @ ((cInt.minus_int_inst.minus_int @ V1) @ V3)))))))))))))))
(TDivides.zmod_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cInt.times_int_inst.times_int @ V1) @ V2))))))))))
(TEnum.class.enum.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ cOrderings.top_class.top) @ (cList.set @ V0))) @ ((c==> @ (cList.distinct @ V0)) @ ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V1 @ V3)) @ ((cSet.Ball @ cOrderings.top_class.top) @ V3))))) @ ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ ((cSet.Bex @ cOrderings.top_class.top) @ V3))))) @ (((cEnum.class.enum @ V0) @ V1) @ V2))))))))))))
(TEnum.enum_all_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_all @ V0)) @ ((cEnum.all_n_lists @ (^[V1]: (V0 @ ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ cEnum.enum_class.enum) @ V1)))))) @ (cNat.size_class.size @ cEnum.enum_class.enum))))))
(TEnum.enum_all_set_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_all @ V0)) @ ((cSet.Ball @ (cList.set @ cEnum.enum_class.enum)) @ (^[V1]: (V0 @ V1)))))))
(TEnum.enum_all_sum_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_all @ V0)) @ ((cHOL.conj @ (cEnum.enum_class.enum_all @ (^[V1]: (V0 @ (cSum_Type.Inl @ V1))))) @ (cEnum.enum_class.enum_all @ (^[V1]: (V0 @ (cSum_Type.Inr @ V1)))))))))
(TEnum.enum_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ ((c==> @ (((cEnum.class.enum @ cEnum.enum_class.enum) @ cEnum.enum_class.enum_all) @ cEnum.enum_class.enum_ex)) @ (cEnum.enum_class @ cTYPE))))
(TEnum.enum_class.super,((c==> @ (cEnum.enum_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TEnum.enum_ex_bool_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_bool_inst.enum_ex_bool @ V0)) @ ((cHOL.disj @ (V0 @ cHOL.False)) @ (V0 @ cHOL.True))))))
(TEnum.enum_ex_fun_code,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_ex @ V0)) @ ((cHOL.Let @ cEnum.enum_class.enum) @ (^[V1]: ((cEnum.ex_n_lists @ (^[V2]: (V0 @ ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ V1) @ V2)))))) @ (cNat.size_class.size @ V1))))))))
(TEnum.enum_ex_prod_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_ex @ V0)) @ (cEnum.enum_class.enum_ex @ (^[V1]: (cEnum.enum_class.enum_ex @ (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TEnum.enum_ex_unit_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_unit_inst.enum_ex_unit @ V0)) @ (V0 @ cProduct_Type.Unity)))))
(TEnum.finite_1.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TEnum.finite_1.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_1.a\<__caret__sub>1)) @ V1)) @ V1))))))
(TEnum.finite_1.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_1.a\<__caret__sub>1)) @ (V0 @ V1)))))))
(TEnum.finite_2.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TEnum.finite_2.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_2.a\<__caret__sub>1)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_2.a\<__caret__sub>2)) @ V1)) @ V1)))))))
(TEnum.finite_2.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_2.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_2.a\<__caret__sub>2)) @ (V0 @ V1))))))))
(TEnum.finite_3.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TEnum.finite_3.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_3.a\<__caret__sub>1)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_3.a\<__caret__sub>2)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_3.a\<__caret__sub>3)) @ V1)) @ V1))))))))
(TEnum.finite_3.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_3.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_3.a\<__caret__sub>2)) @ ((c==> @ (V0 @ cEnum.finite_3.a\<__caret__sub>3)) @ (V0 @ V1)))))))))
(TEnum.finite_4.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TEnum.finite_4.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>1)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>2)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>3)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>4)) @ V1)) @ V1)))))))))
(TEnum.finite_4.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>2)) @ ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>3)) @ ((c==> @ (V0 @ cEnum.finite_4.a\<__caret__sub>4)) @ (V0 @ V1))))))))))
(TEnum.finite_5.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TEnum.finite_5.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>1)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>2)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>3)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>4)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>5)) @ V1)) @ V1))))))))))
(TEnum.finite_5.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>1)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>2)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>3)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>4)) @ ((c==> @ (V0 @ cEnum.finite_5.a\<__caret__sub>5)) @ (V0 @ V1)))))))))))
(TFinite_Set.card.empty,((cHOL.eq @ (cFinite_Set.card @ cOrderings.bot_class.bot)) @ cNat.zero_nat_inst.zero_nat))
(TFinite_Set.card_empty,((cHOL.eq @ (cFinite_Set.card @ cOrderings.bot_class.bot)) @ cNat.zero_nat_inst.zero_nat))
(TFinite_Set.card_image,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.image @ V0) @ V1))) @ (cFinite_Set.card @ V1))))))))
(TFinite_Set.card_seteq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))) @ ((cHOL.eq @ V1) @ V0)))))))))
(TFinite_Set.finite_INT,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Bex @ V0) @ (^[V2]: (cFinite_Set.finite @ (V1 @ V2))))) @ (cFinite_Set.finite @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2))))))))))
(TFinite_Set.finite_Int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ V1))) @ (cFinite_Set.finite @ ((cLattices.inf_class.inf @ V0) @ V1))))))))
(TFinite_Set.finite_UnI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ ((cLattices.sup_class.sup @ V0) @ V1)))))))))
(TFinite_Set.finite_def,((c== @ cFinite_Set.finite) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cSet.insert @ V3) @ V2))) @ (V0 @ V2))))))))))))
(TFinite_Set.finite_set,((cHOL.eq @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TFinite_Set.fold_empty,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V1) @ cOrderings.bot_class.bot)) @ V1))))))
(TFinite_Set.fold_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V2) @ V3) @ ((cSet.image @ V0) @ V1))) @ (((cFinite_Set.fold @ ((cFun.comp @ V2) @ V0)) @ V3) @ V1))))))))))))
(TFinite_Set.pigeonhole,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cFinite_Set.card @ ((cSet.image @ V0) @ V1))) @ (cFinite_Set.card @ V1))) @ (cHOL.Not @ ((cFun.inj_on @ V0) @ V1))))))))
(TFun.bij_betw_comp_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cFun.bij_betw @ V3) @ V2) @ V4)) @ (((cFun.bij_betw @ ((cFun.comp @ V3) @ V0)) @ V1) @ V4))))))))))))))
(TFun.bij_betw_imp_surj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)))))))
(TFun.bij_betw_swap_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ (((cFun.bij_betw @ (((cFun.swap @ V0) @ V2) @ V3)) @ V1) @ V4)) @ (((cFun.bij_betw @ V3) @ V1) @ V4)))))))))))))))
(TFun.inj_image_mem_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.member @ (V0 @ V1)) @ ((cSet.image @ V0) @ V2))) @ ((cSet.member @ V1) @ V2))))))))))
(TFun.surj_vimage_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet.vimage @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))))))
(TFun.the_inv_into_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ ((cSet.image @ V1) @ V2))) @ ((c==> @ ((cFun.inj_on @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ ((cSet.image @ V0) @ ((cSet.image @ V1) @ V2)))) @ ((cHOL.eq @ (((cFun.the_inv_into @ V2) @ ((cFun.comp @ V0) @ V1)) @ V3)) @ (((cFun.comp @ ((cFun.the_inv_into @ V2) @ V1)) @ ((cFun.the_inv_into @ ((cSet.image @ V1) @ V2)) @ V0)) @ V3))))))))))))))
(TFun.the_inv_into_f_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V0 @ V2)) @ V3)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ (((cFun.the_inv_into @ V1) @ V0) @ V3)) @ V2)))))))))))))
(TFun.the_inv_into_into,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ ((cSet.image @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V3)) @ ((cSet.member @ (((cFun.the_inv_into @ V1) @ V0) @ V2)) @ V3)))))))))))))
(TFun.the_inv_into_onto,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.image @ ((cFun.the_inv_into @ V1) @ V0)) @ ((cSet.image @ V0) @ V1))) @ V1)))))))
(TFunDef.fundef_ex1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c== @ V0) @ (^[V5]: ((cFunDef.THE_default @ (V1 @ V5)) @ (^[V6]: ((V2 @ V5) @ V6)))))) @ ((c==> @ (cHOL.Ex1 @ (^[V5]: ((V2 @ V3) @ V5)))) @ ((cHOL.eq @ ((V2 @ V3) @ V4)) @ ((cHOL.eq @ (V0 @ V3)) @ V4)))))))))))))))
(TFunDef.is_measure_def,((c== @ cFunDef.is_measure) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ V2))))))))
(TFunDef.max_ext_compat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ V0) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ (cWellfounded.max_ext @ V0)) @ ((cLattices.sup_class.sup @ (cWellfounded.max_ext @ V1)) @ ((cSet.insert @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot)))) @ (cWellfounded.max_ext @ V0))))))))
(TFunDef.max_strict_def,((cHOL.eq @ cFunDef.max_strict) @ (cWellfounded.max_ext @ cFunDef.pair_less)))
(TFunDef.min_ext_compat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ V0) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ (cWellfounded.min_ext @ V0)) @ ((cLattices.sup_class.sup @ (cWellfounded.min_ext @ V1)) @ ((cSet.insert @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot)))) @ (cWellfounded.min_ext @ V0))))))))
(TFunDef.min_strict_def,((cHOL.eq @ cFunDef.min_strict) @ (cWellfounded.min_ext @ cFunDef.pair_less)))
(TFunDef.prod_size_simp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cProduct_Type.prod.prod_size @ V0) @ V1) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ (cProduct_Type.fst @ V2))) @ (V1 @ (cProduct_Type.snd @ V2)))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TGroebner_Basis.PFalse_2,(call @ (^[V0]: ((c==> @ (cHOL.Not @ V0)) @ ((c== @ V0) @ cHOL.False)))))
(TGroebner_Basis.PFalse_1,(call @ (^[V0]: ((c==> @ ((c== @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(TGroups.plus_class_def,((c== @ (cGroups.plus_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.zero_class_def,((c== @ (cGroups.zero_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THOL.arity_type_itself,(cHOL.type_class @ cTYPE))
(THOL.class.equal.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((cHOL.eq @ V1) @ V2))))))) @ (cHOL.class.equal @ V0)))))
(THOL.conj_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V1) @ V2))) @ ((cHOL.conj @ V1) @ ((cHOL.conj @ V0) @ V2))))))))))
(THOL.default_class_def,((c== @ (cHOL.default_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THOL.disj_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.disj @ V1) @ ((cHOL.disj @ V0) @ V2))))))))))
(THOL.eq_neq_eq_imp_neq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2))) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V3))))))))))))))
(THOL.equal_class.equal,((cHOL.eq @ cHOL.eq) @ cHOL.eq))
(THOL.equal_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ ((c==> @ (cHOL.class.equal @ cHOL.equal_class.equal)) @ (cHOL.equal_class @ cTYPE))))
(THOL.equal_class.super,((c==> @ (cHOL.equal_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THOL.equal_itself_code,((cHOL.eq @ ((cHOL.equal_class.equal @ cTYPE) @ cTYPE)) @ cHOL.True))
(THOL.iff_conv_conj_imp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ V1) @ V0))))))))
(THOL.induct_conj_curry,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((c==> @ ((cHOL.induct_conj @ V0) @ V1)) @ V2)) @ ((c==> @ V0) @ ((c==> @ V1) @ V2))))))))))
(THOL.induct_forall_def,(call @ (^[V0]: ((c== @ (cHOL.induct_forall @ V0)) @ (cHOL.All @ (^[V1]: (V0 @ V1)))))))
(THOL.induct_implies_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c==> @ V0) @ V1)) @ ((cHOL.induct_implies @ V0) @ V1)))))))
(THOL.meta_eq_to_obj_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(THOL.not_False_eq_True,((cHOL.eq @ (cHOL.Not @ cHOL.False)) @ cHOL.True))
(THOL.not_True_eq_False,((cHOL.eq @ (cHOL.Not @ cHOL.True)) @ cHOL.False))
(THOL.simp_implies_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c== @ V0) @ V1)) @ ((c==> @ ((c==> @ V1) @ ((c== @ V2) @ V3))) @ ((c== @ ((c==> @ V0) @ V2)) @ ((c==> @ V1) @ V3)))))))))))))
(THilbert_Choice.choice,(call @ (^[V0]: ((c==> @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((V0 @ V2) @ (V1 @ V2))))))))))
(THilbert_Choice.inv_id,((cHOL.eq @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ cFun.id)) @ cFun.id))
(THilbert_Choice.someI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V2 @ V3))))) @ (V2 @ (cHilbert_Choice.Eps @ (^[V3]: (V0 @ V3)))))))))))))
(TInductive.basic_monos_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cSet.vimage @ V2) @ V0)) @ ((cSet.vimage @ V2) @ V1))))))))))
(TInductive.basic_monos_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.implies @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TInductive.basic_monos_8,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ (cSet.Collect @ V0)) @ (cSet.Collect @ V1))))))))
(TInductive.basic_monos_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cHOL.If @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.implies @ (cHOL.Not @ V0)) @ V2))))))))))
(TInductive.basic_monos_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.implies @ (cHOL.All @ (^[V2]: (V0 @ V2)))) @ (cHOL.All @ (^[V2]: (V1 @ V2))))))))))
(TInductive.basic_monos_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ (cHOL.Ex @ (^[V2]: (V1 @ V2))))))))))
(TInductive.basic_monos_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V2) @ V3)) @ ((cHOL.implies @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V3)))))))))))))
(TInductive.basic_monos_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ ((cHOL.implies @ V2) @ V3)) @ ((cHOL.implies @ ((cHOL.disj @ V0) @ V2)) @ ((cHOL.disj @ V1) @ V3)))))))))))))
(TInductive.basic_monos_2,(call @ (^[V0]: ((cHOL.implies @ V0) @ V0))))
(TInductive.basic_monos_1,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ V0))))
(TInt.infinite_UNIV_int,(cHOL.Not @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TInt.int.Abs_int_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cInt.Abs_int @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cInt.intrel @ V4) @ V4)) @ ((cHOL.eq @ V3) @ (cSet.Collect @ (cInt.intrel @ V4)))))))))) @ V1))))) @ V1))))))
(TInt.int.Rep_int_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cInt.intrel @ V3) @ V3)) @ ((cHOL.eq @ V2) @ (cSet.Collect @ (cInt.intrel @ V3)))))))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cInt.Rep_int @ V2))) @ V1)))) @ V1)))))))
(TInt.int_of_nat_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cNat.semiring_1_class.of_nat @ V2))))) @ ((c==> @ (call @ (^[V2]: (V0 @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V2))))))) @ (V0 @ V1))))))))
(TInt.less_int.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ ((cTransfer.fun_rel @ cInt.cr_int) @ cHOL.eq)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))) @ cInt.ord_int_inst.less_int))
(TInt.nat_diff_distrib',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))))))))))
(TInt.nat_less_eq_zless,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cInt.ord_int_inst.less_int @ V0) @ V1))))))))
(TInt.plus_int.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ ((cTransfer.fun_rel @ cInt.cr_int) @ cInt.cr_int)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3))))))))) @ cInt.plus_int_inst.plus_int))
(TInt.ring_1.Ints_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cSet.member @ V6) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((c==> @ (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V6) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V8))) @ V7)))) @ V7))))))))))))))))))))
(TInt.ring_1.Ints_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cSet.member @ V6) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((cSet.member @ (V5 @ V6)) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4)))))))))))))))))))
(TInt.ring_1.Ints_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cSet.member @ V6) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((cSet.member @ ((((cPower.power.power @ V0) @ V1) @ V6) @ V7)) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4)))))))))))))))))))))
(TInt.ring_1.of_int.rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cTransfer.fun_rel @ cInt.intrel) @ cHOL.eq) @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: ((V4 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V7)))))) @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: ((V4 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V7))))))))))))))))))))
(TInt.ring_1.of_int_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ ((cInt.plus_int_inst.plus_int @ V6) @ V7))) @ ((V2 @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V7)))))))))))))))))))))
(TInt.ring_1.of_int_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c== @ ((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4)) @ (((cFun.map_fun @ cInt.Rep_Integ) @ cFun.id) @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: ((V4 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V7)))))))))))))))))))))
(TInt.ring_1.of_nat_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V6)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ (cInt.nat @ V6))) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)))))))))))))))))))
(TInt.uminus_int.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cInt.uminus_int_inst.uminus_int @ (cInt.Abs_Integ @ V0))) @ (cInt.Abs_Integ @ ((cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cProduct_Type.Pair @ V2) @ V1)))) @ V0))))))
(TInt.zabs_less_one_iff,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cInt.abs_int_inst.abs_int @ V0)) @ cInt.one_int_inst.one_int)) @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)))))
(TInt.zdvd_mult_cancel1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V0)) @ ((cHOL.eq @ (cInt.abs_int_inst.abs_int @ V1)) @ cInt.one_int_inst.one_int))))))))
(TInt.zero_int.transfer,((cInt.cr_int @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)) @ cInt.zero_int_inst.zero_int))
(TInt.zmult_zless_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((cInt.ord_int_inst.less_int @ ((cInt.times_int_inst.times_int @ V2) @ V0)) @ ((cInt.times_int_inst.times_int @ V2) @ V1)))))))))))
(TLattices.fun_diff_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V2]: ((cGroups.minus_class.minus @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TLattices.inf_bool_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_bool_inst.inf_bool @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V1)))))))
(TLattices.sup_bool_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_bool_inst.sup_bool @ V0) @ V1)) @ ((cHOL.disj @ V0) @ V1)))))))
(TLattices.uminus_apply,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.uminus_class.uminus @ V0) @ V1)) @ (cGroups.uminus_class.uminus @ (V0 @ V1))))))))
(TLazy_Sequence.map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.map @ V0) @ V1)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ ((cList.map @ V0) @ (cLazy_Sequence.list_of_lazy_sequence @ V1)))))))))
(TLifting.Quotient_symp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ (cRelation.symp @ V0)))))))))))
(TLifting.bi_unique_iff,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_unique @ V0)) @ ((cHOL.conj @ (cTransfer.right_unique @ V0)) @ (cLifting.left_unique @ V0))))))
(TLifting.equivp_reflp2,(call @ (^[V0]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ (cRelation.reflp @ V0)))))
(TLifting.invariant_def,(call @ (^[V0]: ((cHOL.eq @ (cLifting.invariant @ V0)) @ (^[V1]: (^[V2]: ((cHOL.conj @ (V0 @ V1)) @ ((cHOL.eq @ V1) @ V2))))))))
(TLifting.left_total_eq,(cLifting.left_total @ cHOL.eq))
(TLifting.pos_fun_distr,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cOrderings.ord_class.less_eq @ ((cRelation.relcompp @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ V2) @ V3))) @ ((cTransfer.fun_rel @ ((cRelation.relcompp @ V0) @ V2)) @ ((cRelation.relcompp @ V1) @ V3))))))))))))
(TLifting_Set.set_relD1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLifting_Set.set_rel @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cSet.Bex @ V2) @ (^[V4]: ((V0 @ V3) @ V4))))))))))))))
(TLifting_Set.set_relD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLifting_Set.set_rel @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((cSet.Bex @ V1) @ (^[V4]: ((V0 @ V4) @ V3))))))))))))))
(TList.Cons_eq_map_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.map @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (V2 @ V4))) @ ((cHOL.eq @ V1) @ ((cList.map @ V2) @ V5))))))))))))))))))
(TList.abort_Bleast_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.abort_Bleast @ V0) @ V1)) @ (cOrderings.ord_class.Least @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2))))))))))
(TList.append_listrel1I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.disj @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel1 @ V2))) @ ((cHOL.eq @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (cList.listrel1 @ V2))))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.append @ V0) @ V3)) @ ((cList.append @ V1) @ V4))) @ (cList.listrel1 @ V2))))))))))))))
(TList.append_self_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ V0)) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.arity_equal_list,(cHOL.equal_class @ cTYPE))
(TList.butlast_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0)) @ cList.butlast) @ cList.butlast))))
(TList.concat_injective,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cList.concat @ V0)) @ (cList.concat @ V1))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cSet.Ball @ (cList.set @ ((cList.zip @ V0) @ V1))) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.size_class.size @ V3))))))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TList.distinct1_rotate,(call @ (^[V0]: ((cHOL.eq @ (cList.distinct @ (cList.rotate1 @ V0))) @ (cList.distinct @ V0)))))
(TList.distinct_butlast,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ (cList.butlast @ V0))))))
(TList.distinct_n_lists,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.n_lists @ V1) @ V0))))))))
(TList.distinct_product,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((c==> @ (cList.distinct @ V1)) @ (cList.distinct @ ((cList.product @ V0) @ V1)))))))))
(TList.distinct_remdups,(call @ (^[V0]: (cList.distinct @ (cList.remdups @ V0)))))
(TList.distinct_remove1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.remove1 @ V1) @ V0))))))))
(TList.drop_Suc_conv_tl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.list.Cons @ ((cList.nth @ V1) @ V0)) @ ((cList.drop @ (cNat.Suc @ V0)) @ V1))) @ ((cList.drop @ V0) @ V1))))))))
(TList.enumerate_Suc_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.enumerate @ (cNat.Suc @ V0)) @ V1)) @ ((cList.map @ (cProduct_Type.apfst @ cNat.Suc)) @ ((cList.enumerate @ V0) @ V1))))))))
(TList.enumerate_eq_zip,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.enumerate @ V0) @ V1)) @ ((cList.zip @ ((cList.upt @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ (cNat.size_class.size @ V1)))) @ V1)))))))
(TList.filter_is_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cList.set @ ((cList.filter @ V0) @ V1))) @ (cList.set @ V1)))))))
(TList.filter_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.filter @ V0) @ ((cList.replicate @ V1) @ V2))) @ (((cHOL.If @ (V0 @ V2)) @ ((cList.replicate @ V1) @ V2)) @ cList.list.Nil)))))))))
(TList.foldl.foldl_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ (((cList.foldl @ V0) @ ((V0 @ V1) @ V2)) @ V3)))))))))))
(TList.foldl_conv_foldr,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.foldl @ V0) @ V1) @ V2)) @ (((cList.foldr @ (^[V3]: (^[V4]: ((V0 @ V4) @ V3)))) @ (cList.rev @ V2)) @ V1)))))))))
(TList.foldr.foldr_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.foldr @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cFun.comp @ (V0 @ V1)) @ ((cList.foldr @ V0) @ V2))))))))))
(TList.foldr_conv_foldl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.foldr @ V0) @ V1) @ V2)) @ (((cList.foldl @ (^[V3]: (^[V4]: ((V0 @ V4) @ V3)))) @ V2) @ (cList.rev @ V1))))))))))
(TList.hd_drop_conv_nth,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (cList.hd @ ((cList.drop @ V0) @ V1))) @ ((cList.nth @ V1) @ V0))))))))
(TList.id_take_nth_drop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ V1) @ ((cList.append @ ((cList.take @ V0) @ V1)) @ ((cList.list.Cons @ ((cList.nth @ V1) @ V0)) @ ((cList.drop @ (cNat.Suc @ V0)) @ V1))))))))))
(TList.in_set_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ ((cList.replicate @ V1) @ V2)))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)))))))))))
(TList.inter_coset_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ (cList.coset @ V1))) @ (((cList.fold @ cSet.remove) @ V1) @ V0)))))))
(TList.inter_set_filter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ (cList.set @ V1))) @ (cList.set @ ((cList.filter @ (^[V2]: ((cSet.member @ V2) @ V0))) @ V1))))))))
(TList.last_list_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.last @ (((cList.list_update @ V0) @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat))) @ V2) @ (cList.last @ V0)))))))))))
(TList.length_enumerate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.enumerate @ V0) @ V1))) @ (cNat.size_class.size @ V1)))))))
(TList.length_filter_le,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ ((cList.filter @ V0) @ V1))) @ (cNat.size_class.size @ V1)))))))
(TList.length_replicate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.replicate @ V0) @ V1))) @ V0))))))
(TList.length_transpose,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.transpose @ V0))) @ (((cList.foldr @ (^[V1]: (cOrderings.ord_class.max @ (cNat.size_class.size @ V1)))) @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TList.lexord_Nil_right,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil)) @ (cList.lexord @ V1))))))))
(TList.lexord_cons_cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cList.lexord @ V4))) @ ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cList.lexord @ V4))))))))))))))))
(TList.list_all2_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (((cList.list_all2 @ V2) @ ((cList.append @ V0) @ V3)) @ ((cList.append @ V1) @ V4))) @ ((cHOL.conj @ (((cList.list_all2 @ V2) @ V0) @ V1)) @ (((cList.list_all2 @ V2) @ V3) @ V4)))))))))))))))
(TList.list_all2_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((c==> @ ((V3 @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((V0 @ V4) @ V6)) @ ((c==> @ (((cList.list_all2 @ V0) @ V5) @ V7)) @ ((c==> @ ((V3 @ V5) @ V7)) @ ((V3 @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V6) @ V7)))))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TList.list_ex_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ cHOL.eq)) @ cList.list_ex) @ cList.list_ex))))
(TList.list_size_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list.list_size @ V0) @ ((cList.append @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ V0) @ V1)) @ ((cList.list.list_size @ V0) @ V2))))))))))
(TList.list_update_code_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_update @ ((cList.list.Cons @ V0) @ V1)) @ (cNat.Suc @ V2)) @ V3)) @ ((cList.list.Cons @ V0) @ (((cList.list_update @ V1) @ V2) @ V3))))))))))))
(TList.list_update_code_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.list_update @ ((cList.list.Cons @ V0) @ V1)) @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cList.list.Cons @ V2) @ V1)))))))))
(TList.list_update_code_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list_update @ cList.list.Nil) @ V0) @ V1)) @ cList.list.Nil))))))
(TList.list_update_swap,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ (((cList.list_update @ (((cList.list_update @ V2) @ V0) @ V3)) @ V1) @ V4)) @ (((cList.list_update @ (((cList.list_update @ V2) @ V1) @ V4)) @ V0) @ V3))))))))))))))
(TList.listrelp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cList.listrelp @ V0) @ V1) @ V2)) @ ((c==> @ ((V3 @ cList.list.Nil) @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ (((cList.listrelp @ V0) @ V6) @ V7)) @ ((c==> @ ((V3 @ V6) @ V7)) @ ((V3 @ ((cList.list.Cons @ V4) @ V6)) @ ((cList.list.Cons @ V5) @ V7)))))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TList.listset_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ (cLifting_Set.set_rel @ V0))) @ (cLifting_Set.set_rel @ (cList.list_all2 @ V0))) @ cList.listset) @ cList.listset))))
(TList.listsum_transfer,(call @ (^[V0]: ((c==> @ ((V0 @ cGroups.zero_class.zero) @ cGroups.zero_class.zero)) @ ((c==> @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ V0)) @ cGroups.plus_class.plus) @ cGroups.plus_class.plus)) @ ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ V0) @ cList.monoid_add_class.listsum) @ cList.monoid_add_class.listsum))))))
(TList.map_eq_Cons_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ (V0 @ V4)) @ V2)) @ ((cHOL.eq @ ((cList.map @ V0) @ V5)) @ V3)))))))))))))))))
(TList.map_filter_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cList.map_filter @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.map_filter_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map_filter @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cOption.option.option_case @ ((cList.map_filter @ V0) @ V2)) @ (^[V3]: ((cList.list.Cons @ V3) @ ((cList.map_filter @ V0) @ V2)))) @ (V0 @ V1))))))))))
(TList.not_Nil_listrel1,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ cList.list.Nil) @ V0)) @ (cList.listrel1 @ V1))))))))
(TList.not_listrel1_Nil,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil)) @ (cList.listrel1 @ V1))))))))
(TList.nth_Cons_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ ((cList.nth @ V1) @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V2)) @ cNat.one_nat_inst.one_nat))))))))))
(TList.nth_enumerate_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.nth @ ((cList.enumerate @ V2) @ V1)) @ V0)) @ ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0)) @ ((cList.nth @ V1) @ V0)))))))))))
(TList.product_list_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.product @ V0) @ V1))) @ ((cProduct_Type.Sigma @ (cList.set @ V0)) @ (^[V2]: (cList.set @ V1)))))))))
(TList.product_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ (cList.list_all2 @ ((cLifting_Product.prod_rel @ V0) @ V1)))) @ cList.product) @ cList.product))))))
(TList.remdups_adj_Cons,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ V1))) @ (((cList.list.list_case @ ((cList.list.Cons @ V0) @ cList.list.Nil)) @ (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V0) @ V2)) @ ((cList.list.Cons @ V2) @ V3)) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V2) @ V3)))))) @ (cList.remdups_adj @ V1))))))))
(TList.remdups_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0)) @ cList.remdups) @ cList.remdups)))))
(TList.remove1_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.remove1) @ cList.remove1)))))
(TList.removeAll_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.removeAll @ V0) @ ((cList.append @ V1) @ V2))) @ ((cList.append @ ((cList.removeAll @ V0) @ V1)) @ ((cList.removeAll @ V0) @ V2))))))))))
(TList.rotate1_length01,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ (cList.rotate1 @ V0)) @ V0)))))
(TList.rotate1_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0)) @ cList.rotate1) @ cList.rotate1))))
(TList.rotate_drop_take,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.rotate @ V0) @ V1)) @ ((cList.append @ ((cList.drop @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.size_class.size @ V1))) @ V1)) @ ((cList.take @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.size_class.size @ V1))) @ V1))))))))
(TList.self_append_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cList.append @ V0) @ V1))) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.sorted_transpose,(call @ (^[V0]: (cList.linorder_class.sorted @ (cList.rev @ ((cList.map @ cNat.size_class.size) @ (cList.transpose @ V0)))))))
(TList.splice_graph_def,((c== @ cList.splice_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V4))) @ ((cHOL.eq @ V2) @ V4))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ cList.list.Nil))) @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ V5)))))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V6) @ V7)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V6) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))))) @ ((V0 @ ((cProduct_Type.Pair @ V5) @ V7)) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))))))))))))))))))))))
(TList.splice_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.splice_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V6))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6)))) @ V2))))))))))) @ V2)))))))))
(TList.splice_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.splice_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V5))) @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V3)) @ ((cList.list.Cons @ V4) @ V5))))))))))))))))))
(TList.split_list_first,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V2) @ ((cList.list.Cons @ V0) @ V3)))) @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V2))))))))))))))
(TList.split_list_propE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V3]: (V1 @ V3)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.append @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ (V1 @ V4)) @ V2))))))))) @ V2)))))))))
(TList.sublist_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ cHOL.eq)) @ (cList.list_all2 @ V0))) @ cList.sublist) @ cList.sublist))))
(TList.transpose.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ ((cList.list.Cons @ cList.list.Nil) @ V2)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ ((cList.list.Cons @ V3) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V5]: (^[V6]: ((cList.list.Cons @ V6) @ cList.list.Nil))))) @ V4))))) @ (V0 @ ((cList.list.Cons @ ((cList.list.Cons @ V2) @ V3)) @ V4)))))))))) @ (V0 @ V1)))))))))
(TList.transpose.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cList.transpose @ V0)) @ V1)) @ ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ V0)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ cList.list.Nil)) @ V2)))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ cList.list.Nil) @ V3))) @ ((c==> @ ((cHOL.eq @ V1) @ (cList.transpose @ V3))) @ ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ ((cList.list.Cons @ cList.list.Nil) @ V3))) @ V2)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V6) @ cList.list.Nil))))) @ V5)))) @ (cList.transpose @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5))))))) @ ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))) @ V2)))))))))) @ V2))))))))))))
(TList.transpose.psimps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ ((cList.list.Cons @ ((cList.list.Cons @ V0) @ V1)) @ V2))) @ ((cHOL.eq @ (cList.transpose @ ((cList.list.Cons @ ((cList.list.Cons @ V0) @ V1)) @ V2))) @ ((cList.list.Cons @ ((cList.list.Cons @ V0) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ V3) @ cList.list.Nil))))) @ V2)))) @ (cList.transpose @ ((cList.list.Cons @ V1) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ V4) @ cList.list.Nil))))) @ V2))))))))))))))
(TList.transpose.psimps_2,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ ((cList.list.Cons @ cList.list.Nil) @ V0))) @ ((cHOL.eq @ (cList.transpose @ ((cList.list.Cons @ cList.list.Nil) @ V0))) @ (cList.transpose @ V0))))))
(TList.transpose.psimps_1,((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ cList.list.Nil)) @ ((cHOL.eq @ (cList.transpose @ cList.list.Nil)) @ cList.list.Nil)))
(TList.transpose_column,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ ((cList.map @ cNat.size_class.size) @ V0)))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ ((cList.map @ (^[V2]: ((cList.nth @ V2) @ V1))) @ ((cList.filter @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V2)))) @ (cList.transpose @ V0)))) @ ((cList.nth @ V0) @ V1)))))))))
(TList.upt_eq_Cons_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.upt @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ ((cList.upt @ ((cNat.plus_nat_inst.plus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V1)) @ V3)))))))))))))
(TList.upto.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)) @ V2)) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cList.upto_rel) @ V1))))))))
(TList.upto_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.list.Cons @ V4) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)))) @ cList.list.Nil))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.upto_graph @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))))) @ V2)))))))))) @ V2)))))))))
(TList.upto_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)) @ ((cList.list.Cons @ V3) @ (V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4)))) @ cList.list.Nil))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)) @ ((cList.upto_graph @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4)) @ (V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4))))))))))))))))))
(TList.upto_rec_numeral_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cList.list.Cons @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cInt.one_int_inst.one_int)) @ (cNum.neg_numeral_class.neg_numeral @ V1)))) @ cList.list.Nil)))))))
(TList.upto_rec_numeral_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cList.list.Cons @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cInt.one_int_inst.one_int)) @ (cNum.numeral_class.numeral @ V1)))) @ cList.list.Nil)))))))
(TList.upto_rec_numeral_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cList.list.Cons @ (cNum.numeral_class.numeral @ V0)) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ (cNum.numeral_class.numeral @ V0)) @ cInt.one_int_inst.one_int)) @ (cNum.neg_numeral_class.neg_numeral @ V1)))) @ cList.list.Nil)))))))
(TList.upto_rec_numeral_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.upto @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cList.list.Cons @ (cNum.numeral_class.numeral @ V0)) @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ (cNum.numeral_class.numeral @ V0)) @ cInt.one_int_inst.one_int)) @ (cNum.numeral_class.numeral @ V1)))) @ cList.list.Nil)))))))
(TList.upto_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V4)) @ ((V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)) @ V4)) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TMap.dom_eq_empty_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cMap.dom @ V0)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ (^[V1]: cOption.option.None))))))
(TMap.finite_dom_map_of,(call @ (^[V0]: (cFinite_Set.finite @ (cMap.dom @ (cMap.map_of @ V0))))))
(TMap.finite_range_updI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ ((cSet.image @ V0) @ cOrderings.top_class.top))) @ (cFinite_Set.finite @ ((cSet.image @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2))) @ cOrderings.top_class.top))))))))))
(TMap.map_comp_None_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (((cMap.map_comp @ V0) @ V1) @ V2)) @ cOption.option.None)) @ ((cHOL.disj @ ((cHOL.eq @ (V1 @ V2)) @ cOption.option.None)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ (cOption.option.Some @ V3))) @ ((cHOL.eq @ (V0 @ V3)) @ cOption.option.None)))))))))))))
(TMap.map_comp_Some_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ (((cMap.map_comp @ V0) @ V1) @ V2)) @ (cOption.option.Some @ V3))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ (cOption.option.Some @ V4))) @ ((cHOL.eq @ (V0 @ V4)) @ (cOption.option.Some @ V3)))))))))))))))
(TMap.map_le_imp_upd_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cMap.map_le @ V0) @ V1)) @ ((cMap.map_le @ (((cFun.fun_upd @ V0) @ V2) @ cOption.option.None)) @ (((cFun.fun_upd @ V1) @ V2) @ (cOption.option.Some @ V3)))))))))))))
(TMap.map_of_inject_set,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ ((cList.map @ cProduct_Type.fst) @ V0))) @ ((c==> @ (cList.distinct @ ((cList.map @ cProduct_Type.fst) @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ (cMap.map_of @ V0)) @ (cMap.map_of @ V1))) @ ((cHOL.eq @ (cList.set @ V0)) @ (cList.set @ V1))))))))))
(TMap.map_of_mapk_SomeI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ ((cMap.map_of @ V1) @ V2)) @ (cOption.option.Some @ V3))) @ ((cHOL.eq @ ((cMap.map_of @ ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V4]: (cProduct_Type.Pair @ (V0 @ V4))))) @ V1)) @ (V0 @ V2))) @ (cOption.option.Some @ V3)))))))))))))
(TMap.map_of_zip_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.size_class.size @ V1))) @ ((c==> @ (cList.distinct @ V1)) @ ((c==> @ ((cHOL.eq @ (cMap.map_of @ ((cList.zip @ V1) @ V0))) @ (cMap.map_of @ ((cList.zip @ V1) @ V2)))) @ ((cHOL.eq @ V0) @ V2))))))))))))
(TMap.restrict_map_upds,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (cList.set @ V0)) @ V2)) @ ((cHOL.eq @ ((cMap.restrict_map @ (((cMap.map_upds @ V3) @ V0) @ V1)) @ V2)) @ (((cMap.map_upds @ ((cMap.restrict_map @ V3) @ ((cGroups.minus_class.minus @ V2) @ (cList.set @ V0)))) @ V0) @ V1)))))))))))))
(TMap.restrict_restrict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cMap.restrict_map @ ((cMap.restrict_map @ V0) @ V1)) @ V2)) @ ((cMap.restrict_map @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TMap.restrict_upd_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cMap.restrict_map @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2))) @ (cGroups.uminus_class.uminus @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ ((cMap.restrict_map @ V0) @ (cGroups.uminus_class.uminus @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))
(TMap.weak_map_of_SomeI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.set @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.eq @ ((cMap.map_of @ V2) @ V0)) @ (cOption.option.Some @ V3))))))))))))
(TMeson.not_refl_disj_D,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cHOL.Not @ ((cHOL.eq @ V0) @ V0))) @ V1)) @ V1))))))
(TNat.Suc_eq_plus1_left,(call @ (^[V0]: ((cHOL.eq @ (cNat.Suc @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ cNat.one_nat_inst.one_nat) @ V0)))))
(TNat.add_mult_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))))))))))
(TNat.diff_Suc_diff_eq1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V2) @ (cNat.Suc @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0)) @ (cNat.Suc @ V1)))))))))))
(TNat.diff_Suc_diff_eq2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)))))))))))
(TNat.diff_add_inverse2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V1)) @ V0))))))
(TNat.diff_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V2)) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.dvd.LeastI2_order,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cRings.dvd_class.dvd @ V1) @ V3))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cRings.dvd_class.dvd @ V3) @ V4))))) @ (V2 @ V3)))))) @ (V2 @ ((cOrderings.ord.Least @ cRings.dvd_class.dvd) @ V0))))))))))))
(TNat.dvd.dual_preorder,((cOrderings.class.preorder @ (^[V0]: (^[V1]: ((cRings.dvd_class.dvd @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.dvd.le_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.dvd.less_imp_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ ((cHOL.implies @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))) @ V2)) @ cHOL.True)))))))))
(TNat.dvd.less_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.dvd.order.antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.dvd_plus_eq_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TNat.ex_least_nat_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (V0 @ cNat.zero_nat_inst.zero_nat))) @ ((c==> @ (V0 @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V2) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V2)) @ (cHOL.Not @ (V0 @ V3)))))) @ (V0 @ ((cNat.plus_nat_inst.plus_nat @ V2) @ cNat.one_nat_inst.one_nat)))))))))))))
(TNat.infinite_descent0,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((c==> @ (cHOL.Not @ (V0 @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V3) @ V2)) @ (cHOL.Not @ (V0 @ V3)))))))))) @ (V0 @ V1))))))))
(TNat.less_eq_nat.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V0)) @ V1)) @ (((cNat.nat.nat_case @ cHOL.False) @ (^[V2]: ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V2))) @ V1)))))))
(TNat.less_eq_nat.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cHOL.True))))
(TNat.less_or_eq_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat.linorder_neqE_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ V0)) @ V2)) @ V2))))))))))
(TNat.mult_less_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TNat.mult_less_cancel2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V2) @ V1))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V2))))))))))
(TNat.nat.Abs_Nat_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.Abs_Nat @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ (^[V3]: (cNat.Nat @ V3))))) @ V1))))) @ V1))))))
(TNat.nat.Rep_Nat_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V2]: (cNat.Nat @ V2))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.Rep_Nat @ V2))) @ V1)))) @ V1)))))))
(TNat.nat_1_eq_mult_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cNat.one_nat_inst.one_nat) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ V1) @ cNat.one_nat_inst.one_nat))))))))
(TNat.nat_add_max_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))))))))))
(TNat.nat_minus_add_max,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1)) @ V1)) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TNat.nat_mult_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ V1) @ cNat.one_nat_inst.one_nat))))))))
(TNat.nat_mult_max_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.nat_mult_min_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TNat.semiring_1.Nats_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cSet.member @ V3) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))))))))))))
(TNat.semiring_1.Nats_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cSet.member @ V0) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))))))))))))
(TNat.strict_inc_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ (cNat.Suc @ V3))) @ (V2 @ V3))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V1)) @ ((c==> @ (V2 @ (cNat.Suc @ V3))) @ (V2 @ V3)))))) @ (V2 @ V0)))))))))))
(TNat.zero_induct_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ (cNat.Suc @ V3))) @ (V0 @ V3))))) @ (V0 @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2)))))))))))
(TNat_Transfer.all_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cHOL.eq @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V0 @ V3)) @ (V1 @ V3))))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V0 @ V3)) @ (V2 @ V3)))))))))))))
(TNat_Transfer.tsub_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat_Transfer.tsub @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V0)) @ ((cInt.minus_int_inst.minus_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)))))))
(TNitpick.fun_box.cases,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.fun_box.fun_box_case @ V0) @ (cNitpick.fun_box.FunBox @ V1))) @ (V0 @ V1)))))))
(TNitpick.fun_box.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.fun_box.fun_box_rec @ V0) @ (cNitpick.fun_box.FunBox @ V1))) @ (V0 @ V1)))))))
(TNitpick.fun_box.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.fun_box.fun_box_case @ V0) @ (cNitpick.fun_box.FunBox @ V1))) @ (V0 @ V1)))))))
(TNitpick.fun_box.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNitpick.fun_box.FunBox @ V0)) @ (cNitpick.fun_box.FunBox @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.fun_box.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.fun_box.fun_box_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cNitpick.fun_box.FunBox @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TNitpick.less_frac_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.less_frac @ V0) @ V1)) @ ((cInt.ord_int_inst.less_int @ (cNitpick.num @ ((cNitpick.plus_frac @ V0) @ (cNitpick.uminus_frac @ V1)))) @ cInt.zero_int_inst.zero_int)))))))
(TNitpick.nat_gcd.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TNitpick.nat_gcd.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cNitpick.nat_gcd @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat)) @ V4) @ ((cNitpick.nat_gcd @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))))) @ V3)))))))) @ V3)))))))))))
(TNitpick.nat_gcd.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.nat_gcd @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0) @ ((cNitpick.nat_gcd @ V1) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)))))))))
(TNitpick.norm_frac_def,((c== @ cNitpick.norm_frac) @ (^[V0]: (^[V1]: (cNitpick.norm_frac_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TNitpick.pair_box.recs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNitpick.pair_box.pair_box_rec @ V0) @ ((cNitpick.pair_box.PairBox @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TNitpick.pair_box.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cNitpick.pair_box.PairBox @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TNitpick.pair_box.size_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cNitpick.pair_box.pair_box_size @ V0) @ V1) @ ((cNitpick.pair_box.PairBox @ V2) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (V1 @ V3))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))))
(TNitpick.plus_frac_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.plus_frac @ V0) @ V1)) @ ((cHOL.Let @ ((cNitpick.int_lcm @ (cNitpick.denom @ V0)) @ (cNitpick.denom @ V1))) @ (^[V2]: ((cNitpick.frac @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ (cNitpick.num @ V0)) @ ((cDivides.div_int_inst.div_int @ V2) @ (cNitpick.denom @ V0)))) @ ((cInt.times_int_inst.times_int @ (cNitpick.num @ V1)) @ ((cDivides.div_int_inst.div_int @ V2) @ (cNitpick.denom @ V1))))) @ V2)))))))))
(TNitpick.word.Rep_word,(call @ (^[V0]: ((cSet.member @ (cNitpick.Rep_word @ V0)) @ (cSet.Collect @ cNitpick.word.word_rep_set)))))
(TNitpick.word.Word_def,(call @ (^[V0]: ((c== @ (cNitpick.word.Word @ V0)) @ (cNitpick.Abs_word @ (cDatatype.Leaf @ V0))))))
(TNitpick.word.eq.simps,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cNitpick.word.Word @ V0)) @ (cNitpick.word.Word @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.word.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNitpick.word.Word @ V1)))))))
(TNitpick.zero_frac_def,((c== @ cNitpick.zero_frac) @ (cNitpick.Abs_Frac @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int))))
(TNum.arith_extra_simps_24,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.arith_extra_simps_23,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.arith_extra_simps_22,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TNum.arith_extra_simps_21,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TNum.arith_extra_simps_20,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_extra_simps_19,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_extra_simps_18,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_extra_simps_17,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.arith_extra_simps_16,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TNum.arith_extra_simps_15,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.zero_class.zero) @ V0)) @ (cGroups.uminus_class.uminus @ V0)))))
(TNum.arith_extra_simps_14,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNum.arith_extra_simps_13,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_extra_simps_12,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_extra_simps_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TNum.arith_extra_simps_10,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNum.arith_extra_simps_9,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNum.arith_extra_simps_8,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.arith_extra_simps_7,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TNum.arith_extra_simps_6,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TNum.arith_extra_simps_5,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TNum.arith_extra_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.arith_extra_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNum.arith_extra_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TNum.arith_extra_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.class.numeral_def,(call @ (^[V0]: ((c== @ (cNum.class.numeral @ V0)) @ (cGroups.class.semigroup_add @ V0)))))
(TNum.inverse_numeral_1,((cHOL.eq @ (cFields.inverse_class.inverse @ (cNum.numeral_class.numeral @ cNum.num.One))) @ (cNum.numeral_class.numeral @ cNum.num.One)))
(TNum.mult_numeral_left_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNum.mult_numeral_left_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNum.mult_numeral_left_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNum.mult_numeral_left_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNum.nat_rec_add_eq_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cNat.nat.nat_rec @ V0) @ V1) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ V2)) @ V3))) @ ((cHOL.Let @ (cNum.pred_numeral @ V2)) @ (^[V4]: ((V1 @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V3)) @ (((cNat.nat.nat_rec @ V0) @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V3)))))))))))))))
(TNum.num.Abs_num_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNum.Abs_num @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNum.num.num_rep_set))) @ V1))))) @ V1))))))
(TNum.num.Rep_num_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNum.num.num_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNum.Rep_num @ V2))) @ V1)))) @ V1)))))))
(TNum.num_of_nat_double,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ (cNum.num_of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V0))) @ (cNum.num.Bit0 @ (cNum.num_of_nat @ V0)))))))
(TNum.numeral_class_def,((c== @ (cNum.numeral_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.one_class @ cTYPE)) @ (cGroups.semigroup_add_class @ cTYPE))))
(TNum.ring_1.iszero_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cNum.ring_1.iszero @ V3) @ V6)) @ ((cHOL.eq @ V6) @ V3))))))))))))))))))
(TOption.option.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TOption.option.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cOption.option.None)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cOption.option.Some @ V2))) @ V1)))) @ V1)))))))
(TOption.option.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cOption.option.None)) @ ((c==> @ (call @ (^[V2]: (V0 @ (cOption.option.Some @ V2))))) @ (V0 @ V1))))))))
(TOption.these_empty_eq,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cOption.these @ V0)) @ cOrderings.bot_class.bot)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ ((cSet.insert @ cOption.option.None) @ cOrderings.bot_class.bot)))))))
(TOrderings.bot_fun_def,((cHOL.eq @ cOrderings.bot_class.bot) @ (^[V0]: cOrderings.bot_class.bot)))
(TOrderings.le_bool_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_bool_inst.less_eq_bool @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(TOrderings.max_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V1) @ V0)) @ V1)))))))
(TOrderings.max_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V1)))))))
(TOrderings.min_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V0)))))))
(TOrderings.min_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V1) @ V0)) @ V0)))))))
(TOrderings.ord.max_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cOrderings.ord.max @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((V0 @ V1) @ V2)) @ V2) @ V1)))))))))
(TOrderings.ord.min_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cOrderings.ord.min @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((V0 @ V1) @ V2)) @ V1) @ V2)))))))))
(TOrderings.order.monoD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.mono @ V0) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V3)) @ (V2 @ V4))))))))))))))))
(TOrderings.order.monoE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.mono @ V0) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V3)) @ (V2 @ V4))) @ V5)) @ V5)))))))))))))))))
(TOrderings.order.monoI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V3)) @ (V2 @ V4)))))))) @ ((cOrderings.order.mono @ V0) @ V2))))))))))
(TOrderings.predicate1D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TOrderings.predicate1I,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TOrderings.predicate2D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TOrderings.predicate2I,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TOrderings.top_fun_def,((cHOL.eq @ cOrderings.top_class.top) @ (^[V0]: cOrderings.top_class.top)))
(TPartial_Function.ccpo,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ (((cComplete_Partial_Order.class.ccpo @ V1) @ V0) @ (cPartial_Function.mk_less @ V0))))))))
(TPower.power.power_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPower.power.power @ V0) @ V1)) @ (^[V2]: (^[V3]: ((((cNat.nat.nat_rec @ (^[V4]: V0)) @ (^[V4]: (^[V5]: (^[V6]: ((V1 @ V6) @ (V5 @ V6)))))) @ V3) @ V2)))))))))
(TPower.power_class_def,((c== @ (cPower.power_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.one_class @ cTYPE)) @ (cGroups.times_class @ cTYPE))))
(TPredicate.adjunct_def,((c== @ cPredicate.adjunct) @ (^[V0]: (^[V1]: (((((cPredicate.seq.seq_rec @ (^[V2]: ((cPredicate.seq.Join @ V2) @ cPredicate.seq.Empty))) @ (^[V2]: (^[V3]: (^[V4]: ((cPredicate.seq.Insert @ V2) @ ((cLattices.sup_class.sup @ V3) @ V4)))))) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((cPredicate.seq.Join @ V2) @ (V4 @ V5))))))) @ V1) @ V0)))))
(TPredicate.adjunct_sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.pred_of_seq @ ((cPredicate.adjunct @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ (cPredicate.pred_of_seq @ V1))))))))
(TPredicate.apply.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.apply @ V0) @ ((cPredicate.seq.Join @ V1) @ V2))) @ ((cPredicate.seq.Join @ ((cPredicate.bind @ V1) @ V0)) @ ((cPredicate.apply @ V0) @ V2))))))))))
(TPredicate.apply.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.apply @ V0) @ ((cPredicate.seq.Insert @ V1) @ V2))) @ ((cPredicate.seq.Join @ (V0 @ V1)) @ ((cPredicate.seq.Join @ ((cPredicate.bind @ V2) @ V0)) @ cPredicate.seq.Empty))))))))))
(TPredicate.apply.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.apply @ V0) @ cPredicate.seq.Empty)) @ cPredicate.seq.Empty))))
(TPredicate.bind_single,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.bind @ V0) @ cPredicate.single)) @ V0))))
(TPredicate.bottom_bind,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.bind @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TPredicate.eval_member,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.member @ V0)) @ (cPredicate.eval @ (cPredicate.pred_of_seq @ V0))))))
(TPredicate.eval_single,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.eval @ (cPredicate.single @ V0))) @ (cHOL.eq @ V0)))))
(TPredicate.not_pred_eq,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.not_pred @ V0)) @ (((cHOL.If @ ((cPredicate.eval @ V0) @ cProduct_Type.Unity)) @ cOrderings.bot_class.bot) @ (cPredicate.single @ cProduct_Type.Unity))))))
(TPredicate.of_seq_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.set_of_seq @ ((cPredicate.seq.Join @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cPredicate.set_of_pred @ V0)) @ (cPredicate.set_of_seq @ V1))))))))
(TPredicate.of_seq_code_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.set_of_seq @ ((cPredicate.seq.Insert @ V0) @ V1))) @ ((cSet.insert @ V0) @ (cPredicate.set_of_pred @ V1))))))))
(TPredicate.of_seq_code_1,((cHOL.eq @ (cPredicate.set_of_seq @ cPredicate.seq.Empty)) @ cOrderings.bot_class.bot))
(TPredicate.pred.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cPredicate.pred.Pred @ V2))))) @ (V0 @ V1)))))))
(TPredicate.pred.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cPredicate.pred.Pred @ V0)) @ (cPredicate.pred.Pred @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.pred.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cPredicate.pred.pred_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cPredicate.pred.Pred @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TPredicate.pred.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cPredicate.pred.pred_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cPredicate.pred.Pred @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TPredicate.pred_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cPredicate.eval @ V0) @ V2)) @ ((cPredicate.eval @ V1) @ V2))))))))))
(TPredicate.seq.Rep_seq,(call @ (^[V0]: ((cSet.member @ (cPredicate.Rep_seq @ V0)) @ (cSet.Collect @ cPredicate.seq.seq_rep_set)))))
(TPredicate.seq.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TPredicate.seq.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cPredicate.seq.Empty)) @ V1)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cPredicate.seq.Insert @ V2) @ V3))) @ V1)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cPredicate.seq.Join @ V2) @ V3))) @ V1)))))) @ V1))))))))
(TPredicate.seq.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cPredicate.seq.Empty)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cPredicate.seq.Insert @ V2) @ V3))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cPredicate.seq.Join @ V2) @ V3)))))))) @ (V0 @ V1)))))))))
(TPredicate.single_bind,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.bind @ (cPredicate.single @ V0)) @ V1)) @ (V1 @ V0)))))))
(TPredicate.single_code,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.single @ V0)) @ (cPredicate.Seq @ (^[V1]: ((cPredicate.seq.Insert @ V0) @ cOrderings.bot_class.bot)))))))
(TPresburger.decr_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_int @ ((cInt.minus_int_inst.minus_int @ V1) @ ((cInt.times_int_inst.times_int @ ((cInt.plus_int_inst.plus_int @ (cInt.abs_int_inst.abs_int @ ((cInt.minus_int_inst.minus_int @ V1) @ V2))) @ cInt.one_int_inst.one_int)) @ V0))) @ V2)))))))))
(TPresburger.incr_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_int @ V1) @ ((cInt.plus_int_inst.plus_int @ V2) @ ((cInt.times_int_inst.times_int @ ((cInt.plus_int_inst.plus_int @ (cInt.abs_int_inst.abs_int @ ((cInt.minus_int_inst.minus_int @ V2) @ V1))) @ cInt.one_int_inst.one_int)) @ V0)))))))))))
(TPresburger.inf_period_5,(call @ (^[V0]: (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ V0) @ V0))))))))
(TPresburger.inf_period_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V2)))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))) @ V2))))))))))))))))
(TPresburger.inf_period_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V3) @ V2))) @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))) @ V2)))))))))))))))
(TPresburger.inf_period_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ (V0 @ V3)) @ (V0 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))))))))) @ ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ (V2 @ V3)) @ (V2 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))))))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((cHOL.disj @ (V0 @ V3)) @ (V2 @ V3))) @ ((cHOL.disj @ (V0 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1)))) @ (V2 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))))))))))))))))))
(TPresburger.inf_period_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ (V0 @ V3)) @ (V0 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))))))))) @ ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ (V2 @ V3)) @ (V2 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))))))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((cHOL.conj @ (V0 @ V3)) @ (V2 @ V3))) @ ((cHOL.conj @ (V0 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1)))) @ (V2 @ ((cGroups.minus_class.minus @ V3) @ ((cGroups.times_class.times @ V4) @ V1))))))))))))))))))
(TProduct_Type.Pair_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cProduct_Type.Abs_prod @ ((cProduct_Type.Pair_Rep @ V0) @ V1))))))))
(TProduct_Type.apfst_id,((cHOL.eq @ (cProduct_Type.apfst @ cFun.id)) @ cFun.id))
(TProduct_Type.apsnd_id,((cHOL.eq @ (cProduct_Type.apsnd @ cFun.id)) @ cFun.id))
(TProduct_Type.fst_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cProduct_Type.Pair @ V0) @ V1))) @ V0))))))
(TProduct_Type.prod_def,((cHOL.eq @ cProduct_Type.prod) @ (cSet.Collect @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cProduct_Type.Pair_Rep @ V1) @ V2))))))))))
(TProduct_Type.prod_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cProduct_Type.fst @ V0)) @ (cProduct_Type.fst @ V1))) @ ((c==> @ ((cHOL.eq @ (cProduct_Type.snd @ V0)) @ (cProduct_Type.snd @ V1))) @ ((cHOL.eq @ V0) @ V1))))))))
(TProduct_Type.snd_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cProduct_Type.Pair @ V0) @ V1))) @ V1))))))
(TProduct_Type.splitI2',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)) @ (((V1 @ V3) @ V4) @ V2))))))) @ (((cProduct_Type.prod.prod_case @ V1) @ V0) @ V2)))))))))
(TPure.equal_elim_rule1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TPure.equal_elim_rule2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ V1)) @ ((c==> @ V1) @ V0)))))))
(TPure.sort_constraintI,(cPure.sort_constraint @ cTYPE))
(TQuotient.Bex1_rel_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuotient.Bex1_rel @ V0) @ V1)) @ ((cHOL.conj @ ((cSet.Bex @ (cLifting.Respects @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cSet.Ball @ (cLifting.Respects @ V0)) @ (^[V2]: ((cSet.Ball @ (cLifting.Respects @ V0)) @ (^[V3]: ((cHOL.implies @ ((cHOL.conj @ (V1 @ V2)) @ (V1 @ V3))) @ ((V0 @ V2) @ V3)))))))))))))
(TQuotient.babs_reg_eqv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((cHOL.eq @ ((cQuotient.Babs @ (cLifting.Respects @ V0)) @ V1)) @ V1)))))))
(TQuotient.ball_reg_eqv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((cHOL.eq @ ((cSet.Ball @ (cLifting.Respects @ V0)) @ V1)) @ (cHOL.All @ V1))))))))
(TQuotient.bex1_rel_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V4)))))))) @ ((c==> @ ((cQuotient.Bex1_rel @ V0) @ V1)) @ ((cQuotient.Bex1_rel @ V0) @ V2))))))))))
(TQuotient.bex1_rel_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ (cQuotient.Bex1_rel @ V0)) @ (cQuotient.Bex1_rel @ V0))))))))))
(TQuotient.bex_reg_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.implies @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cHOL.implies @ ((cSet.Bex @ V0) @ V1)) @ (cHOL.Ex @ V2))))))))))
(TQuotient.quot_rel_rsp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ V0) @ V0)))))))))
(TRandom.iterate.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ (((V0 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5) @ V7))))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TRandom.iterate.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cRandom.iterate @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cRandom.iterate_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V7)) @ ((cProduct_Type.scomp @ (V6 @ V7)) @ ((cRandom.iterate @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))) @ ((c==> @ ((cWellfounded.accp @ cRandom.iterate_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TRandom.iterate.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cRandom.iterate_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cRandom.iterate @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V2)) @ ((cProduct_Type.scomp @ (V1 @ V2)) @ ((cRandom.iterate @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1))))))))))))
(TRandom.log_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.log_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3)))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom.log_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V0)))) @ ((cRandom.log_rel @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ V0))) @ ((cProduct_Type.Pair @ V0) @ V1))))))))
(TRandom.pick_drop_zero,(call @ (^[V0]: ((cHOL.eq @ (cRandom.pick @ ((cList.filter @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1))))) @ V0))) @ (cRandom.pick @ V0)))))
(TRandom.split_seed_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom.split_seed @ V0)) @ ((cHOL.Let @ V0) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.Let @ (cProduct_Type.snd @ (cRandom.next @ V0))) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cHOL.Let @ ((cRandom.inc_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ V1)) @ (^[V5]: ((cHOL.Let @ ((cRandom.inc_shift @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))))))))))))))))))) @ V2)) @ (^[V6]: ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V5) @ V4)) @ ((cProduct_Type.Pair @ V3) @ V6))))))))))))))))))
(TRandom_Pred.empty_def,((cHOL.eq @ cRandom_Pred.empty) @ (cProduct_Type.Pair @ cOrderings.bot_class.bot)))
(TRandom_Pred.iter'_def,((c== @ cRandom_Pred.iter') @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cRandom_Pred.iter'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))))))))))
(TRandom_Pred.union_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Pred.union @ V0) @ V1)) @ (^[V2]: ((cHOL.Let @ (V0 @ V2)) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cHOL.Let @ (V1 @ V4)) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cProduct_Type.Pair @ ((cLattices.sup_class.sup @ V3) @ V5)) @ V6))))))))))))))))
(TRelation.Domain.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Domain @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ V2))))))) @ V2)))))))))
(TRelation.Domain.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cRelation.Domain @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))))))))))
(TRelation.Domain_Id_on,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ (cRelation.Id_on @ V0))) @ V0))))
(TRelation.Domain_Un_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.Domain @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cRelation.Domain @ V0)) @ (cRelation.Domain @ V1))))))))
(TRelation.Domain_Union,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: (cRelation.Domain @ V1)))))))
(TRelation.Domain_dprod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.Domain @ ((cDatatype.dprod @ V0) @ V1))) @ ((cDatatype.uprod @ (cRelation.Domain @ V0)) @ (cRelation.Domain @ V1))))))))
(TRelation.Domain_empty,((cHOL.eq @ (cRelation.Domain @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TRelation.Field_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cRelation.Field @ ((cSet.insert @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2))) @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ (cRelation.Field @ V2))))))))))
(TRelation.Image_INT_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRelation.single_valued @ (cRelation.converse @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cRelation.Image @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cRelation.Image @ V0) @ (V2 @ V3))))))))))))))
(TRelation.Image_Int_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRelation.single_valued @ (cRelation.converse @ V0))) @ ((cHOL.eq @ ((cRelation.Image @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cRelation.Image @ V0) @ V1)) @ ((cRelation.Image @ V0) @ V2)))))))))))
(TRelation.Image_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V4]: V2)))) @ ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V0) @ V3)) @ V2)))))))))))
(TRelation.Range.RangeI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ V1) @ (cRelation.Range @ V2))))))))))
(TRelation.Range.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Range @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ (V2 @ V4))))))) @ (V2 @ V0))))))))))
(TRelation.Range.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ V1) @ (cRelation.Range @ V2))))))))))
(TRelation.Range_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cRelation.Range @ ((cSet.insert @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2))) @ ((cSet.insert @ V1) @ (cRelation.Range @ V2))))))))))
(TRelation.Rangep.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Rangep @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((V0 @ V3) @ V4)) @ V2))))))) @ V2)))))))))
(TRelation.Rangep.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Rangep @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((V0 @ V2) @ V3))))))))))))
(TRelation.bot_empty_eq,((cHOL.eq @ cOrderings.bot_class.bot) @ (^[V0]: ((cSet.member @ V0) @ cOrderings.bot_class.bot))))
(TRelation.converse_Int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.converse @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cRelation.converse @ V0)) @ (cRelation.converse @ V1))))))))
(TRelation.converse_def,((c== @ cRelation.converse) @ (^[V0]: (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (((cRelation.conversep @ (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)))) @ V1) @ V2))))))))
(TRelation.converse_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ V2)))))))))
(TRelation.conversep_eq,((cHOL.eq @ (cRelation.conversep @ cHOL.eq)) @ cHOL.eq))
(TRelation.finite_Field,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ (cRelation.Field @ V0))))))
(TRelation.finite_Range,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ (cRelation.Range @ V0))))))
(TRelation.in_inv_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cRelation.inv_image @ V2) @ V3))) @ ((cSet.member @ ((cProduct_Type.Pair @ (V3 @ V0)) @ (V3 @ V1))) @ V2)))))))))))
(TRelation.refl_on_def',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.refl_on @ V0) @ V1)) @ ((cHOL.conj @ ((cSet.Ball @ V1) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V3) @ V0))))))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V2)) @ V1))))))))))
(TRelation.relcompEpair,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cRelation.relcomp @ V2) @ V3))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V5)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ V3)) @ V4))))) @ V4)))))))))))))
(TRelation.relcomp_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cRelation.relcomp @ V0) @ V1)) @ (((cFinite_Set.fold @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (^[V4]: (((cFinite_Set.fold @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (^[V7]: (((cHOL.If @ ((cHOL.eq @ V3) @ V5)) @ ((cSet.insert @ ((cProduct_Type.Pair @ V2) @ V6)) @ V7)) @ V7)))))) @ V4) @ V1)))))) @ cOrderings.bot_class.bot) @ V0)))))))))
(TRelation.relcomp_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ V0) @ V2)) @ ((cRelation.relcomp @ V1) @ V3)))))))))))))
(TRelation.relcompp_def,((c== @ cRelation.relcompp) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V3) @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ V7)) @ ((cHOL.conj @ ((V0 @ V5) @ V6)) @ ((V1 @ V6) @ V7))))))))))))))))))
(TRelation.snd_eq_Range,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cProduct_Type.snd) @ V0)) @ (cRelation.Range @ V0)))))
(TRelation.sym_converse,(call @ (^[V0]: ((cHOL.eq @ (cRelation.sym @ (cRelation.converse @ V0))) @ (cRelation.sym @ V0)))))
(TRelation.top_empty_eq,((cHOL.eq @ cOrderings.top_class.top) @ (^[V0]: ((cSet.member @ V0) @ cOrderings.top_class.top))))
(TRelation.total_on_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.total_on @ V0) @ V1)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V2)) @ V1)))))))))))))
(TRelation.transp_trans,(call @ (^[V0]: ((cHOL.eq @ (cRelation.transp @ V0)) @ (cRelation.trans @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2))))))))))
(TRings.dvd_class.intro,((c==> @ (cGroups.times_class @ cTYPE)) @ (cRings.dvd_class @ cTYPE)))
(TRings.dvd_class.super,((c==> @ (cRings.dvd_class @ cTYPE)) @ (cGroups.times_class @ cTYPE)))
(TSMT.equal_pattern_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TSMT.pattern.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cSMT.pattern.Pattern)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cSMT.pattern.pattern_case @ V2) @ V0)) @ ((cSMT.pattern.pattern_case @ V3) @ V1)))))))))))))
(TSMT.pattern.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cSMT.pattern.pattern_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cSMT.pattern.Pattern)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TSet.Diff_Int_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TSet.Diff_eq_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet.ball_conj_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.conj @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cHOL.conj @ ((cSet.Ball @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cSet.Ball @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TSet.basic_trans_rules_32,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.basic_trans_rules_31,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ V1))))))))))
(TSet.basic_trans_rules_30,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cSet.member @ V0) @ V2))))))))))
(TSet.basic_trans_rules_29,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.eq @ V0) @ V2))))))))))
(TSet.basic_trans_rules_28,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.basic_trans_rules_27,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.basic_trans_rules_26,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet.basic_trans_rules_25,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet.basic_trans_rules_24,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TSet.basic_trans_rules_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet.basic_trans_rules_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.basic_trans_rules_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.basic_trans_rules_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)))))))))
(TSet.basic_trans_rules_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.basic_trans_rules_18,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TSet.basic_trans_rules_17,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TSet.basic_trans_rules_16,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TSet.basic_trans_rules_15,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((cHOL.implies @ V0) @ V1)) @ V1)))))))
(TSet.basic_trans_rules_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ (V0 @ V2))))))))))
(TSet.basic_trans_rules_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (V2 @ V1)) @ (V2 @ V0))))))))))
(TSet.basic_trans_rules_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TSet.basic_trans_rules_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TSet.basic_trans_rules_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V3))))))))))))))
(TSet.basic_trans_rules_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ V3)))))))))))))
(TSet.basic_trans_rules_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V3))))))))))))))
(TSet.basic_trans_rules_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ V3)))))))))))))
(TSet.basic_trans_rules_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TSet.basic_trans_rules_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TSet.basic_trans_rules_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TSet.basic_trans_rules_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TSet.basic_trans_rules_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TSet.basic_trans_rules_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TSet.double_complement,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cGroups.uminus_class.uminus @ V0))) @ V0))))
(TSet.image_diff_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2))) @ ((cSet.image @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))))))))))
(TSet.not_psubset_empty,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ cOrderings.bot_class.bot)))))
(TSet.range_composition,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ (^[V2]: (V0 @ (V1 @ V2)))) @ cOrderings.top_class.top)) @ ((cSet.image @ V0) @ ((cSet.image @ V1) @ cOrderings.top_class.top))))))))
(TSet.subset_insert_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.insert @ V1) @ V2))) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet.subset_singletonD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))
(TSet.vimage_Collect_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.vimage @ V0) @ (cSet.Collect @ V1))) @ (cSet.Collect @ (^[V2]: (V1 @ (V0 @ V2))))))))))
(TSet.vimage_inter_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cHOL.eq @ (V1 @ V4)) @ (V2 @ V4)))))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet.vimage @ V1) @ V3)) @ V0)) @ ((cLattices.inf_class.inf @ ((cSet.vimage @ V2) @ V3)) @ V0))))))))))))
(TSet_Interval.atMost_0,((cHOL.eq @ (cSet_Interval.ord_class.atMost @ cNat.zero_nat_inst.zero_nat)) @ ((cSet.insert @ cNat.zero_nat_inst.zero_nat) @ cOrderings.bot_class.bot)))
(TSet_Interval.ivl_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))))))))))
(TString.Code.abort_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cString.Code.abort @ V0) @ V1)) @ (V1 @ cProduct_Type.Unity)))))))
(TString.card_UNIV_char,((cHOL.eq @ (cFinite_Set.card @ cOrderings.top_class.top)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))
(TString.char.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cString.char.Char @ V4) @ V5))) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))) @ ((cHOL.eq @ ((cString.char.char_case @ V2) @ V0)) @ ((cString.char.char_case @ V3) @ V1)))))))))))))
(TString.char.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cString.char.char_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cString.char.Char @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TString.char_case_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cString.char.char_case @ V0) @ V1)) @ ((cHOL.Let @ (cString.nat_of_char @ V1)) @ (^[V2]: ((V0 @ (cString.nibble_of_nat @ ((cDivides.div_nat_inst.div_nat @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))) @ (cString.nibble_of_nat @ V2))))))))))
(TString.equal_char_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.nibble.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TString.nibble.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble0)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble1)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble2)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble3)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble4)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble5)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble6)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble7)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble8)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.Nibble9)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.NibbleA)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.NibbleB)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.NibbleC)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.NibbleD)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.NibbleE)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cString.nibble.NibbleF)) @ V1)) @ V1)))))))))))))))))))))
(TString.nibble.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cString.nibble.Nibble0)) @ ((c==> @ (V0 @ cString.nibble.Nibble1)) @ ((c==> @ (V0 @ cString.nibble.Nibble2)) @ ((c==> @ (V0 @ cString.nibble.Nibble3)) @ ((c==> @ (V0 @ cString.nibble.Nibble4)) @ ((c==> @ (V0 @ cString.nibble.Nibble5)) @ ((c==> @ (V0 @ cString.nibble.Nibble6)) @ ((c==> @ (V0 @ cString.nibble.Nibble7)) @ ((c==> @ (V0 @ cString.nibble.Nibble8)) @ ((c==> @ (V0 @ cString.nibble.Nibble9)) @ ((c==> @ (V0 @ cString.nibble.NibbleA)) @ ((c==> @ (V0 @ cString.nibble.NibbleB)) @ ((c==> @ (V0 @ cString.nibble.NibbleC)) @ ((c==> @ (V0 @ cString.nibble.NibbleD)) @ ((c==> @ (V0 @ cString.nibble.NibbleE)) @ ((c==> @ (V0 @ cString.nibble.NibbleF)) @ (V0 @ V1))))))))))))))))))))))
(TSum_Type.split_sum_ex,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V1]: (V0 @ (cSum_Type.Inl @ V1))))) @ (cHOL.Ex @ (^[V1]: (V0 @ (cSum_Type.Inr @ V1)))))))))
(TSum_Type.sum.distinct_2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inl @ V1))))))))
(TSum_Type.sum.distinct_1,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inr @ V1))))))))
(TSum_Type.sum.eq.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inl @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inr @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.eq.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cSum_Type.Inl @ V0)) @ (cSum_Type.Inr @ V1))) @ cHOL.False))))))
(TSum_Type.sum.eq.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cSum_Type.Inr @ V0)) @ (cSum_Type.Inl @ V1))) @ cHOL.False))))))
(TSum_Type.sum.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cSum_Type.Inl @ V1))))) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cSum_Type.Inr @ V1))))))))
(TSum_Type.sum_map.comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cFun.comp @ ((cSum_Type.sum_map @ V0) @ V1)) @ ((cSum_Type.sum_map @ V2) @ V3))) @ ((cSum_Type.sum_map @ ((cFun.comp @ V0) @ V2)) @ ((cFun.comp @ V1) @ V3))))))))))))
(TTransfer.All_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ cHOL.All) @ cHOL.All)))))
(TTransfer.Domaimp_refl,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domainp @ V0)) @ (cRelation.Domainp @ V0)))))
(TTransfer.Let_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ V1)) @ cHOL.Let) @ cHOL.Let))))))
(TTransfer.bi_total_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_total @ V0)) @ ((cHOL.conj @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V2) @ V1))))))))))
(TTransfer.bi_total_fun,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.bi_total @ V1)) @ (cTransfer.bi_total @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TTransfer.bi_unique_OO,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.bi_unique @ V1)) @ (cTransfer.bi_unique @ ((cRelation.relcompp @ V0) @ V1)))))))))
(TTransfer.bi_unique_eq,(cTransfer.bi_unique @ cHOL.eq))
(TTyperep.typerep.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cTyperep.typerep.typerep_case @ V0) @ ((cTyperep.typerep.Typerep @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TTyperep.typerep.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ ((cList.list.Cons @ V3) @ V4))) @ ((((V2 @ V3) @ V4) @ ((((cTyperep.typerep.typerep_rec_1 @ V0) @ V1) @ V2) @ V3)) @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ V4))))))))))))))
(TTyperep.typerep.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ cList.list.Nil)) @ V1))))))))
(TTyperep.typerep.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cTyperep.typerep.typerep_rec_1 @ V0) @ V1) @ V2) @ ((cTyperep.typerep.Typerep @ V3) @ V4))) @ (((V0 @ V3) @ V4) @ ((((cTyperep.typerep.typerep_rec_2 @ V0) @ V1) @ V2) @ V4))))))))))))))
(TTyperep.typerep.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cTyperep.typerep.typerep_case @ V0) @ ((cTyperep.typerep.Typerep @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TTyperep.typerep.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cTyperep.typerep.Typerep @ V0) @ V1)) @ ((cTyperep.typerep.Typerep @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TTyperep.typerep.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cTyperep.typerep.typerep_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cTyperep.typerep.Typerep @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TWellfounded.acc.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1)) @ ((cSet.member @ V4) @ (cWellfounded.acc @ V1)))))) @ V2))))) @ V2)))))))))
(TWellfounded.acc.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V2)) @ V1)) @ ((cSet.member @ V3) @ (cWellfounded.acc @ V1))))))))))))))
(TWellfounded.accp.accI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((V0 @ V2) @ V1)) @ ((cWellfounded.accp @ V0) @ V2))))) @ ((cWellfounded.accp @ V0) @ V1)))))))
(TWellfounded.accp_wfPD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wfP @ V0)) @ ((cWellfounded.accp @ V0) @ V1)))))))
(TWellfounded.accp_wfPI,(call @ (^[V0]: ((c==> @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ V0) @ V1)))) @ (cWellfounded.wfP @ V0)))))
(TWellfounded.mlex_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V1)) @ (V0 @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cWellfounded.mlex_prod @ V0) @ V3))))))))))))
(TWellfounded.size_bool,(call @ (^[V0]: ((cHOL.eq @ (cHOL.bool.size_bool_inst.size_bool @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TWellfounded.wfP_empty,(cWellfounded.wfP @ (^[V0]: (^[V1]: cHOL.False))))
(TWellfounded.wfP_wf_eq,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wfP @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (cWellfounded.wf @ V0)))))
(TWellfounded.wf_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))))))
(TWellfounded.wf_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cWellfounded.wf @ ((cSet.insert @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2))) @ ((cHOL.conj @ (cWellfounded.wf @ V2)) @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ (cTransitive_Closure.rtrancl @ V2))))))))))))
(TWellfounded.wf_irrefl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ V0))) @ V2)) @ V2)))))))))
(TWellfounded.wf_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ (cWellfounded.wf @ V1))))))))
(TWellfounded.wf_trancl,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ (cTransitive_Closure.trancl @ V0))))))
(TBig_Operators.setsum_0,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V1]: cGroups.zero_class.zero)) @ V0)) @ cGroups.zero_class.zero))))
(TComplete_Lattices.UN_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V2 @ V4))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((c==> @ ((cSet.member @ V0) @ (V2 @ V4))) @ V3))))) @ V3)))))))))))
(TComplete_Lattices.UN_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (V3 @ V0))) @ ((cSet.member @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TDatatype.Leaf_not_Numb,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cDatatype.Leaf @ V0)) @ (cDatatype.Numb @ V1))))))))
(TDatatype.Numb_not_Leaf,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cDatatype.Numb @ V0)) @ (cDatatype.Leaf @ V1))))))))
(TDatatype.Push_Node_def,((c== @ cDatatype.Push_Node) @ (^[V0]: (^[V1]: (cDatatype.Abs_Node @ ((cProduct_Type.apfst @ (cDatatype.Push @ V0)) @ (cDatatype.Rep_Node @ V1)))))))
(TDatatype.Scons_inject1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDatatype.Scons @ V0) @ V1)) @ ((cDatatype.Scons @ V2) @ V3))) @ ((cHOL.eq @ V0) @ V2)))))))))))
(TDatatype.Scons_inject2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDatatype.Scons @ V0) @ V1)) @ ((cDatatype.Scons @ V2) @ V3))) @ ((cHOL.eq @ V1) @ V3)))))))))))
(TDatatype.node.Rep_Node,(call @ (^[V0]: ((cSet.member @ (cDatatype.Rep_Node @ V0)) @ cDatatype.Node))))
(TDivides.add_self_div_2,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ V0))))
(TDivides.div_int_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ V2)))))))))))
(TDivides.div_nat_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ V2)))))))))))
(TDivides.divmod_abs_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_abs @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ (cInt.abs_int_inst.abs_int @ V0)) @ (cInt.abs_int_inst.abs_int @ V1))) @ ((cDivides.div_int_inst.mod_int @ (cInt.abs_int_inst.abs_int @ V0)) @ (cInt.abs_int_inst.abs_int @ V1)))))))))
(TDivides.divmod_int_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_int @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cDivides.posDivAlg @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.negDivAlg @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1)))))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cDivides.negDivAlg @ V0) @ V1)) @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.posDivAlg @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1)))))))))))
(TDivides.divmod_nat_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_nat @ V0) @ V1)) @ (cHOL.The @ (^[V2]: (((cDivides.divmod_nat_rel @ V0) @ V1) @ V2)))))))))
(TDivides.divmod_nat_rel,(call @ (^[V0]: (call @ (^[V1]: (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))))))))
(TDivides.fst_divmod_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cDivides.divmod_abs @ V0) @ V1))) @ ((cDivides.div_int_inst.div_int @ (cInt.abs_int_inst.abs_int @ V0)) @ (cInt.abs_int_inst.abs_int @ V1))))))))
(TDivides.fst_divmod_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cDivides.divmod_int @ V0) @ V1))) @ ((cDivides.div_int_inst.div_int @ V0) @ V1)))))))
(TDivides.fst_divmod_nat,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cDivides.divmod_nat @ V0) @ V1))) @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)))))))
(TDivides.int_div_neg_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ V2)) @ V3))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V3)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ V2)))))))))))))
(TDivides.int_div_pos_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ V2)) @ V3))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V3)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V3) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ V2)))))))))))))
(TDivides.int_mod_neg_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ V2)) @ V3))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V3)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V3)))))))))))))
(TDivides.int_mod_pos_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ V2)) @ V3))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V3)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V3) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V3)))))))))))))
(TDivides.mod_int_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V3)))))))))))
(TDivides.mod_le_divisor,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0)) @ V0)))))))
(TDivides.mod_mult_self3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ V2)) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ V2) @ V1)))))))))
(TDivides.mod_mult_self4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ V2))) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ V2)) @ V1)))))))))
(TDivides.mod_nat_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ V3)))))))))))
(TDivides.nat_mod_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ V2) @ V1))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ ((cNat.times_nat_inst.times_nat @ V1) @ V4)))))))))))))))
(TDivides.snd_divmod_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cDivides.divmod_abs @ V0) @ V1))) @ ((cDivides.div_int_inst.mod_int @ (cInt.abs_int_inst.abs_int @ V0)) @ (cInt.abs_int_inst.abs_int @ V1))))))))
(TDivides.snd_divmod_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cDivides.divmod_int @ V0) @ V1))) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)))))))
(TDivides.snd_divmod_nat,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cDivides.divmod_nat @ V0) @ V1))) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)))))))
(TDivides.zdiv_mono1_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.div_int @ V1) @ V2)) @ ((cDivides.div_int_inst.div_int @ V0) @ V2)))))))))))
(TDivides.zdiv_mono2_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ ((cDivides.div_int_inst.div_int @ V0) @ V2))))))))))))
(TDivides.zdiv_zmult1_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V2)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ ((cDivides.div_int_inst.div_int @ V1) @ V2))) @ ((cDivides.div_int_inst.div_int @ ((cInt.times_int_inst.times_int @ V0) @ ((cDivides.div_int_inst.mod_int @ V1) @ V2))) @ V2))))))))))
(TDivides.zdiv_zmult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V1) @ ((cInt.times_int_inst.times_int @ V2) @ V0))) @ ((cDivides.div_int_inst.div_int @ ((cDivides.div_int_inst.div_int @ V1) @ V2)) @ V0))))))))))
(TDivides.zmod_zmult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V1) @ ((cInt.times_int_inst.times_int @ V2) @ V0))) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V2) @ ((cDivides.div_int_inst.mod_int @ ((cDivides.div_int_inst.div_int @ V1) @ V2)) @ V0))) @ ((cDivides.div_int_inst.mod_int @ V1) @ V2)))))))))))
(TEnum.arity_enum_option,(cEnum.enum_class @ cTYPE))
(TEnum.enum.enum_ex_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (V2 @ V3)) @ ((cSet.Bex @ cOrderings.top_class.top) @ V3))))))))))))
(TEnum.enum_all_bool_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_bool_inst.enum_all_bool @ V0)) @ ((cHOL.conj @ (V0 @ cHOL.False)) @ (V0 @ cHOL.True))))))
(TEnum.enum_all_fun_code,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_all @ V0)) @ ((cHOL.Let @ cEnum.enum_class.enum) @ (^[V1]: ((cEnum.all_n_lists @ (^[V2]: (V0 @ ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ V1) @ V2)))))) @ (cNat.size_class.size @ V1))))))))
(TEnum.enum_all_prod_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_all @ V0)) @ (cEnum.enum_class.enum_all @ (^[V1]: (cEnum.enum_class.enum_all @ (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TEnum.enum_all_unit_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_unit_inst.enum_all_unit @ V0)) @ (V0 @ cProduct_Type.Unity)))))
(TEnum.enum_class.axioms,(((cEnum.class.enum @ cEnum.enum_class.enum) @ cEnum.enum_class.enum_all) @ cEnum.enum_class.enum_ex))
(TEnum.enum_finite_1_def,((cHOL.eq @ cEnum.enum_finite_1_inst.enum_finite_1) @ ((cList.list.Cons @ cEnum.finite_1.a\<__caret__sub>1) @ cList.list.Nil)))
(TEnum.enum_finite_2_def,((cHOL.eq @ cEnum.enum_finite_2_inst.enum_finite_2) @ ((cList.list.Cons @ cEnum.finite_2.a\<__caret__sub>1) @ ((cList.list.Cons @ cEnum.finite_2.a\<__caret__sub>2) @ cList.list.Nil))))
(TEnum.enum_finite_3_def,((cHOL.eq @ cEnum.enum_finite_3_inst.enum_finite_3) @ ((cList.list.Cons @ cEnum.finite_3.a\<__caret__sub>1) @ ((cList.list.Cons @ cEnum.finite_3.a\<__caret__sub>2) @ ((cList.list.Cons @ cEnum.finite_3.a\<__caret__sub>3) @ cList.list.Nil)))))
(TEnum.enum_finite_4_def,((cHOL.eq @ cEnum.enum_finite_4_inst.enum_finite_4) @ ((cList.list.Cons @ cEnum.finite_4.a\<__caret__sub>1) @ ((cList.list.Cons @ cEnum.finite_4.a\<__caret__sub>2) @ ((cList.list.Cons @ cEnum.finite_4.a\<__caret__sub>3) @ ((cList.list.Cons @ cEnum.finite_4.a\<__caret__sub>4) @ cList.list.Nil))))))
(TEnum.enum_finite_5_def,((cHOL.eq @ cEnum.enum_finite_5_inst.enum_finite_5) @ ((cList.list.Cons @ cEnum.finite_5.a\<__caret__sub>1) @ ((cList.list.Cons @ cEnum.finite_5.a\<__caret__sub>2) @ ((cList.list.Cons @ cEnum.finite_5.a\<__caret__sub>3) @ ((cList.list.Cons @ cEnum.finite_5.a\<__caret__sub>4) @ ((cList.list.Cons @ cEnum.finite_5.a\<__caret__sub>5) @ cList.list.Nil)))))))
(TEnum.finite_1.eq.simps,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_1.a\<__caret__sub>1) @ cEnum.finite_1.a\<__caret__sub>1)) @ cHOL.True))
(TEnum.finite_1.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.eq @ V0) @ cEnum.finite_1.a\<__caret__sub>1))))
(TEnum.finite_2.distinct_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_2.a\<__caret__sub>2) @ cEnum.finite_2.a\<__caret__sub>1)))
(TEnum.finite_2.distinct_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_2.a\<__caret__sub>1) @ cEnum.finite_2.a\<__caret__sub>2)))
(TEnum.finite_2.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_2.a\<__caret__sub>1) @ cEnum.finite_2.a\<__caret__sub>1)) @ cHOL.True))
(TEnum.finite_2.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_2.a\<__caret__sub>2) @ cEnum.finite_2.a\<__caret__sub>2)) @ cHOL.True))
(TEnum.finite_2.eq.simps_2,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_2.a\<__caret__sub>1) @ cEnum.finite_2.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_2.eq.simps_1,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_2.a\<__caret__sub>2) @ cEnum.finite_2.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_2.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_2.a\<__caret__sub>1)) @ ((cHOL.eq @ V0) @ cEnum.finite_2.a\<__caret__sub>2)))))
(TEnum.finite_3.distinct_6,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>3) @ cEnum.finite_3.a\<__caret__sub>2)))
(TEnum.finite_3.distinct_5,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>2) @ cEnum.finite_3.a\<__caret__sub>3)))
(TEnum.finite_3.distinct_4,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>3) @ cEnum.finite_3.a\<__caret__sub>1)))
(TEnum.finite_3.distinct_3,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>1) @ cEnum.finite_3.a\<__caret__sub>3)))
(TEnum.finite_3.distinct_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>2) @ cEnum.finite_3.a\<__caret__sub>1)))
(TEnum.finite_3.distinct_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_3.a\<__caret__sub>1) @ cEnum.finite_3.a\<__caret__sub>2)))
(TEnum.finite_3.eq.simps_9,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>1) @ cEnum.finite_3.a\<__caret__sub>1)) @ cHOL.True))
(TEnum.finite_3.eq.simps_8,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>2) @ cEnum.finite_3.a\<__caret__sub>2)) @ cHOL.True))
(TEnum.finite_3.eq.simps_7,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>3) @ cEnum.finite_3.a\<__caret__sub>3)) @ cHOL.True))
(TEnum.finite_3.eq.simps_6,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>1) @ cEnum.finite_3.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_3.eq.simps_5,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>2) @ cEnum.finite_3.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_3.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>1) @ cEnum.finite_3.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_3.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>3) @ cEnum.finite_3.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_3.eq.simps_2,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>2) @ cEnum.finite_3.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_3.eq.simps_1,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_3.a\<__caret__sub>3) @ cEnum.finite_3.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_3.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_3.a\<__caret__sub>1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_3.a\<__caret__sub>2)) @ ((cHOL.eq @ V0) @ cEnum.finite_3.a\<__caret__sub>3))))))
(TEnum.finite_4.distinct_12,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>3)))
(TEnum.finite_4.distinct_11,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>4)))
(TEnum.finite_4.distinct_10,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>2)))
(TEnum.finite_4.distinct_9,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>4)))
(TEnum.finite_4.distinct_8,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>2)))
(TEnum.finite_4.distinct_7,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>3)))
(TEnum.finite_4.distinct_6,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>1)))
(TEnum.finite_4.distinct_5,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>4)))
(TEnum.finite_4.distinct_4,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>1)))
(TEnum.finite_4.distinct_3,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>3)))
(TEnum.finite_4.distinct_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>1)))
(TEnum.finite_4.distinct_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>2)))
(TEnum.finite_4.eq.simps_16,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>1)) @ cHOL.True))
(TEnum.finite_4.eq.simps_15,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>2)) @ cHOL.True))
(TEnum.finite_4.eq.simps_14,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>3)) @ cHOL.True))
(TEnum.finite_4.eq.simps_13,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>4)) @ cHOL.True))
(TEnum.finite_4.eq.simps_12,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_4.eq.simps_11,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_4.eq.simps_10,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_4.eq.simps_9,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_4.eq.simps_8,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>1) @ cEnum.finite_4.a\<__caret__sub>4)) @ cHOL.False))
(TEnum.finite_4.eq.simps_7,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_4.eq.simps_6,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_4.eq.simps_5,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_4.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>2) @ cEnum.finite_4.a\<__caret__sub>4)) @ cHOL.False))
(TEnum.finite_4.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_4.eq.simps_2,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>3) @ cEnum.finite_4.a\<__caret__sub>4)) @ cHOL.False))
(TEnum.finite_4.eq.simps_1,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_4.a\<__caret__sub>4) @ cEnum.finite_4.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_4.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>2)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>3)) @ ((cHOL.eq @ V0) @ cEnum.finite_4.a\<__caret__sub>4)))))))
(TEnum.finite_5.distinct_20,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.distinct_19,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.distinct_18,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.distinct_17,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.distinct_16,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.distinct_15,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.distinct_14,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.distinct_13,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.distinct_12,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.distinct_11,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.distinct_10,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.distinct_9,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.distinct_8,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.distinct_7,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>5)))
(TEnum.finite_5.distinct_6,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.distinct_5,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>4)))
(TEnum.finite_5.distinct_4,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.distinct_3,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>3)))
(TEnum.finite_5.distinct_2,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>1)))
(TEnum.finite_5.distinct_1,(cHOL.Not @ ((cHOL.eq @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>2)))
(TEnum.finite_5.eq.simps_25,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>1)) @ cHOL.True))
(TEnum.finite_5.eq.simps_24,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>2)) @ cHOL.True))
(TEnum.finite_5.eq.simps_23,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>3)) @ cHOL.True))
(TEnum.finite_5.eq.simps_22,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>4)) @ cHOL.True))
(TEnum.finite_5.eq.simps_21,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>5)) @ cHOL.True))
(TEnum.finite_5.eq.simps_20,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_5.eq.simps_19,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_5.eq.simps_18,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_5.eq.simps_17,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_5.eq.simps_16,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>4)) @ cHOL.False))
(TEnum.finite_5.eq.simps_15,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_5.eq.simps_14,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>1) @ cEnum.finite_5.a\<__caret__sub>5)) @ cHOL.False))
(TEnum.finite_5.eq.simps_13,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>1)) @ cHOL.False))
(TEnum.finite_5.eq.simps_12,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_5.eq.simps_11,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_5.eq.simps_10,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>4)) @ cHOL.False))
(TEnum.finite_5.eq.simps_9,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_5.eq.simps_8,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>2) @ cEnum.finite_5.a\<__caret__sub>5)) @ cHOL.False))
(TEnum.finite_5.eq.simps_7,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>2)) @ cHOL.False))
(TEnum.finite_5.eq.simps_6,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>4)) @ cHOL.False))
(TEnum.finite_5.eq.simps_5,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_5.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>3) @ cEnum.finite_5.a\<__caret__sub>5)) @ cHOL.False))
(TEnum.finite_5.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>3)) @ cHOL.False))
(TEnum.finite_5.eq.simps_2,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>4) @ cEnum.finite_5.a\<__caret__sub>5)) @ cHOL.False))
(TEnum.finite_5.eq.simps_1,((c== @ ((cHOL.equal_class.equal @ cEnum.finite_5.a\<__caret__sub>5) @ cEnum.finite_5.a\<__caret__sub>4)) @ cHOL.False))
(TEnum.finite_5.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>2)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>3)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>4)) @ ((cHOL.eq @ V0) @ cEnum.finite_5.a\<__caret__sub>5))))))))
(TEnum.less_finite_1_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.ord_finite_1_inst.less_finite_1 @ V0) @ V1)) @ cHOL.False))))))
(TEnum.less_finite_2_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.ord_finite_2_inst.less_finite_2 @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cEnum.finite_2.a\<__caret__sub>1)) @ ((cHOL.eq @ V1) @ cEnum.finite_2.a\<__caret__sub>2))))))))
(TEnum.less_finite_3_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.ord_finite_3_inst.less_finite_3 @ V0) @ V1)) @ ((((cEnum.finite_3.finite_3_case @ (cHOL.Not @ ((cHOL.eq @ V1) @ cEnum.finite_3.a\<__caret__sub>1))) @ ((cHOL.eq @ V1) @ cEnum.finite_3.a\<__caret__sub>3)) @ cHOL.False) @ V0)))))))
(TEquiv_Relations.equivE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((c==> @ (cRelation.sym @ V1)) @ ((c==> @ (cRelation.trans @ V1)) @ V2)))) @ V2)))))))))
(TEquiv_Relations.equivI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((c==> @ (cRelation.sym @ V1)) @ ((c==> @ (cRelation.trans @ V1)) @ ((cEquiv_Relations.equiv @ V0) @ V1)))))))))
(TFields.class.field_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((cRings.class.comm_ring_1 @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cFields.class.field_axioms @ V0) @ V1) @ V2) @ V3) @ V5))))))))))))))))))))
(TFields.field_class_def,((c== @ (cFields.field_class @ cTYPE)) @ ((cPure.conjunction @ (cFields.inverse_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_ring_1_class @ cTYPE)) @ (((((cFields.class.field_axioms @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.zero_class.zero)))))
(TFinite_Set.card.insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.insert @ V1) @ V0))) @ (cNat.Suc @ (cFinite_Set.card @ V0))))))))))
(TFinite_Set.card.remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cNat.Suc @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))
(TFinite_Set.card_Suc_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cNat.Suc @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cSet.insert @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ (cFinite_Set.card @ V3)) @ V1)) @ ((cHOL.implies @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot)))))))))))))))
(TFinite_Set.card_Un_Int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cFinite_Set.card @ ((cLattices.sup_class.sup @ V0) @ V1))) @ (cFinite_Set.card @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))))
(TFinite_Set.card_bij_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((c==> @ ((cFun.inj_on @ V3) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V3) @ V2)) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V2)))))))))))))))))
(TFinite_Set.card_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.insert @ V1) @ V0))) @ (cNat.Suc @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))
(TFinite_Set.finite_Diff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ ((cGroups.minus_class.minus @ V0) @ V1))))))))
(TFinite_Set.finite_Plus,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ ((cSum_Type.Plus @ V0) @ V1)))))))))
(TFinite_Set.finite_UN_I,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (cFinite_Set.finite @ (V1 @ V2)))))) @ (cFinite_Set.finite @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2)))))))))))
(TFinite_Set.finite_prod,((cHOL.eq @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((cHOL.conj @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ cOrderings.top_class.top))))
(TFinite_Set.finite_surj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cSet.image @ V2) @ V0))) @ (cFinite_Set.finite @ V1))))))))))
(TFinite_Set.folding_def,(call @ (^[V0]: ((c== @ (cFinite_Set.folding @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V2))) @ ((cFun.comp @ (V0 @ V2)) @ (V0 @ V1)))))))))))
(TFun.bij_betw_comp_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V3) @ V4)) @ V1)) @ ((cHOL.eq @ (((cFun.bij_betw @ V3) @ V4) @ V1)) @ (((cFun.bij_betw @ ((cFun.comp @ V0) @ V3)) @ V4) @ V2)))))))))))))))
(TFun.bij_image_Compl_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cSet.image @ V0) @ V1)))))))))
(TFun.inj_on_UNION_chain,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ (V1 @ V4))) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V3)))))))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cFun.inj_on @ V2) @ (V1 @ V3)))))) @ ((cFun.inj_on @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))))))))))))
(TFun.surj_imp_surj_swap,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ (((cFun.swap @ V1) @ V2) @ V0)) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)))))))))
(TFunDef.THE_default_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFunDef.THE_default @ V0) @ V1)) @ (((cHOL.If @ (cHOL.Ex1 @ (^[V2]: (V1 @ V2)))) @ (cHOL.The @ (^[V2]: (V1 @ V2)))) @ V0)))))))
(TFunDef.reduction_pairI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ V0) @ V1)) @ V0)) @ (cFunDef.reduction_pair @ ((cProduct_Type.Pair @ V0) @ V1)))))))))
(TFunDef.rp_inv_image_rp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFunDef.reduction_pair @ V0)) @ (cFunDef.reduction_pair @ ((cFunDef.rp_inv_image @ V0) @ V1))))))))
(TGroups.abs_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.abs_class @ cTYPE)))
(TGroups.abs_class.super,((c==> @ (cGroups.abs_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.comm_monoid_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.comm_monoid @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.abel_semigroup @ V0)) @ ((cGroups.comm_monoid_axioms @ V0) @ V1))))))))
(TGroups.minus_class_def,((c== @ (cGroups.minus_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.one_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.one_class @ cTYPE)))
(TGroups.one_class.super,((c==> @ (cGroups.one_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.semigroup.assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.semigroup @ V0)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TGroups.semigroup.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))) @ (cGroups.semigroup @ V0)))))
(TGroups.sgn_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.sgn_class @ cTYPE)))
(TGroups.sgn_class.super,((c==> @ (cGroups.sgn_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.times_class_def,((c== @ (cGroups.times_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THOL.arity_equal_itself,(cHOL.equal_class @ cTYPE))
(THOL.bool.bool_size_def,((c== @ cHOL.bool.bool_size) @ ((cProduct_Type.bool.bool_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(THOL.conj_disj_distribL,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V2))))))))))
(THOL.conj_disj_distribR,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ ((cHOL.disj @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V2))))))))))
(THOL.disj_conj_distribL,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.conj @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ V0) @ V2))))))))))
(THOL.disj_conj_distribR,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cHOL.disj @ V0) @ V2)) @ ((cHOL.disj @ V1) @ V2))))))))))
(THOL.equal_class.axioms,(cHOL.class.equal @ cHOL.eq))
(THOL.induct_forall_conj,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.induct_forall @ (^[V2]: ((cHOL.induct_conj @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.induct_conj @ (cHOL.induct_forall @ V0)) @ (cHOL.induct_forall @ V1))))))))
(THOL.induct_implies_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_implies @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(THOL.the_sym_eq_trivial,(call @ (^[V0]: ((cHOL.eq @ (cHOL.The @ (^[V1]: ((cHOL.eq @ V0) @ V1)))) @ V0))))
(THilbert_Choice.bchoice,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cHOL.Ex @ (^[V3]: ((V1 @ V2) @ V3)))))) @ (cHOL.Ex @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((V1 @ V3) @ (V2 @ V3))))))))))))
(THilbert_Choice.inj_iff,(call @ (^[V0]: ((cHOL.eq @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cFun.comp @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ V0)) @ cFun.id)))))
(THilbert_Choice.inv_def,(call @ (^[V0]: ((cHOL.eq @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ (^[V1]: (cHilbert_Choice.Eps @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ V1))))))))
(THilbert_Choice.inv_f_f,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0) @ (V0 @ V1))) @ V1)))))))
(TInductive.coinduct_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V0 @ ((cLattices.sup_class.sup @ V2) @ (cInductive.complete_lattice_class.gfp @ V0))))) @ ((cSet.member @ V1) @ (cInductive.complete_lattice_class.gfp @ V0))))))))))))
(TInductive.def_coinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.gfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V1 @ ((cLattices.sup_class.sup @ V2) @ V0)))) @ ((cOrderings.ord_class.less_eq @ V2) @ V0)))))))))))
(TInductive.gfp_fun_UnI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cSet.member @ V1) @ (cInductive.complete_lattice_class.gfp @ V0))) @ ((cSet.member @ V1) @ (V0 @ ((cLattices.sup_class.sup @ V2) @ (cInductive.complete_lattice_class.gfp @ V0)))))))))))))
(TInt.arity_linorder_int,(cOrderings.linorder_class @ cTYPE))
(TInt.divide_const_simps_16,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ V0))) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)))))))))
(TInt.divide_const_simps_15,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ V1)))))))))
(TInt.divide_const_simps_14,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)))))))))
(TInt.divide_const_simps_13,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))))
(TInt.divide_const_simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1))) @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ cGroups.zero_class.zero))))))))))
(TInt.divide_const_simps_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1))) @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V2)) @ cGroups.zero_class.zero))))))))))
(TInt.divide_const_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2)) @ V1)) @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))))))))
(TInt.divide_const_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2)) @ V1)) @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero))))))))))
(TInt.divide_const_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V2))))))))))))
(TInt.divide_const_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V2))))))))))))
(TInt.divide_const_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.divide_const_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.divide_const_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V2))))))))))))
(TInt.divide_const_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V2))))))))))))
(TInt.divide_const_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.divide_const_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.int.Abs_int_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cInt.intrel @ V4) @ V4)) @ ((cHOL.eq @ V3) @ (cSet.Collect @ (cInt.intrel @ V4)))))))))) @ (V0 @ (cInt.Abs_int @ V2)))))) @ (V0 @ V1)))))))
(TInt.int.Abs_int_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cInt.intrel @ V3) @ V3)) @ ((cHOL.eq @ V2) @ (cSet.Collect @ (cInt.intrel @ V3)))))))))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cInt.intrel @ V3) @ V3)) @ ((cHOL.eq @ V2) @ (cSet.Collect @ (cInt.intrel @ V3)))))))))) @ ((cHOL.eq @ ((cHOL.eq @ (cInt.Abs_int @ V0)) @ (cInt.Abs_int @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TInt.int.Rep_int_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cInt.intrel @ V3) @ V3)) @ ((cHOL.eq @ V2) @ (cSet.Collect @ (cInt.intrel @ V3)))))))))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cInt.Rep_int @ V2))))) @ (V1 @ V0))))))))
(TInt.int.Rep_int_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cInt.Rep_int @ V0)) @ (cInt.Rep_int @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TInt.int_eq_iff_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ (cInt.nat @ (cNum.numeral_class.numeral @ V1)))) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cNum.numeral_class.numeral @ V1)))))))))
(TInt.less_eq_int.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cInt.Abs_Integ @ V0)) @ (cInt.Abs_Integ @ V1))) @ (((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V5)) @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V3)))))))) @ V0) @ V1)))))))
(TInt.less_eq_int.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ (((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V5)) @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V3)))))))) @ (cInt.Rep_Integ @ V0)) @ (cInt.Rep_Integ @ V1))))))))
(TInt.minus_int.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ ((cTransfer.fun_rel @ cInt.cr_int) @ cInt.cr_int)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))) @ cInt.minus_int_inst.minus_int))
(TInt.nat_numeral_diff_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ cNat.one_nat_inst.one_nat)) @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ cInt.one_int_inst.one_int))))))
(TInt.not_zle_0_negative,(call @ (^[V0]: (cHOL.Not @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V0))))))))
(TInt.pos_zmult_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ cInt.one_int_inst.one_int)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cInt.one_int_inst.one_int)) @ ((cHOL.eq @ V1) @ cInt.one_int_inst.one_int)))))))))
(TInt.ring_1.Ints_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cSet.member @ V6) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))) @ ((c==> @ (call @ (^[V8]: (V7 @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V8))))) @ (V7 @ V6)))))))))))))))))))))
(TInt.ring_1.Ints_of_int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cSet.member @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))))))))))))))))))
(TInt.ring_1.Ints_of_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cSet.member @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6)) @ ((((cInt.ring_1.Ints @ V0) @ V2) @ V3) @ V4))))))))))))))))))
(TInt.ring_1.of_int_code_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ (cInt.Pos @ V6))) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6))))))))))))))))))
(TInt.ring_1.of_int_code_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ cInt.zero_int_inst.zero_int)) @ V3)))))))))))))))
(TInt.ring_1.of_int_code_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ (cInt.Neg @ V6))) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6))))))))))))))))))
(TInt.ring_1.of_int_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ ((cInt.minus_int_inst.minus_int @ V6) @ V7))) @ ((V4 @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V7)))))))))))))))))))))
(TInt.ring_1.of_int_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ ((cInt.times_int_inst.times_int @ V6) @ V7))) @ ((V1 @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V7)))))))))))))))))))))
(TInt.times_int.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ ((cTransfer.fun_rel @ cInt.cr_int) @ cInt.cr_int)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V3)) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)))))))))) @ cInt.times_int_inst.times_int))
(TInt.zero_le_imp_eq_int,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TInt.zero_less_int_conv,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ (cNat.semiring_1_class.of_nat @ V0))) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)))))
(TInt.zless_iff_Suc_zadd,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ ((cInt.plus_int_inst.plus_int @ V0) @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V2))))))))))))
(TInt.zless_imp_add1_zle,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)))))))
(TInt.zpower_numeral_odd,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V1)))) @ ((cHOL.Let @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ V1))) @ (^[V2]: ((cInt.times_int_inst.times_int @ ((cInt.times_int_inst.times_int @ V0) @ V2)) @ V2)))))))))
(TLattices.bool_diff_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.minus_bool_inst.minus_bool @ V0) @ V1)) @ ((cHOL.conj @ V0) @ (cHOL.Not @ V1))))))))
(TLattices.fun_Compl_def,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (^[V1]: (cGroups.uminus_class.uminus @ (V0 @ V1)))))))
(TLattices.inf_class_def,((c== @ (cLattices.inf_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TLattices.sup_class_def,((c== @ (cLattices.sup_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TLazy_Sequence.bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.bind @ V0) @ V1)) @ (cLazy_Sequence.flat @ ((cLazy_Sequence.map @ V1) @ V0))))))))
(TLazy_Sequence.flat_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.flat @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ (cList.concat @ ((cList.map @ cLazy_Sequence.list_of_lazy_sequence) @ (cLazy_Sequence.list_of_lazy_sequence @ V0))))))))
(TLazy_Sequence.map_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.map @ V0) @ V1)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V2]: ((cOption.map @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cProduct_Type.Pair @ (V0 @ V3)) @ ((cLazy_Sequence.map @ V0) @ V4)))))) @ (cLazy_Sequence.yield @ V1))))))))))
(TLifting.Quotient_refl1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V4))))))))))))))))
(TLifting.Quotient_refl2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((V0 @ V5) @ V5))))))))))))))))
(TLifting.left_total_def,(call @ (^[V0]: ((cHOL.eq @ (cLifting.left_total @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TLifting.left_total_fun,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_unique @ V0)) @ ((c==> @ (cLifting.left_total @ V1)) @ (cLifting.left_total @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TLifting.left_unique_eq,(cLifting.left_unique @ cHOL.eq))
(TLifting.neg_fun_distr1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cLifting.left_unique @ V0)) @ ((c==> @ (cTransfer.right_total @ V0)) @ ((c==> @ (cTransfer.right_unique @ V1)) @ ((c==> @ (cLifting.left_total @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cTransfer.fun_rel @ ((cRelation.relcompp @ V0) @ V1)) @ ((cRelation.relcompp @ V2) @ V3))) @ ((cRelation.relcompp @ ((cTransfer.fun_rel @ V0) @ V2)) @ ((cTransfer.fun_rel @ V1) @ V3))))))))))))))))
(TLifting.neg_fun_distr2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((c==> @ (cLifting.left_total @ V0)) @ ((c==> @ (cLifting.left_unique @ V1)) @ ((c==> @ (cTransfer.right_total @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cTransfer.fun_rel @ ((cRelation.relcompp @ V2) @ V0)) @ ((cRelation.relcompp @ V3) @ V1))) @ ((cRelation.relcompp @ ((cTransfer.fun_rel @ V2) @ V3)) @ ((cTransfer.fun_rel @ V0) @ V1))))))))))))))))
(TLifting.reflp_equality,(cRelation.reflp @ cHOL.eq))
(TLifting_Set.set_rel_OO,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcompp @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V1))) @ (cLifting_Set.set_rel @ ((cRelation.relcompp @ V0) @ V1))))))))
(TLifting_Set.set_rel_eq,((cHOL.eq @ (cLifting_Set.set_rel @ cHOL.eq)) @ cHOL.eq))
(TLifting_Sum.sum_rel_OO,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cRelation.relcompp @ ((cLifting_Sum.sum_rel @ V0) @ V1)) @ ((cLifting_Sum.sum_rel @ V2) @ V3))) @ ((cLifting_Sum.sum_rel @ ((cRelation.relcompp @ V0) @ V2)) @ ((cRelation.relcompp @ V1) @ V3))))))))))))
(TLifting_Sum.sum_rel_eq,((cHOL.eq @ ((cLifting_Sum.sum_rel @ cHOL.eq) @ cHOL.eq)) @ cHOL.eq))
(TList.Ball_set_list_all,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ (cList.set @ V0)) @ V1)) @ ((cList.list_all @ V1) @ V0)))))))
(TList.Bex_set_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ (cList.set @ ((cList.replicate @ V0) @ V1))) @ (^[V3]: (V2 @ V3)))) @ ((cHOL.conj @ (V2 @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))))))))
(TList.Cons_in_lists_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cList.list.Cons @ V0) @ V1)) @ (cList.lists @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V2)) @ ((cSet.member @ V1) @ (cList.lists @ V2)))))))))))
(TList.Cons_replicate_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.replicate @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cHOL.eq @ V1) @ ((cList.replicate @ ((cNat.minus_nat_inst.minus_nat @ V2) @ cNat.one_nat_inst.one_nat)) @ V0))))))))))))))
(TList.Ex_list_of_length,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ V1)) @ V0))))))
(TList.append.append_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.append @ cList.list.Nil) @ V0)) @ V0))))
(TList.append_eq_appendI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ V2)) @ ((c==> @ ((cHOL.eq @ V3) @ ((cList.append @ V1) @ V4))) @ ((cHOL.eq @ ((cList.append @ V0) @ V3)) @ ((cList.append @ V2) @ V4)))))))))))))))
(TList.append_self_conv2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ V1)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))))
(TList.atLeastAtMost_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cList.set @ ((cList.upt @ V0) @ (cNat.Suc @ V1)))))))))
(TList.butlast_conv_take,(call @ (^[V0]: ((cHOL.eq @ (cList.butlast @ V0)) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat)) @ V0)))))
(TList.concat_conv_foldr,(call @ (^[V0]: ((cHOL.eq @ (cList.concat @ V0)) @ (((cList.foldr @ cList.append) @ V0) @ cList.list.Nil)))))
(TList.distinct_conv_nth,(call @ (^[V0]: ((cHOL.eq @ (cList.distinct @ V0)) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V0))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.eq @ ((cList.nth @ V0) @ V1)) @ ((cList.nth @ V0) @ V2))))))))))))))
(TList.distinct_sublistI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.sublist @ V0) @ V1))))))))
(TList.distinct_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ cHOL.eq) @ cList.distinct) @ cList.distinct)))))
(TList.dropWhile_append1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ (cHOL.Not @ (V2 @ V0))) @ ((cHOL.eq @ ((cList.dropWhile @ V2) @ ((cList.append @ V1) @ V3))) @ ((cList.append @ ((cList.dropWhile @ V2) @ V1)) @ V3)))))))))))))
(TList.dropWhile_append2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ (V1 @ V3))))) @ ((cHOL.eq @ ((cList.dropWhile @ V1) @ ((cList.append @ V0) @ V2))) @ ((cList.dropWhile @ V1) @ V2))))))))))
(TList.dropWhile_append3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ (V0 @ V1))) @ ((cHOL.eq @ ((cList.dropWhile @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V1) @ V3)))) @ ((cList.append @ ((cList.dropWhile @ V0) @ V2)) @ ((cList.list.Cons @ V1) @ V3)))))))))))))
(TList.dropWhile_eq_drop,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.dropWhile @ V0) @ V1)) @ ((cList.drop @ (cNat.size_class.size @ ((cList.takeWhile @ V0) @ V1))) @ V1)))))))
(TList.dropWhile_neq_rev,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((c==> @ ((cSet.member @ V1) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cList.dropWhile @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ V2) @ V1)))) @ (cList.rev @ V0))) @ ((cList.list.Cons @ V1) @ (cList.rev @ ((cList.takeWhile @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ V2) @ V1)))) @ V0)))))))))))
(TList.drop_Cons_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.drop @ (cNum.numeral_class.numeral @ V0)) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.drop @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ cNat.one_nat_inst.one_nat)) @ V2)))))))))
(TList.filter_empty_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.filter @ V0) @ V1)) @ cList.list.Nil)) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: (cHOL.Not @ (V0 @ V2))))))))))
(TList.filter_in_sublist,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ ((cList.filter @ (^[V2]: ((cSet.member @ V2) @ (cList.set @ ((cList.sublist @ V0) @ V1))))) @ V0)) @ ((cList.sublist @ V0) @ V1))))))))
(TList.in_lists_conv_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.lists @ V1))) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cSet.member @ V2) @ V1)))))))))
(TList.inj_on_map_eq_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ ((cLattices.sup_class.sup @ (cList.set @ V1)) @ (cList.set @ V2)))) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TList.length_filter_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.filter @ V0) @ ((cList.map @ V1) @ V2)))) @ (cNat.size_class.size @ ((cList.filter @ ((cFun.comp @ V0) @ V1)) @ V2))))))))))
(TList.length_remdups_eq,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNat.size_class.size @ (cList.remdups @ V0))) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ (cList.remdups @ V0)) @ V0)))))
(TList.linorder.set_sort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cList.set @ (((cList.linorder.sort_key @ V0) @ V2) @ V3))) @ (cList.set @ V3))))))))))))
(TList.list.list_rec_def,((c== @ cList.list.list_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cList.list.list_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TList.list_all2_antisym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ ((V1 @ V5) @ V4)) @ ((cHOL.eq @ V4) @ V5)))))))) @ ((c==> @ (((cList.list_all2 @ V0) @ V2) @ V3)) @ ((c==> @ (((cList.list_all2 @ V1) @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TList.list_all2_append1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ ((cList.append @ V1) @ V2)) @ V3)) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.append @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V4)) @ (cNat.size_class.size @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V5)) @ (cNat.size_class.size @ V2))) @ ((cHOL.conj @ (((cList.list_all2 @ V0) @ V1) @ V4)) @ (((cList.list_all2 @ V0) @ V2) @ V5)))))))))))))))))))
(TList.list_all2_append2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ V1) @ ((cList.append @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V4)) @ (cNat.size_class.size @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V5)) @ (cNat.size_class.size @ V3))) @ ((cHOL.conj @ (((cList.list_all2 @ V0) @ V4) @ V2)) @ (((cList.list_all2 @ V0) @ V5) @ V3)))))))))))))))))))
(TList.list_all2_appendI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((c==> @ (((cList.list_all2 @ V0) @ V3) @ V4)) @ (((cList.list_all2 @ V0) @ ((cList.append @ V1) @ V3)) @ ((cList.append @ V2) @ V4)))))))))))))))
(TList.list_all2_lengthD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))))))))))
(TList.list_all_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ cHOL.eq)) @ cList.list_all) @ cList.list_all))))
(TList.list_rec_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ ((cTransfer.fun_rel @ V0) @ V0)))) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ V0))) @ cList.list.list_rec) @ cList.list.list_rec))))))
(TList.list_update.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_update @ ((cList.list.Cons @ V0) @ V1)) @ V2) @ V3)) @ (((cNat.nat.nat_case @ ((cList.list.Cons @ V3) @ V1)) @ (^[V4]: ((cList.list.Cons @ V0) @ (((cList.list_update @ V1) @ V4) @ V3)))) @ V2)))))))))))
(TList.list_update.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.list_update @ cList.list.Nil) @ V0) @ V1)) @ cList.list.Nil))))))
(TList.listrel1_converse,(call @ (^[V0]: ((cHOL.eq @ (cList.listrel1 @ (cRelation.converse @ V0))) @ (cRelation.converse @ (cList.listrel1 @ V0))))))
(TList.map_fst_enumerate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ cProduct_Type.fst) @ ((cList.enumerate @ V0) @ V1))) @ ((cList.upt @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ (cNat.size_class.size @ V1)))))))))
(TList.map_removeAll_inj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cList.map @ V0) @ ((cList.removeAll @ V1) @ V2))) @ ((cList.removeAll @ (V0 @ V1)) @ ((cList.map @ V0) @ V2)))))))))))
(TList.map_snd_enumerate,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ cProduct_Type.snd) @ ((cList.enumerate @ V0) @ V1))) @ V1))))))
(TList.neq_if_length_neq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1)))) @ ((c== @ ((cHOL.eq @ V0) @ V1)) @ cHOL.False)))))))
(TList.not_in_set_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((cHOL.eq @ ((cList.insert @ V0) @ V1)) @ ((cList.list.Cons @ V0) @ V1))))))))
(TList.notin_set_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ ((cList.remove1 @ V2) @ V1))))))))))))
(TList.nth_append_length,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (cNat.size_class.size @ V0))) @ V1))))))))
(TList.partition_filter1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cList.partition @ V0) @ V1))) @ ((cList.filter @ V0) @ V1)))))))
(TList.partition_filter2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cList.partition @ V0) @ V1))) @ ((cList.filter @ ((cFun.comp @ cHOL.Not) @ V0)) @ V1)))))))
(TList.product_lists_def,((c== @ cList.product_lists) @ (^[V0]: (((cList.list.list_rec @ ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil)) @ (^[V1]: (^[V2]: (^[V3]: (cList.concat @ ((cList.map @ (^[V4]: ((cList.map @ (cList.list.Cons @ V4)) @ V3))) @ V1)))))) @ V0))))
(TList.product_lists_set,(call @ (^[V0]: ((cHOL.eq @ (cList.set @ (cList.product_lists @ V0))) @ (cSet.Collect @ (^[V1]: (((cList.list_all2 @ (^[V2]: (^[V3]: ((cSet.member @ V2) @ (cList.set @ V3))))) @ V1) @ V0)))))))
(TList.remdups_adj.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ cList.list.Nil))) @ V1)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ V1)))))))) @ V1))))))))
(TList.remdups_adj.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cList.remdups_adj @ V0)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ V2))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ cList.list.Nil))) @ V2))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V3) @ V4)) @ (cList.remdups_adj @ ((cList.list.Cons @ V3) @ V5))) @ ((cList.list.Cons @ V3) @ (cList.remdups_adj @ ((cList.list.Cons @ V4) @ V5)))))) @ V2))))))))) @ V2)))))))))))
(TList.remdups_adj.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V1)) @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ V2))) @ ((cList.list.Cons @ V0) @ (cList.remdups_adj @ ((cList.list.Cons @ V1) @ V2))))))))))))
(TList.remdups_adj.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ cList.list.Nil))) @ ((cList.list.Cons @ V0) @ cList.list.Nil)))))
(TList.remdups_adj.simps_1,((cHOL.eq @ (cList.remdups_adj @ cList.list.Nil)) @ cList.list.Nil))
(TList.self_append_conv2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cList.append @ V1) @ V0))) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.set_Cons_sing_Nil,(call @ (^[V0]: ((cHOL.eq @ ((cList.set_Cons @ V0) @ ((cSet.insert @ cList.list.Nil) @ cOrderings.bot_class.bot))) @ ((cSet.image @ (^[V1]: ((cList.list.Cons @ V1) @ cList.list.Nil))) @ V0)))))
(TList.set_Cons_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ (cList.list_all2 @ V0))) @ (cLifting_Set.set_rel @ (cList.list_all2 @ V0)))) @ cList.set_Cons) @ cList.set_Cons))))
(TList.set_replicate_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.replicate @ (cNat.Suc @ V0)) @ V1))) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))
(TList.splice_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.splice_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V4) @ V6)) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TList.splice_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cList.splice_rel @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V0)) @ ((cList.list.Cons @ V3) @ V1))))))))))))
(TList.sublist_singleton,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.sublist @ ((cList.list.Cons @ V0) @ cList.list.Nil)) @ V1)) @ (((cHOL.If @ ((cSet.member @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cList.list.Cons @ V0) @ cList.list.Nil)) @ cList.list.Nil)))))))
(TList.takeWhile_append1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ (cHOL.Not @ (V2 @ V0))) @ ((cHOL.eq @ ((cList.takeWhile @ V2) @ ((cList.append @ V1) @ V3))) @ ((cList.takeWhile @ V2) @ V1)))))))))))))
(TList.takeWhile_append2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ (V1 @ V3))))) @ ((cHOL.eq @ ((cList.takeWhile @ V1) @ ((cList.append @ V0) @ V2))) @ ((cList.append @ V0) @ ((cList.takeWhile @ V1) @ V2)))))))))))
(TList.takeWhile_eq_take,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.takeWhile @ V0) @ V1)) @ ((cList.take @ (cNat.size_class.size @ ((cList.takeWhile @ V0) @ V1))) @ V1)))))))
(TList.takeWhile_neq_rev,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((c==> @ ((cSet.member @ V1) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cList.takeWhile @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ V2) @ V1)))) @ (cList.rev @ V0))) @ (cList.rev @ (cList.tl @ ((cList.dropWhile @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ V2) @ V1)))) @ V0)))))))))))
(TList.take_Cons_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.take @ (cNum.numeral_class.numeral @ V0)) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.list.Cons @ V1) @ ((cList.take @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ cNat.one_nat_inst.one_nat)) @ V2))))))))))
(TList.transpose.pinduct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ V0)) @ ((c==> @ ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ cList.list.Nil)) @ (V1 @ cList.list.Nil))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ ((cList.list.Cons @ cList.list.Nil) @ V2))) @ ((c==> @ (V1 @ V2)) @ (V1 @ ((cList.list.Cons @ cList.list.Nil) @ V2))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cList.transpose_rel) @ ((cList.list.Cons @ ((cList.list.Cons @ V2) @ V3)) @ V4))) @ ((c==> @ (V1 @ ((cList.list.Cons @ V3) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V5]: (^[V6]: ((cList.list.Cons @ V6) @ cList.list.Nil))))) @ V4))))) @ (V1 @ ((cList.list.Cons @ ((cList.list.Cons @ V2) @ V3)) @ V4))))))))))) @ (V1 @ V0))))))))))
(TList.transpose_aux_max,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ (cNat.Suc @ (cNat.size_class.size @ V0))) @ (((cList.foldr @ (^[V2]: (cOrderings.ord_class.max @ (cNat.size_class.size @ V2)))) @ V1) @ cNat.zero_nat_inst.zero_nat))) @ (cNat.Suc @ ((cOrderings.ord_class.max @ (cNat.size_class.size @ V0)) @ (((cList.foldr @ (^[V2]: (cOrderings.ord_class.max @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))) @ ((cList.filter @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ V2) @ cList.list.Nil)))) @ V1)) @ cNat.zero_nat_inst.zero_nat)))))))))
(TList.transpose_map_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.transpose @ ((cList.map @ (cList.map @ V0)) @ V1))) @ ((cList.map @ (cList.map @ V0)) @ (cList.transpose @ V1))))))))
(TList.transpose_rel_def,((c== @ cList.transpose_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ cList.list.Nil) @ V3)))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5))))) @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))))))))))))))))
(TList.upt_add_eq_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cList.upt @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((cList.append @ ((cList.upt @ V0) @ V1)) @ ((cList.upt @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))))
(TList.upto_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.upto_graph @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.list.Cons @ V4) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)))) @ cList.list.Nil))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TList.upto_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cList.upto_graph @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)) @ (V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1))))) @ ((cList.upto_graph @ ((cProduct_Type.Pair @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cList.list.Cons @ V0) @ (V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)))) @ cList.list.Nil))))))))))
(TList.zip_same_conv_map,(call @ (^[V0]: ((cHOL.eq @ ((cList.zip @ V0) @ V0)) @ ((cList.map @ (^[V1]: ((cProduct_Type.Pair @ V1) @ V1))) @ V0)))))
(TList.zip_takeWhile_fst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ ((cList.takeWhile @ V0) @ V1)) @ V2)) @ ((cList.takeWhile @ ((cFun.comp @ V0) @ cProduct_Type.fst)) @ ((cList.zip @ V1) @ V2))))))))))
(TList.zip_takeWhile_snd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.zip @ V0) @ ((cList.takeWhile @ V1) @ V2))) @ ((cList.takeWhile @ ((cFun.comp @ V1) @ cProduct_Type.snd)) @ ((cList.zip @ V0) @ V2))))))))))
(TMap.Some_eq_map_of_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.distinct @ ((cList.map @ cProduct_Type.fst) @ V0))) @ ((cHOL.eq @ ((cHOL.eq @ (cOption.option.Some @ V1)) @ ((cMap.map_of @ V0) @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ (cList.set @ V0)))))))))))
(TMap.inj_on_map_add_dom,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.inj_on @ ((cMap.map_add @ V0) @ V1)) @ (cMap.dom @ V1))) @ ((cFun.inj_on @ V1) @ (cMap.dom @ V1))))))))
(TMap.map_add_find_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ (cOption.option.Some @ V2))) @ ((cHOL.eq @ (((cMap.map_add @ V3) @ V0) @ V1)) @ (cOption.option.Some @ V2))))))))))))
(TMap.map_of_eq_None_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cMap.map_of @ V0) @ V1)) @ cOption.option.None)) @ (cHOL.Not @ ((cSet.member @ V1) @ ((cSet.image @ cProduct_Type.fst) @ (cList.set @ V0))))))))))
(TMap.map_of_eq_Some_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.distinct @ ((cList.map @ cProduct_Type.fst) @ V0))) @ ((cHOL.eq @ ((cHOL.eq @ ((cMap.map_of @ V0) @ V1)) @ (cOption.option.Some @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.set @ V0)))))))))))
(TMap.map_of_zip_is_None,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ ((cMap.map_of @ ((cList.zip @ V0) @ V1)) @ V2)) @ cOption.option.None)) @ (cHOL.Not @ ((cSet.member @ V2) @ (cList.set @ V0))))))))))))
(TMap.map_of_zip_is_Some,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cSet.member @ V2) @ (cList.set @ V0))) @ (cHOL.Ex @ (^[V3]: ((cHOL.eq @ ((cMap.map_of @ ((cList.zip @ V0) @ V1)) @ V2)) @ (cOption.option.Some @ V3)))))))))))))
(TMap.option_map_o_empty,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ (cOption.map @ V0)) @ (^[V1]: cOption.option.None))) @ (^[V1]: cOption.option.None)))))
(TMap.restrict_map_empty,(call @ (^[V0]: ((cHOL.eq @ ((cMap.restrict_map @ (^[V1]: cOption.option.None)) @ V0)) @ (^[V1]: cOption.option.None)))))
(TMeson.skolem_COMBK_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ V0) @ (cMeson.skolem @ ((cMeson.COMBK @ V0) @ V1))))))))
(TNat.Nat_Abs_Nat_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat.Nat @ V0)) @ ((c==> @ (cNat.Nat @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (cNat.Abs_Nat @ V0)) @ (cNat.Abs_Nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TNat.arity_linorder_nat,(cOrderings.linorder_class @ cTYPE))
(TNat.diff_mult_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))))))))))
(TNat.dvd.Least_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cRings.dvd_class.dvd @ V1) @ V2))))) @ ((cHOL.eq @ ((cOrderings.ord.Least @ cRings.dvd_class.dvd) @ V0)) @ V1))))))))
(TNat.dvd.less_le_not_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))))
(TNat.funpow_simps_right_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ (cNat.Suc @ V0)) @ V1)) @ ((cFun.comp @ ((cNat.compow @ V0) @ V1)) @ V1)))))))
(TNat.funpow_simps_right_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cFun.id))))
(TNat.le_imp_diff_is_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ ((cHOL.eq @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0)))))))))))
(TNat.less_Suc_eq_0_disj,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ (cNat.Suc @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V2) @ V1)))))))))))
(TNat.less_imp_diff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V2)) @ V1)))))))))
(TNat.less_nat_zero_code,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cHOL.False))))
(TNat.minus_nat.diff_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.Suc @ V1))) @ (((cNat.nat.nat_case @ cNat.zero_nat_inst.zero_nat) @ (^[V2]: V2)) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))))))))
(TNat.mono_nat_linear_lb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V4)) @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V3)) @ (V0 @ V4)))))))) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ V2)) @ (V0 @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2)))))))))))
(TNat.nat.Abs_Nat_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ (^[V3]: (cNat.Nat @ V3))))) @ (V0 @ (cNat.Abs_Nat @ V2)))))) @ (V0 @ V1)))))))
(TNat.nat.Abs_Nat_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V2]: (cNat.Nat @ V2))))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ (^[V2]: (cNat.Nat @ V2))))) @ ((cHOL.eq @ ((cHOL.eq @ (cNat.Abs_Nat @ V0)) @ (cNat.Abs_Nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TNat.nat.Rep_Nat_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V2]: (cNat.Nat @ V2))))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cNat.Rep_Nat @ V2))))) @ (V1 @ V0))))))))
(TNat.nat.Rep_Nat_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.Rep_Nat @ V0)) @ (cNat.Rep_Nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat.nat.arity_size_nat,(cNat.size_class @ cTYPE))
(TNat.nat.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cNat.nat.nat_case @ V2) @ V3) @ V0)) @ (((cNat.nat.nat_case @ V2) @ V3) @ V1))))))))))))
(TNat.nat_diff_split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ (cHOL.Not @ (V0 @ cNat.zero_nat_inst.zero_nat)))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3))) @ (cHOL.Not @ (V0 @ V3)))))))))))))))
(TNat.nat_mult_max_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))))))))))
(TNat.nat_mult_min_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))))))))))
(TNat.ring_1.of_nat_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V6) @ V7)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ ((cNat.minus_nat_inst.minus_nat @ V7) @ V6))) @ ((V4 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V7)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6))))))))))))))))))))))
(TNat.times_nat.mult_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))))))))
(TNitpick.equal_word_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.fun_box.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cNitpick.fun_box.FunBox @ V2))))) @ (V0 @ V1)))))))
(TNitpick.fun_box.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNitpick.fun_box.FunBox @ V0)) @ (cNitpick.fun_box.FunBox @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.fun_box.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.fun_box.fun_box_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cNitpick.fun_box.FunBox @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TNitpick.fun_box.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.fun_box.fun_box_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cNitpick.fun_box.FunBox @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TNitpick.list_size_simp_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ (cNat.size_class.size @ (cList.tl @ V0))))))))
(TNitpick.list_size_simp_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list.list_size @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ cNat.zero_nat_inst.zero_nat) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ (cList.hd @ V1))) @ ((cList.list.list_size @ V0) @ (cList.tl @ V1)))))))))))
(TNitpick.nat_gcd.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))) @ ((V0 @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TNitpick.nat_gcd.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cNitpick.nat_gcd @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cNitpick.nat_gcd_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat)) @ V4) @ ((cNitpick.nat_gcd @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))))) @ ((c==> @ ((cWellfounded.accp @ cNitpick.nat_gcd_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TNitpick.nat_gcd.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cNitpick.nat_gcd_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cNitpick.nat_gcd @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ V0) @ ((cNitpick.nat_gcd @ V1) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))))))))))
(TNitpick.pair_box.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNitpick.pair_box.pair_box_case @ V0) @ ((cNitpick.pair_box.PairBox @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TNitpick.pair_box.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNitpick.pair_box.pair_box_rec @ V0) @ ((cNitpick.pair_box.PairBox @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TNitpick.pair_box.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNitpick.pair_box.pair_box_case @ V0) @ ((cNitpick.pair_box.PairBox @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TNitpick.pair_box.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cNitpick.pair_box.PairBox @ V0) @ V1)) @ ((cNitpick.pair_box.PairBox @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TNitpick.pair_box.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.pair_box.pair_box_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cNitpick.pair_box.PairBox @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TNitpick.rtrancl_unfold,(call @ (^[V0]: ((c== @ (cTransitive_Closure.rtrancl @ V0)) @ ((cLattices.sup_class.sup @ (cTransitive_Closure.trancl @ V0)) @ cRelation.Id)))))
(TNitpick.times_frac_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.times_frac @ V0) @ V1)) @ ((cNitpick.frac @ ((cInt.times_int_inst.times_int @ (cNitpick.num @ V0)) @ (cNitpick.num @ V1))) @ ((cInt.times_int_inst.times_int @ (cNitpick.denom @ V0)) @ (cNitpick.denom @ V1)))))))))
(TNitpick.tranclp_unfold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cTransitive_Closure.trancl @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4)))))))))))))))
(TNitpick.word.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cNitpick.word.Word @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cNitpick.word.word_case @ V2) @ V0)) @ ((cNitpick.word.word_case @ V3) @ V1)))))))))))))
(TNitpick.word.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.word.word_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cNitpick.word.Word @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TNum.arity_linorder_num,(cOrderings.linorder_class @ cTYPE))
(TNum.nat_case_add_eq_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cNat.nat.nat_case @ V0) @ V1) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ V2)) @ V3))) @ ((cHOL.Let @ (cNum.pred_numeral @ V2)) @ (^[V4]: (V1 @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V3))))))))))))))
(TNum.nat_of_num_inverse,(call @ (^[V0]: ((cHOL.eq @ (cNum.num_of_nat @ (cNum.nat_of_num @ V0))) @ V0))))
(TNum.nat_of_num_numeral,((cHOL.eq @ cNum.nat_of_num) @ cNum.numeral_class.numeral))
(TNum.num.Abs_num_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNum.num.num_rep_set))) @ (V0 @ (cNum.Abs_num @ V2)))))) @ (V0 @ V1)))))))
(TNum.num.Abs_num_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNum.num.num_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cNum.num.num_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cNum.Abs_num @ V0)) @ (cNum.Abs_num @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TNum.num.Rep_num_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNum.num.num_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cNum.Rep_num @ V2))))) @ (V1 @ V0))))))))
(TNum.num.Rep_num_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.Rep_num @ V0)) @ (cNum.Rep_num @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.num.arity_size_num,(cNat.size_class @ cTYPE))
(TNum.num.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((((cNum.num.num_case @ V2) @ V3) @ V4) @ V0)) @ ((((cNum.num.num_case @ V2) @ V3) @ V4) @ V1))))))))))))))
(TNum.num_of_nat_inverse,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ (cNum.nat_of_num @ (cNum.num_of_nat @ V0))) @ V0)))))
(TNum.numeral_1_eq_Suc_0,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))
(TNum.pred_numeral_simps_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.pred_numeral @ (cNum.num.Bit1 @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.pred_numeral_simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.pred_numeral @ (cNum.num.Bit0 @ V0))) @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))))))
(TNum.pred_numeral_simps_1,((cHOL.eq @ (cNum.pred_numeral @ cNum.num.One)) @ cNat.zero_nat_inst.zero_nat))
(TNum.ring_1.mult_minus1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ cNum.num.One)) @ V6)) @ (V5 @ V6))))))))))))))))))
(TOption.bind.bind_lunit,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOption.bind @ (cOption.option.Some @ V0)) @ V1)) @ (V1 @ V0)))))))
(TOption.bind.bind_lzero,(call @ (^[V0]: ((cHOL.eq @ ((cOption.bind @ cOption.option.None) @ V0)) @ cOption.option.None))))
(TOption.option.None_def,((c== @ cOption.option.None) @ (cOption.Abs_option @ (cDatatype.In0 @ cHOL.undefined))))
(TOption.option.Some_def,(call @ (^[V0]: ((c== @ (cOption.option.Some @ V0)) @ (cOption.Abs_option @ (cDatatype.In1 @ (cDatatype.Leaf @ V0)))))))
(TOption.option.distinct_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cOption.option.Some @ V0)) @ cOption.option.None)))))
(TOption.option.distinct_1,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOption.option.None) @ (cOption.option.Some @ V0))))))
(TOption.option.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cOption.option.None) @ cOption.option.None)) @ cHOL.True))
(TOption.option.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cOption.option.Some @ V0)) @ (cOption.option.Some @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TOption.option.eq.simps_2,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ cOption.option.None) @ (cOption.option.Some @ V0))) @ cHOL.False))))
(TOption.option.eq.simps_1,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ (cOption.option.Some @ V0)) @ cOption.option.None)) @ cHOL.False))))
(TOption.option.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cOption.option.None)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cOption.option.Some @ V1))))))))
(TOption.option_case_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cOption.option.option_case @ V0) @ V1) @ ((cOption.map @ V2) @ V3))) @ (((cOption.option.option_case @ V0) @ ((cFun.comp @ V1) @ V2)) @ V3)))))))))))
(TOption.option_map_None,(call @ (^[V0]: ((cHOL.eq @ ((cOption.map @ V0) @ cOption.option.None)) @ cOption.option.None))))
(TOption.option_map_Some,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOption.map @ V0) @ (cOption.option.Some @ V1))) @ (cOption.option.Some @ (V0 @ V1))))))))
(TOption.option_map_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOption.map @ V0) @ ((cOption.map @ V1) @ V2))) @ ((cOption.map @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TOption.split_option_ex,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ ((cHOL.disj @ (V0 @ cOption.option.None)) @ (cHOL.Ex @ (^[V1]: (V0 @ (cOption.option.Some @ V1)))))))))
(TOrderings.bot_bool_def,((cHOL.eq @ cOrderings.bot_bool_inst.bot_bool) @ cHOL.False))
(TOrderings.less_fun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))))
(TOrderings.linorder.leD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (cHOL.Not @ ((V1 @ V3) @ V2)))))))))))))
(TOrderings.linorder.leI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((V1 @ V2) @ V3))) @ ((V0 @ V3) @ V2))))))))))))
(TOrderings.no_bot.lt_ex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Ex @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TOrderings.no_top.gt_ex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Ex @ (^[V3]: ((V1 @ V2) @ V3)))))))))))
(TOrderings.order.eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V2) @ V3)) @ ((V0 @ V3) @ V2)))))))))))))
(TOrderings.order_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TOrderings.order_subst1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_subst2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.ordering_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.ordering @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))))))))) @ (cHOL.All @ (^[V2]: ((V0 @ V2) @ V2))))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.implies @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((V0 @ V2) @ V4)))))))))))))))))
(TOrderings.top_bool_def,((cHOL.eq @ cOrderings.top_bool_inst.top_bool) @ cHOL.True))
(TPower.field.power_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V9) @ V10)) @ ((cHOL.eq @ ((((cPower.power.power @ V3) @ V2) @ V8) @ ((cNat.minus_nat_inst.minus_nat @ V10) @ V9))) @ ((V1 @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V10)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V9)))))))))))))))))))))))))))))
(TPower.nat_one_le_power,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPower.power_dvd_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.one_nat_inst.one_nat) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2))))))))))
(TPredicate.Inf_pred_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cPredicate.pred.Pred @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ cPredicate.eval))))))
(TPredicate.Sup_pred_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cPredicate.pred.Pred @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ cPredicate.eval))))))
(TPredicate.bot_pred_def,((cHOL.eq @ cOrderings.bot_class.bot) @ (cPredicate.pred.Pred @ cOrderings.bot_class.bot)))
(TPredicate.bot_set_code,((cHOL.eq @ cOrderings.bot_class.bot) @ (cPredicate.Seq @ (^[V0]: cPredicate.seq.Empty))))
(TPredicate.eq_pred_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TPredicate.inf_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (cPredicate.pred.Pred @ ((cLattices.inf_class.inf @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1)))))))))
(TPredicate.is_empty_bot,(cPredicate.is_empty @ cOrderings.bot_class.bot))
(TPredicate.is_empty_def,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.is_empty @ V0)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TPredicate.is_empty_sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.is_empty @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cHOL.conj @ (cPredicate.is_empty @ V0)) @ (cPredicate.is_empty @ V1))))))))
(TPredicate.map.identity,((cHOL.eq @ (cPredicate.map @ (^[V0]: V0))) @ cFun.id))
(TPredicate.member.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.member @ ((cPredicate.seq.Join @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cPredicate.eval @ V0) @ V2)) @ ((cPredicate.member @ V1) @ V2))))))))))
(TPredicate.member.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.member @ ((cPredicate.seq.Insert @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ V0)) @ ((cPredicate.eval @ V1) @ V2))))))))))
(TPredicate.member.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.member @ cPredicate.seq.Empty) @ V0)) @ cHOL.False))))
(TPredicate.of_pred_code,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.set_of_pred @ (cPredicate.Seq @ V0))) @ ((((cPredicate.seq.seq_case @ cOrderings.bot_class.bot) @ (^[V1]: (^[V2]: ((cSet.insert @ V1) @ (cPredicate.set_of_pred @ V2))))) @ (^[V1]: (^[V2]: ((cLattices.sup_class.sup @ (cPredicate.set_of_pred @ V1)) @ (cPredicate.set_of_seq @ V2))))) @ (V0 @ cProduct_Type.Unity))))))
(TPredicate.pred.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TPredicate.pred.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cPredicate.pred.Pred @ V2))) @ V1)))) @ V1))))))
(TPredicate.pred.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cPredicate.pred.Pred @ V2))))) @ (V0 @ V1)))))))
(TPredicate.seq.Join_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPredicate.seq.Join @ V0) @ V1)) @ (cPredicate.Abs_seq @ (cDatatype.In1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V0))) @ (cPredicate.Rep_seq @ V1)))))))))))
(TPredicate.seq.distinct_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Join @ V0) @ V1)) @ ((cPredicate.seq.Insert @ V2) @ V3))))))))))))
(TPredicate.seq.distinct_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Insert @ V0) @ V1)) @ ((cPredicate.seq.Join @ V2) @ V3))))))))))))
(TPredicate.seq.distinct_4,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Join @ V0) @ V1)) @ cPredicate.seq.Empty)))))))
(TPredicate.seq.distinct_3,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cPredicate.seq.Empty) @ ((cPredicate.seq.Join @ V0) @ V1))))))))
(TPredicate.seq.distinct_2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cPredicate.seq.Insert @ V0) @ V1)) @ cPredicate.seq.Empty)))))))
(TPredicate.seq.distinct_1,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ V0) @ V1))))))))
(TPredicate.seq.eq.simps_9,((c== @ ((cHOL.equal_class.equal @ cPredicate.seq.Empty) @ cPredicate.seq.Empty)) @ cHOL.True))
(TPredicate.seq.eq.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cPredicate.seq.Insert @ V0) @ V1)) @ ((cPredicate.seq.Insert @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TPredicate.seq.eq.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cPredicate.seq.Join @ V0) @ V1)) @ ((cPredicate.seq.Join @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TPredicate.seq.eq.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ V0) @ V1))) @ cHOL.False))))))
(TPredicate.seq.eq.simps_5,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ ((cPredicate.seq.Insert @ V0) @ V1)) @ cPredicate.seq.Empty)) @ cHOL.False))))))
(TPredicate.seq.eq.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ cPredicate.seq.Empty) @ ((cPredicate.seq.Join @ V0) @ V1))) @ cHOL.False))))))
(TPredicate.seq.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ ((cPredicate.seq.Join @ V0) @ V1)) @ cPredicate.seq.Empty)) @ cHOL.False))))))
(TPredicate.seq.eq.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cPredicate.seq.Insert @ V0) @ V1)) @ ((cPredicate.seq.Join @ V2) @ V3))) @ cHOL.False))))))))))
(TPredicate.seq.eq.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cPredicate.seq.Join @ V0) @ V1)) @ ((cPredicate.seq.Insert @ V2) @ V3))) @ cHOL.False))))))))))
(TPredicate.seq.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cPredicate.seq.Empty)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cPredicate.seq.Insert @ V1) @ V2))))))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cPredicate.seq.Join @ V1) @ V2)))))))))))
(TPredicate.singleI_unit,(call @ (^[V0]: ((cPredicate.eval @ (cPredicate.single @ cProduct_Type.Unity)) @ V0))))
(TPredicate.sup_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (cPredicate.pred.Pred @ ((cLattices.sup_class.sup @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1)))))))))
(TPredicate.the_only_def,((c== @ cPredicate.the_only) @ (^[V0]: (^[V1]: (((((cPredicate.seq.seq_rec @ (^[V2]: (V2 @ cProduct_Type.Unity))) @ (^[V2]: (^[V3]: (^[V4]: (((cHOL.If @ (cPredicate.is_empty @ V3)) @ V2) @ ((cHOL.Let @ ((cPredicate.singleton @ V4) @ V3)) @ (^[V5]: (((cHOL.If @ ((cHOL.eq @ V2) @ V5)) @ V2) @ (V4 @ cProduct_Type.Unity))))))))) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ (cPredicate.is_empty @ V2)) @ (V4 @ V5)) @ (((cHOL.If @ (cPredicate.null @ V3)) @ ((cPredicate.singleton @ V5) @ V2)) @ ((cHOL.Let @ ((cPredicate.singleton @ V5) @ V2)) @ (^[V6]: ((cHOL.Let @ (V4 @ V5)) @ (^[V7]: (((cHOL.If @ ((cHOL.eq @ V6) @ V7)) @ V6) @ (V5 @ cProduct_Type.Unity))))))))))))) @ V1) @ V0)))))
(TPredicate.top_pred_def,((cHOL.eq @ cOrderings.top_class.top) @ (cPredicate.pred.Pred @ cOrderings.top_class.top)))
(TPresburger.imp_le_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ V2)) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ V3)))))))))))))
(TProduct_Type.Sigma_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cProduct_Type.Sigma @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cComplete_Lattices.complete_lattice_class.SUPR @ (V1 @ V2)) @ (^[V3]: ((cSet.insert @ ((cProduct_Type.Pair @ V2) @ V3)) @ cOrderings.bot_class.bot)))))))))))
(TProduct_Type.The_split,(call @ (^[V0]: ((cHOL.eq @ (cHOL.The @ (cProduct_Type.prod.prod_case @ V0))) @ (cHOL.The @ (^[V1]: ((V0 @ (cProduct_Type.fst @ V1)) @ (cProduct_Type.snd @ V1))))))))
(TProduct_Type.UNIV_unit,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cProduct_Type.Unity) @ cOrderings.bot_class.bot)))
(TProduct_Type.Unity_def,((cHOL.eq @ cProduct_Type.Unity) @ (cProduct_Type.Abs_unit @ cHOL.True)))
(TProduct_Type.apfst_def,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.apfst @ V0)) @ ((cProduct_Type.map_pair @ V0) @ cFun.id)))))
(TProduct_Type.apsnd_def,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.apsnd @ V0)) @ ((cProduct_Type.map_pair @ cFun.id) @ V0)))))
(TProduct_Type.bool.recs_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_rec @ V0) @ V1) @ cHOL.False)) @ V1))))))
(TProduct_Type.bool.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_rec @ V0) @ V1) @ cHOL.True)) @ V0))))))
(TProduct_Type.curry_def,((cHOL.eq @ cProduct_Type.curry) @ (^[V0]: (^[V1]: (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2)))))))
(TProduct_Type.fst_apfst,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cProduct_Type.apfst @ V0) @ V1))) @ (V0 @ (cProduct_Type.fst @ V1))))))))
(TProduct_Type.fst_apsnd,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cProduct_Type.apsnd @ V0) @ V1))) @ (cProduct_Type.fst @ V1)))))))
(TProduct_Type.prod.recs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_rec @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.prod.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cProduct_Type.Pair @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TProduct_Type.prod.size_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cProduct_Type.prod.prod_size @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (V1 @ V3))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))))
(TProduct_Type.scomp_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.scomp @ V0) @ V1)) @ (^[V2]: ((cProduct_Type.prod.prod_case @ V1) @ (V0 @ V2)))))))))
(TProduct_Type.snd_apfst,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cProduct_Type.apfst @ V0) @ V1))) @ (cProduct_Type.snd @ V1)))))))
(TProduct_Type.snd_apsnd,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cProduct_Type.apsnd @ V0) @ V1))) @ (V0 @ (cProduct_Type.snd @ V1))))))))
(TProduct_Type.split_def,((cHOL.eq @ cProduct_Type.prod.prod_case) @ (^[V0]: (^[V1]: ((V0 @ (cProduct_Type.fst @ V1)) @ (cProduct_Type.snd @ V1))))))
(TProduct_Type.split_eta,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2)))))) @ V0))))
(TProduct_Type.surj_pair,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))))))))
(TProduct_Type.unit.recs,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.unit.unit_rec @ V0) @ cProduct_Type.Unity)) @ V0))))
(TProduct_Type.unit.size_2,((cHOL.eq @ (cProduct_Type.unit.size_unit_inst.size_unit @ cProduct_Type.Unity)) @ cNat.zero_nat_inst.zero_nat))
(TProduct_Type.unit.size_1,((cHOL.eq @ (cProduct_Type.unit.unit_size @ cProduct_Type.Unity)) @ cNat.zero_nat_inst.zero_nat))
(TPure.distinct_prems_rl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ V0) @ ((c==> @ V0) @ V1))) @ ((c==> @ V0) @ V1)))))))
(TQuotient.OOO_quotient3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((V6 @ V7) @ V8)) @ ((c==> @ ((V0 @ V7) @ V7)) @ ((c==> @ ((V0 @ V8) @ V8)) @ ((V3 @ (V1 @ V7)) @ (V1 @ V8)))))))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((V3 @ V7) @ V8)) @ ((V6 @ (V2 @ V7)) @ (V2 @ V8)))))))) @ (((cQuotient.Quotient3 @ ((cRelation.relcompp @ V0) @ ((cRelation.relcompp @ V6) @ V0))) @ ((cFun.comp @ V4) @ V1)) @ ((cFun.comp @ V2) @ V5)))))))))))))))))))))
(TQuotient.Quot_True_def,(call @ (^[V0]: ((cHOL.eq @ (cQuotient.Quot_True @ V0)) @ cHOL.True))))
(TQuotient.Quotient3_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.eq @ (V1 @ (V2 @ V3))) @ V3)))) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((V0 @ (V2 @ V3)) @ (V2 @ V3))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V0 @ V3) @ V4)) @ ((cHOL.conj @ ((V0 @ V3) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V4)))))))))))))))))))
(TQuotient.Quotient3_rel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cHOL.conj @ ((V0 @ V3) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V4))))) @ ((V0 @ V3) @ V4))))))))))))))
(TQuotient.apply_rspQ3'',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((((cTransfer.fun_rel @ V0) @ V3) @ V4) @ V4)) @ ((V3 @ (V4 @ (V2 @ V5))) @ (V4 @ (V2 @ V5))))))))))))))))))
(TQuotient.ball_all_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.implies @ ((cSet.Ball @ V0) @ (^[V4]: ((V1 @ V4) @ V3)))) @ (cHOL.All @ (^[V4]: ((V2 @ V4) @ V3))))))) @ ((cHOL.implies @ ((cSet.Ball @ V0) @ (^[V3]: (cHOL.All @ (^[V4]: ((V1 @ V3) @ V4)))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((V2 @ V3) @ V4))))))))))))))
(TQuotient.ball_reg_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((c==> @ (call @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cHOL.implies @ ((cSet.Ball @ (cLifting.Respects @ V0)) @ V1)) @ (cHOL.All @ V2)))))))))))
(TQuotient.bex1_rel_aux2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V4)))))))) @ ((c==> @ ((cQuotient.Bex1_rel @ V0) @ V2)) @ ((cQuotient.Bex1_rel @ V0) @ V1))))))))))
(TQuotient.bex_reg_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((c==> @ (call @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cHOL.implies @ (cHOL.Ex @ V1)) @ ((cSet.Bex @ (cLifting.Respects @ V0)) @ V2)))))))))))
(TQuotient.fun_quotient3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ V3) @ V4) @ V5)) @ (((cQuotient.Quotient3 @ ((cTransfer.fun_rel @ V0) @ V3)) @ ((cFun.map_fun @ V2) @ V4)) @ ((cFun.map_fun @ V1) @ V5)))))))))))))))))
(TQuotient.quot_type_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.conj @ (cEquiv_Relations.part_equivp @ V0)) @ (cHOL.All @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V2 @ V3)) @ (cSet.Collect @ (V0 @ V4)))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.eq @ (V1 @ (V2 @ V3))) @ V3)))) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ V3) @ (cSet.Collect @ (V0 @ V4))))))) @ ((cHOL.eq @ (V2 @ (V1 @ V3))) @ V3))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((cHOL.eq @ (V2 @ V3)) @ (V2 @ V4))) @ ((cHOL.eq @ V3) @ V4)))))))))))))))))
(TRandom.iterate.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cRandom.iterate_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cRandom.iterate_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ (((V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5) @ V7))))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TRandom.iterate_rel_def,((c== @ cRandom.iterate_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))))))
(TRandom.log.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ V1)))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cCode_Numeral.div_natural_inst.div_natural @ V2) @ V1))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cRandom.log_rel) @ V1))))))))
(TRandom.log_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.log_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)))) @ ((cRandom.log_graph @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))) @ V2)))))))))) @ V2)))))))))
(TRandom.log_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom.log_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3)))) @ ((cRandom.log_graph @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3)))))))))))))))))))
(TRandom.log_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.log_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3)))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.div_natural_inst.div_natural @ V4) @ V3))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom.minus_shift_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRandom.minus_shift @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V2)) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V0) @ V1)) @ V2)) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ V2))))))))))
(TRandom_Pred.Random_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Pred.Random @ V0)) @ ((cProduct_Type.scomp @ V0) @ ((cFun.comp @ cProduct_Type.Pair) @ ((cFun.comp @ cPredicate.single) @ cProduct_Type.fst)))))))
(TRandom_Pred.single_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Pred.single @ V0)) @ (cProduct_Type.Pair @ (cPredicate.single @ V0))))))
(TRecord.tuple_iso_tuple,(cRecord.isomorphic_tuple @ cRecord.tuple_iso_tuple))
(TRelation.Domain.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Domain @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ (V2 @ V3))))))) @ (V2 @ V0))))))))))
(TRelation.Domain.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ V0) @ (cRelation.Domain @ V2))))))))))
(TRelation.Domain_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cRelation.Domain @ ((cSet.insert @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2))) @ ((cSet.insert @ V0) @ (cRelation.Domain @ V2))))))))))
(TRelation.Domain_unfold,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ V0)) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)))))))))
(TRelation.Domainp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Domainp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ V3)) @ ((c==> @ ((V0 @ V3) @ V4)) @ V2))))))) @ V2)))))))))
(TRelation.Domainp.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Domainp @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ ((V0 @ V2) @ V3))))))))))))
(TRelation.Range.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Range @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ (V2 @ V4))))))) @ (V2 @ V0))))))))))
(TRelation.Rangep.RangeI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cRelation.Rangep @ V0) @ V2)))))))))
(TRelation.Rangep.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Rangep @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ (V2 @ V4))))))) @ (V2 @ V1))))))))))
(TRelation.Rangep.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cRelation.Rangep @ V0) @ V2)))))))))
(TRelation.antisym_Id_on,(call @ (^[V0]: (cRelation.antisym @ (cRelation.Id_on @ V0)))))
(TRelation.antisym_empty,(cRelation.antisym @ cOrderings.bot_class.bot))
(TRelation.bot_empty_eq2,((cHOL.eq @ cOrderings.bot_class.bot) @ (^[V0]: (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ cOrderings.bot_class.bot)))))
(TRelation.converse_UNIV,((cHOL.eq @ (cRelation.converse @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(TRelation.converse_join,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.conversep @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cRelation.conversep @ V0)) @ (cRelation.conversep @ V1))))))))
(TRelation.converse_meet,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.conversep @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cRelation.conversep @ V0)) @ (cRelation.conversep @ V1))))))))
(TRelation.converse_mono,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cRelation.converse @ V0)) @ (cRelation.converse @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TRelation.conversep_def,((c== @ cRelation.conversep) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V4)) @ ((V0 @ V4) @ V5))))))))))))))
(TRelation.conversep_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRelation.conversep @ V0) @ V1) @ V2)) @ ((V0 @ V2) @ V1)))))))))
(TRelation.finite_Domain,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ (cRelation.Domain @ V0))))))
(TRelation.fst_eq_Domain,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cProduct_Type.fst) @ V0)) @ (cRelation.Domain @ V0)))))
(TRelation.in_inv_imagep,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cRelation.inv_imagep @ V0) @ V1) @ V2) @ V3)) @ ((V0 @ (V1 @ V2)) @ (V1 @ V3))))))))))))
(TRelation.inv_image_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.inv_image @ V0) @ V1)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ (V1 @ V2)) @ (V1 @ V3))) @ V0)))))))))))
(TRelation.refl_on_INTER,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cRelation.refl_on @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cRelation.refl_on @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V2))))))))))
(TRelation.refl_on_Id_on,(call @ (^[V0]: ((cRelation.refl_on @ V0) @ (cRelation.Id_on @ V0)))))
(TRelation.refl_on_UNION,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cRelation.refl_on @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cRelation.refl_on @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V2))))))))))
(TRelation.refl_on_empty,((cRelation.refl_on @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot))
(TRelation.reflp_refl_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.reflp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ ((cRelation.refl_on @ cOrderings.top_class.top) @ V0)))))
(TRelation.relcomp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cRelation.relcomp @ V2) @ V3))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V7)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ V3)) @ V4))))))))))) @ V4)))))))))))))
(TRelation.relcomp.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cRelation.relcomp @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V6)) @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V3))))))))))))))))))))
(TRelation.relcompp_bot1,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcompp @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TRelation.relcompp_bot2,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcompp @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TRelation.relcompp_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcompp @ V0) @ V2)) @ ((cRelation.relcompp @ V1) @ V3)))))))))))))
(TRelation.sym_inv_image,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.sym @ V0)) @ (cRelation.sym @ ((cRelation.inv_image @ V0) @ V1))))))))
(TRelation.top_empty_eq2,((cHOL.eq @ cOrderings.top_class.top) @ (^[V0]: (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ cOrderings.top_class.top)))))
(TRelation.trans_diff_Id,(call @ (^[V0]: ((c==> @ (cRelation.trans @ V0)) @ ((c==> @ (cRelation.antisym @ V0)) @ (cRelation.trans @ ((cGroups.minus_class.minus @ V0) @ cRelation.Id)))))))
(TRings.class.idom.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cRings.class.no_zero_divisors @ V0) @ V3)) @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TRings.class.ring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cRings.class.semiring @ V0) @ V4)) @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TRings.class.ring_1_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.conj @ (((((cRings.class.ring @ V2) @ V3) @ V4) @ V5) @ V1)) @ ((cRings.class.zero_neq_one @ V0) @ V3)))))))))))))))))
(TRings.idom_class.intro,((c==> @ (cRings.comm_ring_1_class @ cTYPE)) @ ((c==> @ (cRings.no_zero_divisors_class @ cTYPE)) @ (cRings.idom_class @ cTYPE))))
(TRings.idom_class.super_2,((c==> @ (cRings.idom_class @ cTYPE)) @ (cRings.no_zero_divisors_class @ cTYPE)))
(TRings.idom_class.super_1,((c==> @ (cRings.idom_class @ cTYPE)) @ (cRings.comm_ring_1_class @ cTYPE)))
(TRings.mult_sign_intros_8,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.mult_sign_intros_7,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.mult_sign_intros_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.mult_sign_intros_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.mult_sign_intros_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.mult_sign_intros_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.mult_sign_intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.mult_sign_intros_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.ring.eq_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ ((V4 @ V5) @ V6)) @ V7)) @ ((V0 @ ((V4 @ V8) @ V6)) @ V9))) @ ((cHOL.eq @ ((V0 @ ((V4 @ ((V2 @ V5) @ V8)) @ V6)) @ V7)) @ V9))))))))))))))))))))))))
(TRings.ring.eq_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ ((V4 @ V5) @ V6)) @ V7)) @ ((V0 @ ((V4 @ V8) @ V6)) @ V9))) @ ((cHOL.eq @ V7) @ ((V0 @ ((V4 @ ((V2 @ V8) @ V5)) @ V6)) @ V9)))))))))))))))))))))))))
(TRings.ring_1_class_def,((c== @ (cRings.ring_1_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.monoid_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.ring_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))))
(TRings.ring_class.intro,((c==> @ (cGroups.ab_group_add_class @ cTYPE)) @ ((c==> @ (cRings.semiring_class @ cTYPE)) @ (cRings.ring_class @ cTYPE))))
(TRings.ring_class.super_2,((c==> @ (cRings.ring_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))
(TRings.ring_class.super_1,((c==> @ (cRings.ring_class @ cTYPE)) @ (cGroups.ab_group_add_class @ cTYPE)))
(TSMT.arity_type_pattern,(cHOL.type_class @ cTYPE))
(TSMT.random_pattern_def,(call @ (^[V0]: ((cHOL.eq @ (cSMT.random_pattern_inst.random_pattern @ V0)) @ ((cSMT.random_aux_pattern @ V0) @ V0)))))
(TSet.Compl_eq_Compl_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet.Compl_eq_Diff_UNIV,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ ((cGroups.minus_class.minus @ cOrderings.top_class.top) @ V0)))))
(TSet.Diff_insert_absorb,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cSet.insert @ V0) @ V1)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V1)))))))
(TSet.diff_single_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.insert @ V1) @ V2))))))))))
(TSet.insert_Diff_single,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.insert @ V0) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))) @ ((cSet.insert @ V0) @ V1)))))))
(TSet.mk_disjoint_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cSet.insert @ V0) @ V2))) @ (cHOL.Not @ ((cSet.member @ V0) @ V2)))))))))))
(TSet.psubset_imp_ex_mem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cSet.member @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))))))))))
(TSet.psubset_imp_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet.psubset_insert_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cSet.insert @ V1) @ V2))) @ (((cHOL.If @ ((cSet.member @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2)))))))))))
(TSet_Interval.atLeast_0,((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ cNat.zero_nat_inst.zero_nat)) @ cOrderings.top_class.top))
(TSet_Interval.card_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (cHOL.Not @ ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.Suc @ V1))))))) @ cNat.zero_nat_inst.zero_nat))))))))
(TSet_Interval.gauss_sum,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V1]: (cNat.semiring_1_class.of_nat @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ cNat.one_nat_inst.one_nat) @ V0)))) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ V0)) @ ((cGroups.plus_class.plus @ (cNat.semiring_1_class.of_nat @ V0)) @ cGroups.one_class.one))))))
(TString.Code.abort_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cString.Code.abort @ V0) @ V2)) @ ((cString.Code.abort @ V1) @ V2))))))))))
(TString.arity_enum_char,(cEnum.enum_class @ cTYPE))
(TString.arity_type_char,(cHOL.type_class @ cTYPE))
(TString.char_of_nat_def,(call @ (^[V0]: ((cHOL.eq @ (cString.char_of_nat @ V0)) @ ((cList.nth @ cString.enum_char_inst.enum_char) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))
(TString.enum_nibble_def,((cHOL.eq @ cString.enum_nibble_inst.enum_nibble) @ ((cList.list.Cons @ cString.nibble.Nibble0) @ ((cList.list.Cons @ cString.nibble.Nibble1) @ ((cList.list.Cons @ cString.nibble.Nibble2) @ ((cList.list.Cons @ cString.nibble.Nibble3) @ ((cList.list.Cons @ cString.nibble.Nibble4) @ ((cList.list.Cons @ cString.nibble.Nibble5) @ ((cList.list.Cons @ cString.nibble.Nibble6) @ ((cList.list.Cons @ cString.nibble.Nibble7) @ ((cList.list.Cons @ cString.nibble.Nibble8) @ ((cList.list.Cons @ cString.nibble.Nibble9) @ ((cList.list.Cons @ cString.nibble.NibbleA) @ ((cList.list.Cons @ cString.nibble.NibbleB) @ ((cList.list.Cons @ cString.nibble.NibbleC) @ ((cList.list.Cons @ cString.nibble.NibbleD) @ ((cList.list.Cons @ cString.nibble.NibbleE) @ ((cList.list.Cons @ cString.nibble.NibbleF) @ cList.list.Nil))))))))))))))))))
(TString.inj_nat_of_char,((cFun.inj_on @ cString.nat_of_char) @ cOrderings.top_class.top))
(TString.literal.explode,(call @ (^[V0]: ((cSet.member @ (cString.explode @ V0)) @ cOrderings.top_class.top))))
(TString.nat_of_char_def,(call @ (^[V0]: ((cHOL.eq @ (cString.nat_of_char @ V0)) @ ((cString.char.char_case @ (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ (cString.nat_of_nibble @ V1)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))) @ (cString.nat_of_nibble @ V2))))) @ V0)))))
(TString.nibble.distinct_240,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_239,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_238,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_237,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_236,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_235,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_234,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_233,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_232,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_231,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_230,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_229,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_228,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_227,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_226,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_225,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_224,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_223,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_222,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_221,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_220,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_219,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_218,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_217,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_216,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_215,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_214,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_213,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_212,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_211,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_210,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_209,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_208,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_207,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_206,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_205,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_204,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_203,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_202,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_201,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_200,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_199,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_198,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_197,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_196,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_195,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_194,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_193,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_192,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_191,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_190,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_189,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_188,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_187,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_186,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_185,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_184,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_183,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_182,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_181,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_180,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_179,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_178,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_177,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_176,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_175,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_174,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_173,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_172,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_171,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_170,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_169,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_168,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_167,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_166,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_165,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_164,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_163,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_162,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_161,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_160,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_159,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_158,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_157,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_156,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_155,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_154,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_153,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_152,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_151,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_150,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_149,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_148,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_147,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_146,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_145,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_144,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_143,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_142,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_141,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_140,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_139,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_138,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_137,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_136,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_135,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_134,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_133,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_132,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_131,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_130,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_129,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_128,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_127,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_126,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_125,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_124,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_123,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_122,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_121,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_120,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_119,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_118,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_117,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_116,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_115,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_114,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_113,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_112,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_111,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_110,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_109,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_108,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_107,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_106,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_105,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_104,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_103,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_102,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_101,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_100,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_99,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_98,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_97,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_96,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_95,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_94,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_93,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_92,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_91,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_90,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_89,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_88,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_87,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_86,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_85,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_84,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_83,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_82,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_81,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_80,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_79,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_78,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_77,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_76,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_75,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_74,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_73,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_72,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_71,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_70,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_69,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_68,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_67,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_66,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_65,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_64,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_63,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_62,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_61,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_60,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_59,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_58,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_57,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_56,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_55,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_54,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_53,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_52,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_51,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_50,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_49,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_48,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_47,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_46,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_45,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_44,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_43,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_42,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_41,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_40,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_39,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_38,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_37,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_36,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_35,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_34,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_33,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_32,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble1)))
(TString.nibble.distinct_31,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_30,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleF) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_29,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleF)))
(TString.nibble.distinct_28,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleE) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_27,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleE)))
(TString.nibble.distinct_26,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleD) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_25,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleD)))
(TString.nibble.distinct_24,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleC) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_23,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleC)))
(TString.nibble.distinct_22,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleB) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_21,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleB)))
(TString.nibble.distinct_20,(cHOL.Not @ ((cHOL.eq @ cString.nibble.NibbleA) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_19,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.NibbleA)))
(TString.nibble.distinct_18,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble9) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_17,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble9)))
(TString.nibble.distinct_16,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble8) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_15,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble8)))
(TString.nibble.distinct_14,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_13,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble7)))
(TString.nibble.distinct_12,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble6) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_11,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble6)))
(TString.nibble.distinct_10,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_9,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble5)))
(TString.nibble.distinct_8,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble4) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_7,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble4)))
(TString.nibble.distinct_6,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_5,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble3)))
(TString.nibble.distinct_4,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble2) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_3,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble2)))
(TString.nibble.distinct_2,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble1) @ cString.nibble.Nibble0)))
(TString.nibble.distinct_1,(cHOL.Not @ ((cHOL.eq @ cString.nibble.Nibble0) @ cString.nibble.Nibble1)))
(TString.nibble.eq.simps_256,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble0)) @ cHOL.True))
(TString.nibble.eq.simps_255,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble1)) @ cHOL.True))
(TString.nibble.eq.simps_254,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble2)) @ cHOL.True))
(TString.nibble.eq.simps_253,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cHOL.True))
(TString.nibble.eq.simps_252,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ cHOL.True))
(TString.nibble.eq.simps_251,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ cHOL.True))
(TString.nibble.eq.simps_250,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ cHOL.True))
(TString.nibble.eq.simps_249,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ cHOL.True))
(TString.nibble.eq.simps_248,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble8)) @ cHOL.True))
(TString.nibble.eq.simps_247,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble9)) @ cHOL.True))
(TString.nibble.eq.simps_246,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.NibbleA)) @ cHOL.True))
(TString.nibble.eq.simps_245,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.NibbleB)) @ cHOL.True))
(TString.nibble.eq.simps_244,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.NibbleC)) @ cHOL.True))
(TString.nibble.eq.simps_243,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.NibbleD)) @ cHOL.True))
(TString.nibble.eq.simps_242,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.NibbleE)) @ cHOL.True))
(TString.nibble.eq.simps_241,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.NibbleF)) @ cHOL.True))
(TString.nibble.eq.simps_240,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_239,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_238,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_237,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_236,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_235,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_234,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_233,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_232,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_231,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_230,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_229,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_228,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_227,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_226,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_225,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_224,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_223,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_222,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_221,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_220,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_219,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_218,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_217,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_216,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_215,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_214,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_213,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_212,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble0) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_211,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble0)) @ cHOL.False))
(TString.nibble.eq.simps_210,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_209,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_208,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_207,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_206,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_205,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_204,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_203,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_202,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_201,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_200,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_199,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_198,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_197,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_196,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_195,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_194,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_193,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_192,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_191,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_190,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_189,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_188,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_187,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_186,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_185,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_184,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble1) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_183,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble1)) @ cHOL.False))
(TString.nibble.eq.simps_182,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_181,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_180,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_179,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_178,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_177,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_176,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_175,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_174,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_173,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_172,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_171,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_170,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_169,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_168,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_167,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_166,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_165,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_164,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_163,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_162,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_161,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_160,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_159,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_158,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble2) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_157,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble2)) @ cHOL.False))
(TString.nibble.eq.simps_156,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_155,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_154,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_153,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_152,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_151,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_150,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_149,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_148,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_147,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_146,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_145,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_144,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_143,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_142,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_141,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_140,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_139,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_138,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_137,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_136,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_135,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_134,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble3) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_133,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble3)) @ cHOL.False))
(TString.nibble.eq.simps_132,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_131,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_130,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_129,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_128,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_127,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_126,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_125,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_124,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_123,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_122,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_121,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_120,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_119,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_118,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_117,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_116,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_115,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_114,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_113,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_112,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_111,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble4)) @ cHOL.False))
(TString.nibble.eq.simps_110,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_109,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_108,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_107,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_106,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_105,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_104,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_103,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_102,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_101,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_100,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_99,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_98,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_97,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_96,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_95,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_94,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_93,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_92,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_91,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble5)) @ cHOL.False))
(TString.nibble.eq.simps_90,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_89,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_88,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_87,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_86,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_85,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_84,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_83,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_82,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_81,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_80,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_79,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_78,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_77,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_76,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_75,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_74,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_73,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble6)) @ cHOL.False))
(TString.nibble.eq.simps_72,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_71,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_70,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_69,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_68,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_67,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_66,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_65,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_64,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_63,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_62,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_61,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_60,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_59,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_58,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble7) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_57,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble7)) @ cHOL.False))
(TString.nibble.eq.simps_56,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_55,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_54,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_53,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_52,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_51,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_50,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_49,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_48,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_47,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_46,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_45,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_44,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble8) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_43,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble8)) @ cHOL.False))
(TString.nibble.eq.simps_42,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_41,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_40,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_39,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_38,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_37,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_36,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_35,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_34,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_33,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_32,((c== @ ((cHOL.equal_class.equal @ cString.nibble.Nibble9) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_31,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.Nibble9)) @ cHOL.False))
(TString.nibble.eq.simps_30,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_29,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_28,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_27,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_26,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_25,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_24,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_23,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_22,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleA) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_21,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.NibbleA)) @ cHOL.False))
(TString.nibble.eq.simps_20,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_19,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_18,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_17,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_16,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_15,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_14,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleB) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_13,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.NibbleB)) @ cHOL.False))
(TString.nibble.eq.simps_12,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_11,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_10,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_9,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_8,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleC) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_7,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.NibbleC)) @ cHOL.False))
(TString.nibble.eq.simps_6,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.eq.simps_5,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleD) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.NibbleD)) @ cHOL.False))
(TString.nibble.eq.simps_2,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleE) @ cString.nibble.NibbleF)) @ cHOL.False))
(TString.nibble.eq.simps_1,((c== @ ((cHOL.equal_class.equal @ cString.nibble.NibbleF) @ cString.nibble.NibbleE)) @ cHOL.False))
(TString.nibble.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble0)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble2)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble3)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble4)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble5)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble6)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble7)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble8)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.Nibble9)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.NibbleA)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.NibbleB)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.NibbleC)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.NibbleD)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cString.nibble.NibbleE)) @ ((cHOL.eq @ V0) @ cString.nibble.NibbleF)))))))))))))))))))
(TSum_Type.equal_sum_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.split_sum_all,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ ((cHOL.conj @ (cHOL.All @ (^[V1]: (V0 @ (cSum_Type.Inl @ V1))))) @ (cHOL.All @ (^[V1]: (V0 @ (cSum_Type.Inr @ V1)))))))))
(TSum_Type.sum.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ (cSum_Type.Inl @ V6))) @ ((cHOL.eq @ (V2 @ V6)) @ (V3 @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ (cSum_Type.Inr @ V6))) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ (((cSum_Type.sum.sum_case @ V2) @ V4) @ V0)) @ (((cSum_Type.sum.sum_case @ V3) @ V5) @ V1))))))))))))))))))
(TSum_Type.sum.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cSum_Type.sum.sum_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cSum_Type.Inl @ V4))) @ (cHOL.Not @ (V0 @ (V1 @ V4))))))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cSum_Type.Inr @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TSum_Type.sum_map.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum_map @ V0) @ V1) @ (cSum_Type.Inr @ V2))) @ (cSum_Type.Inr @ (V1 @ V2))))))))))
(TSum_Type.sum_map.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSum_Type.sum_map @ V0) @ V1) @ (cSum_Type.Inl @ V2))) @ (cSum_Type.Inl @ (V0 @ V2))))))))))
(TTransfer.bi_unique_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_unique @ V0)) @ ((cHOL.conj @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V1) @ V2)) @ ((cHOL.implies @ ((V0 @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V1) @ V3)) @ ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V1) @ V2))))))))))))))
(TTransfer.bi_unique_fun,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((c==> @ (cTransfer.bi_unique @ V1)) @ (cTransfer.bi_unique @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TTransfer.comp_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V2) @ V0)) @ ((cTransfer.fun_rel @ V2) @ V1))) @ cFun.comp) @ cFun.comp))))))))
(TTransfer.mono_transfer,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((c==> @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq)) @ ((c==> @ ((((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq)) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ cHOL.eq) @ cOrderings.order_class.mono) @ cOrderings.order_class.mono)))))))))
(TTransfer.right_uniqueD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TTransfer.right_uniqueI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))) @ (cTransfer.right_unique @ V0)))))
(TTyperep.typerep.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V0 @ V5)) @ (V1 @ ((cTyperep.typerep.Typerep @ V4) @ V5)))))))) @ ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V1 @ V4)) @ ((c==> @ (V0 @ V5)) @ (V0 @ ((cList.list.Cons @ V4) @ V5))))))))) @ ((cHOL.conj @ (V1 @ V2)) @ (V0 @ V3))))))))))))))
(TTyperep.typerep.inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cTyperep.typerep.Typerep @ V0) @ V1)) @ ((cTyperep.typerep.Typerep @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TTyperep.typerep.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cTyperep.typerep.typerep_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cTyperep.typerep.Typerep @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TTyperep.typerep.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cTyperep.typerep.typerep_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cTyperep.typerep.Typerep @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TWellfounded.acc.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1)) @ ((cSet.member @ V4) @ (cWellfounded.acc @ V1)))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V0))))))))))
(TWellfounded.acc.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ V1)) @ ((cSet.member @ V2) @ (cWellfounded.acc @ V1)))))) @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))))))))
(TWellfounded.acc_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cWellfounded.acc @ V1))) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V0))))))))))
(TWellfounded.acc_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cWellfounded.acc @ V1)) @ (cWellfounded.acc @ V0))))))))
(TWellfounded.accp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ ((cWellfounded.accp @ V0) @ V4))))) @ V2))))) @ V2)))))))))
(TWellfounded.accp.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cWellfounded.accp @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V3) @ V2)) @ ((cWellfounded.accp @ V0) @ V3)))))))))))))
(TWellfounded.in_measure,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.measure @ V2))) @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V0)) @ (V2 @ V1))))))))))
(TWellfounded.max_ext_wf,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ (cWellfounded.max_ext @ V0))))))
(TWellfounded.min_ext_wf,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ (cWellfounded.min_ext @ V0))))))
(TWellfounded.wfP_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cWellfounded.wfP @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))))))
(TWellfounded.wfP_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wfP @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ (cWellfounded.wfP @ V1))))))))
(TWellfounded.wfP_trancl,(call @ (^[V0]: ((c==> @ (cWellfounded.wfP @ V0)) @ (cWellfounded.wfP @ (cTransitive_Closure.tranclp @ V0))))))
(TWellfounded.wf_acc_iff,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wf @ V0)) @ (cHOL.All @ (^[V1]: ((cSet.member @ V1) @ (cWellfounded.acc @ V0))))))))
(TWellfounded.wf_acyclic,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cTransitive_Closure.acyclic @ V0)))))
(TWellfounded.wf_measure,(call @ (^[V0]: (cWellfounded.wf @ (cWellfounded.measure @ V0)))))
(TWellfounded.wf_not_sym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0)))))))))))
(TBig_Operators.setprod_1,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V1]: cGroups.one_class.one)) @ V0)) @ cGroups.one_class.one))))
(TBig_Operators.setsum_0',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ cGroups.zero_class.zero)))))))
(TBig_Operators.setsum_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))))))
(TCode_Evaluation.Abs_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cCode_Evaluation.Abs @ V0) @ V1) @ V2)) @ cCode_Evaluation.term.dummy_term))))))))
(TCode_Evaluation.App_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Evaluation.App @ V0) @ V1)) @ cCode_Evaluation.term.dummy_term))))))
(TCode_Numeral.Nat.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.Nat @ (cCode_Numeral.integer_of_int @ V0))) @ (cCode_Numeral.natural_of_nat @ (cInt.nat @ V0))))))
(TCode_Numeral.Nat.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ (cCode_Numeral.Nat @ V0))) @ (cInt.nat @ (cCode_Numeral.int_of_integer @ V0))))))
(TCode_Numeral.Suc.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.Suc @ (cCode_Numeral.natural_of_nat @ V0))) @ (cCode_Numeral.natural_of_nat @ (cNat.Suc @ V0))))))
(TCode_Numeral.Suc.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ (cCode_Numeral.Suc @ V0))) @ (cNat.Suc @ (cCode_Numeral.nat_of_natural @ V0))))))
(TCode_Numeral.dup.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.dup @ (cCode_Numeral.integer_of_int @ V0))) @ (cCode_Numeral.integer_of_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V0))))))
(TCode_Numeral.dup.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.dup @ V0))) @ ((cInt.plus_int_inst.plus_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V0))))))
(TCode_Numeral.fst_divmod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cCode_Numeral.divmod_integer @ V0) @ V1))) @ ((cCode_Numeral.div_integer_inst.div_integer @ V0) @ V1)))))))
(TCode_Numeral.snd_divmod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cCode_Numeral.divmod_integer @ V0) @ V1))) @ ((cCode_Numeral.div_integer_inst.mod_integer @ V0) @ V1)))))))
(TCode_Numeral.sub.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.sub @ V0) @ V1)) @ (cCode_Numeral.integer_of_int @ ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TCode_Numeral.sub.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cCode_Numeral.sub @ V0) @ V1))) @ ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TComplete_Lattices.INT_D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V2 @ V4))))) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cSet.member @ V0) @ (V2 @ V3)))))))))))))
(TComplete_Lattices.INT_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V5]: (V2 @ V5))))) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ (V2 @ V3))) @ V4)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V3) @ V1))) @ V4)) @ V4))))))))))))))
(TComplete_Lattices.INT_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ V1) @ (V2 @ V3)))))) @ ((cSet.member @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.UN_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TDatatype.Atom_not_Scons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (cDatatype.Atom @ V0)) @ ((cDatatype.Scons @ V1) @ V2))))))))))
(TDatatype.Leaf_not_Scons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (cDatatype.Leaf @ V0)) @ ((cDatatype.Scons @ V1) @ V2))))))))))
(TDatatype.Numb_not_Scons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (cDatatype.Numb @ V0)) @ ((cDatatype.Scons @ V1) @ V2))))))))))
(TDatatype.Scons_Scons_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cDatatype.Scons @ V0) @ V1)) @ ((cDatatype.Scons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TDatatype.Scons_not_Atom,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ ((cDatatype.Scons @ V0) @ V1)) @ (cDatatype.Atom @ V2))))))))))
(TDatatype.Scons_not_Leaf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ ((cDatatype.Scons @ V0) @ V1)) @ (cDatatype.Leaf @ V2))))))))))
(TDatatype.Scons_not_Numb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ ((cDatatype.Scons @ V0) @ V1)) @ (cDatatype.Numb @ V2))))))))))
(TDatatype.ntrunc_one_In0,(call @ (^[V0]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ (cDatatype.In0 @ V0))) @ cOrderings.bot_class.bot))))
(TDatatype.ntrunc_one_In1,(call @ (^[V0]: ((cHOL.eq @ ((cDatatype.ntrunc @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ (cDatatype.In1 @ V0))) @ cOrderings.bot_class.bot))))
(TDatatype.ntrunc_subsetD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cDatatype.ntrunc @ V2) @ V0)) @ V1)))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TDatatype.ntrunc_subsetI,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cDatatype.ntrunc @ V0) @ V1)) @ V1))))))
(TDivides.Suc_div_le_mono,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ ((cDivides.div_nat_inst.div_nat @ (cNat.Suc @ V0)) @ V1)))))))
(TDivides.div_class.intro,((c==> @ (cRings.dvd_class @ cTYPE)) @ (cDivides.div_class @ cTYPE)))
(TDivides.div_class.super,((c==> @ (cDivides.div_class @ cTYPE)) @ (cRings.dvd_class @ cTYPE)))
(TDivides.div_le_dividend,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ V0))))))
(TDivides.div_nat_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cInt.nat @ ((cDivides.div_int_inst.div_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TDivides.divmod_abs_code_6,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.divmod_abs @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)))))
(TDivides.divmod_abs_code_5,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.divmod_abs @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ (cInt.abs_int_inst.abs_int @ V0))))))
(TDivides.divmod_abs_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_abs @ (cInt.Pos @ V0)) @ (cInt.Neg @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TDivides.divmod_abs_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_abs @ (cInt.Neg @ V0)) @ (cInt.Pos @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TDivides.divmod_abs_code_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_abs @ (cInt.Neg @ V0)) @ (cInt.Neg @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TDivides.divmod_abs_code_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_abs @ (cInt.Pos @ V0)) @ (cInt.Pos @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TDivides.divmod_int_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_int @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cProduct_Type.apsnd @ (cInt.times_int_inst.times_int @ (cInt.sgn_int_inst.sgn_int @ V1))) @ (((cHOL.If @ ((cHOL.eq @ (cInt.sgn_int_inst.sgn_int @ V0)) @ (cInt.sgn_int_inst.sgn_int @ V1))) @ ((cDivides.divmod_abs @ V0) @ V1)) @ ((cHOL.Let @ ((cDivides.divmod_abs @ V0) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V2)) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ ((cInt.minus_int_inst.minus_int @ (cInt.uminus_int_inst.uminus_int @ V2)) @ cInt.one_int_inst.one_int)) @ ((cInt.minus_int_inst.minus_int @ (cInt.abs_int_inst.abs_int @ V1)) @ V3)))))))))))))))))
(TDivides.divmod_nat_base,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.divmod_nat @ V0) @ V1)) @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ V0))))))))
(TDivides.divmod_nat_step,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.divmod_nat @ V1) @ V0)) @ ((cProduct_Type.Pair @ (cNat.Suc @ ((cDivides.div_nat_inst.div_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V0))) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V0))))))))))
(TDivides.divmod_nat_zero,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.divmod_nat @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ V0)))))
(TDivides.mod_nat_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cInt.nat @ ((cDivides.div_int_inst.mod_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TDivides.mult_div_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ ((cDivides.div_nat_inst.div_nat @ V1) @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0))))))))
(TDivides.nat_div_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ (cInt.nat @ ((cDivides.div_int_inst.div_int @ V0) @ V1))) @ ((cDivides.div_nat_inst.div_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1)))))))))
(TDivides.nat_mod_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ (cInt.nat @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))) @ ((cDivides.div_nat_inst.mod_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))))))))))
(TDivides.negDivAlg.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TDivides.negDivAlg.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDivides.negDivAlg @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cDivides.adjust @ V5) @ ((cDivides.negDivAlg @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ V3)))))))) @ V3)))))))))))
(TDivides.negDivAlg.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.negDivAlg @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cDivides.adjust @ V1) @ ((cDivides.negDivAlg @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))))))))))
(TDivides.neg_zdiv_mult_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ ((cDivides.div_int_inst.div_int @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)) @ V0))))))))
(TDivides.neg_zmod_mult_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ ((cInt.minus_int_inst.minus_int @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cDivides.div_int_inst.mod_int @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)) @ V0))) @ cInt.one_int_inst.one_int))))))))
(TDivides.posDivAlg.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TDivides.posDivAlg.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDivides.posDivAlg @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cDivides.adjust @ V5) @ ((cDivides.posDivAlg @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ V3)))))))) @ V3)))))))))))
(TDivides.posDivAlg.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.posDivAlg @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cDivides.adjust @ V1) @ ((cDivides.posDivAlg @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))))))))))
(TDivides.pos_zdiv_mult_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ ((cDivides.div_int_inst.div_int @ V1) @ V0))))))))
(TDivides.pos_zmod_mult_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cDivides.div_int_inst.mod_int @ V1) @ V0))))))))))
(TDivides.split_div_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ V2)) @ ((cNat.ord_nat_inst.less_nat @ V2) @ ((cNat.times_nat_inst.times_nat @ V0) @ (cNat.Suc @ V1))))) @ ((cHOL.eq @ V1) @ ((cDivides.div_nat_inst.div_nat @ V2) @ V0)))))))))))
(TDivides.split_neg_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((V1 @ ((cDivides.div_int_inst.div_int @ V2) @ V0)) @ ((cDivides.div_int_inst.mod_int @ V2) @ V0))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V0) @ V4)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V2) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V3)) @ V4))))) @ ((V1 @ V3) @ V4)))))))))))))))
(TDivides.split_pos_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((V1 @ ((cDivides.div_int_inst.div_int @ V2) @ V0)) @ ((cDivides.div_int_inst.mod_int @ V2) @ V0))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V4) @ V0)) @ ((cHOL.eq @ V2) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V3)) @ V4))))) @ ((V1 @ V3) @ V4)))))))))))))))
(TDivides.unique_quotient,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.eq @ V2) @ V4))))))))))))))))
(TDivides.zdiff_zmod_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V2)) @ V1)) @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ V0) @ V2)) @ V1)))))))))
(TDivides.zmod_eq_dvd_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ ((cDivides.div_int_inst.mod_int @ V2) @ V1))) @ ((cRings.dvd_class.dvd @ V1) @ ((cInt.minus_int_inst.minus_int @ V0) @ V2))))))))))
(TEnum.enum.enum_all_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (V1 @ V3)) @ ((cSet.Ball @ cOrderings.top_class.top) @ V3))))))))))))
(TEnum.enum.enum_distinct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ (cList.distinct @ V0)))))))))
(TEnum.enum_class.enum_ex,((cHOL.eq @ cEnum.enum_class.enum_ex) @ cHOL.Ex))
(TEnum.enum_class.in_enum,(call @ (^[V0]: ((cSet.member @ V0) @ (cList.set @ cEnum.enum_class.enum)))))
(TEnum.enum_ex_option_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_ex @ V0)) @ ((cHOL.disj @ (V0 @ cOption.option.None)) @ (cEnum.enum_class.enum_ex @ (^[V1]: (V0 @ (cOption.option.Some @ V1)))))))))
(TEnum.equal_finite_1_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.equal_finite_2_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.equal_finite_3_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.equal_finite_4_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.equal_finite_5_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.finite_1.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_1.a\<__caret__sub>1)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cEnum.finite_1.finite_1_case @ V2) @ V0)) @ ((cEnum.finite_1.finite_1_case @ V3) @ V1)))))))))))))
(TEnum.finite_1.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cEnum.finite_1.finite_1_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cEnum.finite_1.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TEnum.finite_2.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_2.a\<__caret__sub>1)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_2.a\<__caret__sub>2)) @ ((cHOL.eq @ V4) @ V5))) @ ((cHOL.eq @ (((cEnum.finite_2.finite_2_case @ V2) @ V4) @ V0)) @ (((cEnum.finite_2.finite_2_case @ V3) @ V5) @ V1))))))))))))))))))
(TEnum.finite_2.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cEnum.finite_2.finite_2_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))))))))))))))
(TEnum.finite_3.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_3.a\<__caret__sub>1)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_3.a\<__caret__sub>2)) @ ((cHOL.eq @ V4) @ V5))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_3.a\<__caret__sub>3)) @ ((cHOL.eq @ V6) @ V7))) @ ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V2) @ V4) @ V6) @ V0)) @ ((((cEnum.finite_3.finite_3_case @ V3) @ V5) @ V7) @ V1)))))))))))))))))))))))
(TEnum.finite_3.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cEnum.finite_3.finite_3_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>3)) @ (cHOL.Not @ (V0 @ V3))))))))))))))))))
(TEnum.finite_4.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_4.a\<__caret__sub>1)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_4.a\<__caret__sub>2)) @ ((cHOL.eq @ V4) @ V5))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_4.a\<__caret__sub>3)) @ ((cHOL.eq @ V6) @ V7))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_4.a\<__caret__sub>4)) @ ((cHOL.eq @ V8) @ V9))) @ ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V2) @ V4) @ V6) @ V8) @ V0)) @ (((((cEnum.finite_4.finite_4_case @ V3) @ V5) @ V7) @ V9) @ V1))))))))))))))))))))))))))))
(TEnum.finite_4.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (V0 @ (((((cEnum.finite_4.finite_4_case @ V1) @ V2) @ V3) @ V4) @ V5))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>3)) @ (cHOL.Not @ (V0 @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>4)) @ (cHOL.Not @ (V0 @ V4)))))))))))))))))))))
(TEnum.finite_5.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_5.a\<__caret__sub>1)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_5.a\<__caret__sub>2)) @ ((cHOL.eq @ V4) @ V5))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_5.a\<__caret__sub>3)) @ ((cHOL.eq @ V6) @ V7))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_5.a\<__caret__sub>4)) @ ((cHOL.eq @ V8) @ V9))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_5.a\<__caret__sub>5)) @ ((cHOL.eq @ V10) @ V11))) @ ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V2) @ V4) @ V6) @ V8) @ V10) @ V0)) @ ((((((cEnum.finite_5.finite_5_case @ V3) @ V5) @ V7) @ V9) @ V11) @ V1)))))))))))))))))))))))))))))))))
(TEnum.finite_5.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (V0 @ ((((((cEnum.finite_5.finite_5_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>1)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>2)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>3)) @ (cHOL.Not @ (V0 @ V3)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>4)) @ (cHOL.Not @ (V0 @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>5)) @ (cHOL.Not @ (V0 @ V5))))))))))))))))))))))))
(TEquiv_Relations.equivpE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((c==> @ ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ (cRelation.transp @ V0)) @ V1)))) @ V1)))))))
(TEquiv_Relations.equivpI,(call @ (^[V0]: ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ (cRelation.transp @ V0)) @ (cEquiv_Relations.equivp @ V0)))))))
(TExtraction.exE_realizer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ (cProduct_Type.snd @ V1)) @ (cProduct_Type.fst @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V5) @ V4)) @ (V2 @ ((V3 @ V4) @ V5)))))))) @ (V2 @ ((cHOL.Let @ V1) @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((V3 @ V4) @ V5)))))))))))))))))
(TExtraction.exI_realizer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ (cProduct_Type.snd @ ((cProduct_Type.Pair @ V2) @ V1))) @ (cProduct_Type.fst @ ((cProduct_Type.Pair @ V2) @ V1)))))))))))
(TExtraction.sumbool.recs_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_rec @ V0) @ V1) @ cExtraction.sumbool.Right)) @ V1))))))
(TExtraction.sumbool.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_rec @ V0) @ V1) @ cExtraction.sumbool.Left)) @ V0))))))
(TExtraction.sumbool.size_4,((cHOL.eq @ (cExtraction.sumbool.size_sumbool_inst.size_sumbool @ cExtraction.sumbool.Right)) @ cNat.zero_nat_inst.zero_nat))
(TExtraction.sumbool.size_3,((cHOL.eq @ (cExtraction.sumbool.size_sumbool_inst.size_sumbool @ cExtraction.sumbool.Left)) @ cNat.zero_nat_inst.zero_nat))
(TExtraction.sumbool.size_2,((cHOL.eq @ (cExtraction.sumbool.sumbool_size @ cExtraction.sumbool.Right)) @ cNat.zero_nat_inst.zero_nat))
(TExtraction.sumbool.size_1,((cHOL.eq @ (cExtraction.sumbool.sumbool_size @ cExtraction.sumbool.Left)) @ cNat.zero_nat_inst.zero_nat))
(TFields.field.frac_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V10) @ V8)) @ ((V1 @ V11) @ V9))) @ ((cHOL.eq @ ((V2 @ V10) @ V9)) @ ((V2 @ V11) @ V8)))))))))))))))))))))))))))))))
(TFinite_Set.card.eq_fold,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (((cFinite_Set.fold @ (^[V1]: cNat.Suc)) @ cNat.zero_nat_inst.zero_nat) @ V0)))))
(TFinite_Set.card_eq_SucD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cNat.Suc @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cSet.insert @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ (cFinite_Set.card @ V3)) @ V1)) @ ((cHOL.implies @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot)))))))))))))))
(TFinite_Set.card_psubset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V0))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))))
(TFinite_Set.finite.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ V1)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cSet.insert @ V3) @ V2))) @ ((c==> @ (cFinite_Set.finite @ V2)) @ V1))))))) @ V1))))))))
(TFinite_Set.finite.simps,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cSet.insert @ V2) @ V1))) @ (cFinite_Set.finite @ V1)))))))))))
(TFinite_Set.finite_Diff2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.finite @ ((cGroups.minus_class.minus @ V1) @ V0))) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.finite_Inter,(call @ (^[V0]: ((c==> @ ((cSet.Bex @ V0) @ (^[V1]: (cFinite_Set.finite @ V1)))) @ (cFinite_Set.finite @ (cComplete_Lattices.Inf_class.Inf @ V0))))))
(TFinite_Set.finite_PlusD_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cSum_Type.Plus @ V0) @ V1))) @ (cFinite_Set.finite @ V1)))))))
(TFinite_Set.finite_PlusD_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cSum_Type.Plus @ V0) @ V1))) @ (cFinite_Set.finite @ V0)))))))
(TFinite_Set.finite_Union,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V1]: ((c==> @ ((cSet.member @ V1) @ V0)) @ (cFinite_Set.finite @ V1))))) @ (cFinite_Set.finite @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))
(TFinite_Set.finite_compl,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.finite @ (cGroups.uminus_class.uminus @ V0))) @ (cFinite_Set.finite @ cOrderings.top_class.top))))))
(TFinite_Set.product_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1))) @ (((cFinite_Set.fold @ (^[V2]: (^[V3]: (((cFinite_Set.fold @ (^[V4]: (cSet.insert @ ((cProduct_Type.Pair @ V2) @ V4)))) @ V3) @ V1)))) @ cOrderings.bot_class.bot) @ V0)))))))))
(TFun.bij_betw_imp_inj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((cFun.inj_on @ V0) @ V1)))))))))
(TFun.inj_on_image_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ V0) @ V2)) @ ((cSet.image @ V0) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))))
(TFun.inj_on_imp_bij_betw,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ (((cFun.bij_betw @ V0) @ V1) @ ((cSet.image @ V0) @ V1))))))))
(TFun.inj_on_the_inv_into,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cFun.inj_on @ ((cFun.the_inv_into @ V1) @ V0)) @ ((cSet.image @ V0) @ V1))))))))
(TFun.inj_vimage_image_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cSet.image @ V0) @ V1))) @ V1)))))))
(TFunDef.THE_default_none,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2))))) @ ((cHOL.eq @ ((cFunDef.THE_default @ V1) @ V0)) @ V1)))))))
(TFunDef.is_measure.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFunDef.is_measure @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V2)) @ V1)))) @ V1)))))))
(TFunDef.is_measure.simps,(call @ (^[V0]: ((cHOL.eq @ (cFunDef.is_measure @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ V1)))))))
(TFunDef.rp_inv_image_def,((cHOL.eq @ cFunDef.rp_inv_image) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (^[V2]: ((cProduct_Type.Pair @ ((cRelation.inv_image @ V0) @ V2)) @ ((cRelation.inv_image @ V1) @ V2))))))))
(TGroups.abs_if_class_def,((c== @ (cGroups.abs_if_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.abs_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.minus_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE)))) @ ((cPure.conjunction @ (cGroups.zero_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.ord_class @ cTYPE)) @ ((((cGroups.class.abs_if @ cGroups.abs_class.abs) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less))))))
(TGroups.class.abs_if_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cGroups.class.abs_if @ V0) @ V1) @ V2) @ V3)) @ (cHOL.All @ (^[V4]: ((cHOL.eq @ (V0 @ V4)) @ (((cHOL.If @ ((V3 @ V4) @ V2)) @ (V1 @ V4)) @ V4))))))))))))))
(TGroups.class.sgn_if_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cGroups.class.sgn_if @ V0) @ V1) @ V2) @ V3) @ V4)) @ (cHOL.All @ (^[V5]: ((cHOL.eq @ (V1 @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ V3)) @ V3) @ (((cHOL.If @ ((V4 @ V3) @ V5)) @ V0) @ (V2 @ V0))))))))))))))))))
(TGroups.group_add.diff_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V2) @ V4)) @ (V3 @ V4))))))))))))))
(TGroups.plus_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.plus_class @ cTYPE)))
(TGroups.plus_class.super,((c==> @ (cGroups.plus_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.sgn_if_class_def,((c== @ (cGroups.sgn_if_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.minus_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.one_class @ cTYPE)) @ (cGroups.sgn_class @ cTYPE)))) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.uminus_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE))) @ ((cPure.conjunction @ (cOrderings.ord_class @ cTYPE)) @ (((((cGroups.class.sgn_if @ cGroups.one_class.one) @ cGroups.sgn_class.sgn) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less))))))
(TGroups.uminus_class_def,((c== @ (cGroups.uminus_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.zero_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TGroups.zero_class.super,((c==> @ (cGroups.zero_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THOL.True_implies_equals,(call @ (^[V0]: ((c== @ ((c==> @ cHOL.True) @ V0)) @ V0))))
(THOL.default_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cHOL.default_class @ cTYPE)))
(THOL.default_class.super,((c==> @ (cHOL.default_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THOL.induct_implies_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.induct_implies @ V0) @ ((cHOL.induct_conj @ V1) @ V2))) @ ((cHOL.induct_conj @ ((cHOL.induct_implies @ V0) @ V1)) @ ((cHOL.induct_implies @ V0) @ V2))))))))))
(THilbert_Choice.LeastMI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ (V2 @ V4)))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((c==> @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (V0 @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))) @ (V3 @ V4)))))) @ (V3 @ ((cHilbert_Choice.LeastM @ V2) @ V0))))))))))))))
(THilbert_Choice.bacc_def,((c== @ cHilbert_Choice.bacc) @ (^[V0]: (^[V1]: ((((cNat.nat.nat_rec @ (^[V2]: (cSet.Collect @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V2)))))))) @ (^[V2]: (^[V3]: (^[V4]: ((cLattices.sup_class.sup @ (V3 @ V4)) @ (cSet.Collect @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V5)) @ V4)) @ ((cSet.member @ V6) @ (V3 @ V4)))))))))))) @ V1) @ V0)))))
(THilbert_Choice.exE_some,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex @ V0)) @ ((c==> @ ((c== @ V1) @ (cHilbert_Choice.Eps @ V0))) @ (V0 @ V1))))))))
(THilbert_Choice.inv_f_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ V2)) @ ((cHOL.eq @ (((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0) @ V2)) @ V1))))))))))
(THilbert_Choice.someI_ex,(call @ (^[V0]: ((c==> @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ (V0 @ (cHilbert_Choice.Eps @ (^[V1]: (V0 @ V1))))))))
(THilbert_Choice.surj_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cFun.comp @ V0) @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0))) @ cFun.id)))))
(THilbert_Choice.tfl_some,(cHOL.All @ (^[V0]: (cHOL.All @ (^[V1]: ((cHOL.implies @ (V0 @ V1)) @ (V0 @ (cHilbert_Choice.Eps @ V0))))))))
(TInductive.def_coinduct3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.gfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ (V1 @ (cInductive.complete_lattice_class.lfp @ (^[V4]: ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ (V1 @ V4)) @ V3)) @ V0)))))) @ ((cSet.member @ V2) @ V0))))))))))))))
(TInductive.weak_coinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ (V2 @ V1))) @ ((cSet.member @ V0) @ (cInductive.complete_lattice_class.gfp @ V2)))))))))))
(TInt.abs_power_minus_one,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cPower.power_class.power @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0))) @ cGroups.one_class.one))))
(TInt.int.Abs_int_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cInt.intrel @ V2) @ V2)) @ ((cHOL.eq @ V1) @ (cSet.Collect @ (cInt.intrel @ V2)))))))))) @ ((cHOL.eq @ (cInt.Rep_int @ (cInt.Abs_int @ V0))) @ V0)))))
(TInt.int.Rep_int_inverse,(call @ (^[V0]: ((cHOL.eq @ (cInt.Abs_int @ (cInt.Rep_int @ V0))) @ V0))))
(TInt.int.id_abs_transfer,((((cTransfer.fun_rel @ cHOL.eq) @ cInt.cr_int) @ (^[V0]: V0)) @ cInt.Abs_Integ))
(TInt.int.rel_eq_transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ ((cTransfer.fun_rel @ cInt.cr_int) @ cHOL.eq)) @ cInt.intrel) @ cHOL.eq))
(TInt.ring_1.of_int_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ (cInt.uminus_int_inst.uminus_int @ V6))) @ (V5 @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)))))))))))))))))))
(TInt.ring_1.of_int_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ ((cPower.power_class.power @ V6) @ V7))) @ ((((cPower.power.power @ V0) @ V1) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ V7))))))))))))))))))))
(TInt.ring_1_class.Ints_0,((cSet.member @ cGroups.zero_class.zero) @ cInt.ring_1_class.Ints))
(TInt.ring_1_class.Ints_1,((cSet.member @ cGroups.one_class.one) @ cInt.ring_1_class.Ints))
(TInt.type_definition_int,(((cTypedef.type_definition @ cInt.Rep_int) @ cInt.Abs_int) @ (cSet.Collect @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cInt.intrel @ V1) @ V1)) @ ((cHOL.eq @ V0) @ (cSet.Collect @ (cInt.intrel @ V1))))))))))
(TInt.uminus_int.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ cInt.cr_int) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cProduct_Type.Pair @ V1) @ V0))))) @ cInt.uminus_int_inst.uminus_int))
(TInt.wf_int_ge_less_than,(call @ (^[V0]: (cWellfounded.wf @ (cInt.int_ge_less_than @ V0)))))
(TInt.zdvd_antisym_nonneg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))))
(TInt.zpower_numeral_even,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ ((cHOL.Let @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ V1))) @ (^[V2]: ((cInt.times_int_inst.times_int @ V2) @ V2)))))))))
(TLattices.bool_Compl_def,((cHOL.eq @ cLattices.uminus_bool_inst.uminus_bool) @ cHOL.Not))
(TLazy_Sequence.empty_def,((cHOL.eq @ cLazy_Sequence.empty) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ cList.list.Nil)))
(TLazy_Sequence.flat_code,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.flat @ V0)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V1]: (((cOption.option.option_case @ cOption.option.None) @ (^[V2]: ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (cLazy_Sequence.yield @ ((cLazy_Sequence.append @ V3) @ (cLazy_Sequence.flat @ V4)))))) @ V2))) @ (cLazy_Sequence.yield @ V0))))))))
(TLazy_Sequence.those_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.those @ V0)) @ ((cOption.map @ cLazy_Sequence.lazy_sequence.lazy_sequence_of_list) @ (cList.those @ (cLazy_Sequence.list_of_lazy_sequence @ V0)))))))
(TLazy_Sequence.yield_Seq,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.yield @ (cLazy_Sequence.Lazy_Sequence @ V0))) @ (V0 @ cProduct_Type.Unity)))))
(TLazy_Sequence.yield_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.yield @ V0)) @ (((cList.list.list_case @ cOption.option.None) @ (^[V1]: (^[V2]: (cOption.option.Some @ ((cProduct_Type.Pair @ V1) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V2)))))) @ (cLazy_Sequence.list_of_lazy_sequence @ V0))))))
(TLifting.Quotient_Rep_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c== @ V4) @ (V1 @ V5))) @ ((c== @ (V2 @ V4)) @ (V2 @ V4)))))))))))))))))
(TLifting.Quotient_cr_rel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ V3) @ (^[V4]: (^[V5]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V1 @ V4)) @ V5)))))))))))))))
(TLifting.Quotient_transp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ (cRelation.transp @ V0)))))))))))
(TLifting.invariant_to_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLifting.invariant @ V0) @ V1) @ V2)) @ ((cHOL.eq @ V1) @ V2)))))))))
(TLifting.left_unique_def,(call @ (^[V0]: ((cHOL.eq @ (cLifting.left_unique @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V1) @ V3)) @ ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V1) @ V2)))))))))))))
(TLifting.left_unique_fun,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_total @ V0)) @ ((c==> @ (cLifting.left_unique @ V1)) @ (cLifting.left_unique @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TLifting.pcr_Domainp_par,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V2)) @ V3)) @ ((c==> @ ((((cTransfer.fun_rel @ V2) @ cHOL.eq) @ V4) @ V1)) @ ((cHOL.eq @ (cRelation.Domainp @ ((cRelation.relcompp @ V2) @ V0))) @ ((cLattices.inf_class.inf @ V3) @ V4))))))))))))))))
(TLifting_Set.Domainp_set,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((cHOL.eq @ (cRelation.Domainp @ (cLifting_Set.set_rel @ V0))) @ (^[V2]: ((cSet.Ball @ V2) @ V1)))))))))
(TLifting_Set.set_rel_def,(call @ (^[V0]: ((cHOL.eq @ (cLifting_Set.set_rel @ V0)) @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cSet.Ball @ V1) @ (^[V3]: ((cSet.Bex @ V2) @ (^[V4]: ((V0 @ V3) @ V4)))))) @ ((cSet.Ball @ V2) @ (^[V3]: ((cSet.Bex @ V1) @ (^[V4]: ((V0 @ V4) @ V3))))))))))))
(TLifting_Sum.Domainp_sum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V2)) @ V3)) @ ((cHOL.eq @ (cRelation.Domainp @ ((cLifting_Sum.sum_rel @ V0) @ V2))) @ ((cSum_Type.sum.sum_case @ V1) @ V3)))))))))))))
(TLifting_Sum.sum_rel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting_Sum.sum_rel @ V0) @ V1) @ V2) @ V3)) @ ((cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (((cSum_Type.sum.sum_case @ (^[V6]: (((cSum_Type.sum.sum_case @ (^[V7]: ((V0 @ V6) @ V7))) @ (^[V7]: cHOL.False)) @ V5))) @ (^[V6]: (((cSum_Type.sum.sum_case @ (^[V7]: cHOL.False)) @ (^[V7]: ((V1 @ V6) @ V7))) @ V5))) @ V4)))) @ ((cProduct_Type.Pair @ V2) @ V3))))))))))))
(TList.Ball_set_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ (cList.set @ ((cList.replicate @ V0) @ V1))) @ (^[V3]: (V2 @ V3)))) @ ((cHOL.disj @ (V2 @ V1)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))))))))))
(TList.Cons_acc_listrel1I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ ((cSet.member @ V2) @ (cWellfounded.acc @ (cList.listrel1 @ V1)))) @ ((cSet.member @ ((cList.list.Cons @ V0) @ V2)) @ (cWellfounded.acc @ (cList.listrel1 @ V1))))))))))))
(TList.Cons_eq_filter_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.filter @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.append @ V4) @ ((cList.list.Cons @ V0) @ V5)))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: (cHOL.Not @ (V2 @ V6))))) @ ((cHOL.conj @ (V2 @ V0)) @ ((cHOL.eq @ V1) @ ((cList.filter @ V2) @ V5)))))))))))))))))))
(TList.Cons_listrel1_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cList.listrel1 @ V4))) @ ((cHOL.disj @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ V4)) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cList.listrel1 @ V4))))))))))))))))
(TList.Nil_eq_concat_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cList.list.Nil) @ (cList.concat @ V0))) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V1]: ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.Nil_is_append_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cList.list.Nil) @ ((cList.append @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil))))))))
(TList.append.append_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.append @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ ((cList.list.Cons @ V0) @ ((cList.append @ V1) @ V2))))))))))
(TList.append_is_Nil_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ cList.list.Nil)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil))))))))
(TList.atLeastAtMost_upto,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cList.set @ ((cList.upto @ V0) @ V1))))))))
(TList.bi_total_list_all2,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ (cTransfer.bi_total @ (cList.list_all2 @ V0))))))
(TList.concat_eq_Nil_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.concat @ V0)) @ cList.list.Nil)) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V1]: ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.distinct_dropWhile,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.dropWhile @ V1) @ V0))))))))
(TList.distinct_enumerate,(call @ (^[V0]: (call @ (^[V1]: (cList.distinct @ ((cList.enumerate @ V0) @ V1)))))))
(TList.distinct_removeAll,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.removeAll @ V1) @ V0))))))))
(TList.distinct_singleton,(call @ (^[V0]: (cList.distinct @ ((cList.list.Cons @ V0) @ cList.list.Nil)))))
(TList.distinct_takeWhile,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.takeWhile @ V1) @ V0))))))))
(TList.dropWhile_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.dropWhile) @ cList.dropWhile))))
(TList.filter_eq_Cons_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.filter @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V4) @ ((cList.list.Cons @ V2) @ V5)))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: (cHOL.Not @ (V0 @ V6))))) @ ((cHOL.conj @ (V0 @ V2)) @ ((cHOL.eq @ V3) @ ((cList.filter @ V0) @ V5)))))))))))))))))))
(TList.fold_commute_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cFun.comp @ V1) @ (V2 @ V5))) @ ((cFun.comp @ (V3 @ V5)) @ V1)))))) @ ((cHOL.eq @ (V1 @ (((cList.fold @ V2) @ V0) @ V4))) @ (((cList.fold @ V3) @ V0) @ (V1 @ V4)))))))))))))))
(TList.fold_remove1_split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ ((c==> @ ((cSet.member @ V4) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V3)) @ (V1 @ V4))) @ ((cFun.comp @ (V1 @ V4)) @ (V1 @ V3)))))))))) @ ((c==> @ ((cSet.member @ V2) @ (cList.set @ V0))) @ ((cHOL.eq @ ((cList.fold @ V1) @ V0)) @ ((cFun.comp @ ((cList.fold @ V1) @ ((cList.remove1 @ V2) @ V0))) @ (V1 @ V2))))))))))))
(TList.hd_rotate_conv_nth,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.hd @ ((cList.rotate @ V1) @ V0))) @ ((cList.nth @ V0) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ (cNat.size_class.size @ V0))))))))))
(TList.in_listsp_conv_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.listsp @ V0) @ V1)) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: (V0 @ V2)))))))))
(TList.in_set_conv_decomp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V1) @ ((cList.append @ V2) @ ((cList.list.Cons @ V0) @ V3)))))))))))))
(TList.length_filter_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ (cHOL.Not @ (V2 @ V0))) @ ((cNat.ord_nat_inst.less_nat @ (cNat.size_class.size @ ((cList.filter @ V2) @ V1))) @ (cNat.size_class.size @ V1)))))))))))
(TList.length_list_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cNat.size_class.size @ (((cList.list_update @ V0) @ V1) @ V2))) @ (cNat.size_class.size @ V0)))))))))
(TList.length_remdups_leq,(call @ (^[V0]: ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ (cList.remdups @ V0))) @ (cNat.size_class.size @ V0)))))
(TList.lexord_irreflexive,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.All @ (^[V2]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V2)) @ V0))))) @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ (cList.lexord @ V0)))))))))
(TList.linorder.sorted_tl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ (cList.tl @ V2)))))))))))
(TList.list.list_case_def,((c== @ cList.list.list_case) @ (^[V0]: (^[V1]: ((cList.list.list_rec @ V0) @ (^[V2]: (^[V3]: (^[V4]: ((V1 @ V2) @ V3)))))))))
(TList.list.list_size_def,(call @ (^[V0]: ((c== @ (cList.list.list_size @ V0)) @ ((cList.list.list_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TList.list_all2_all_nthI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V0))) @ ((V2 @ ((cList.nth @ V0) @ V3)) @ ((cList.nth @ V1) @ V3)))))) @ (((cList.list_all2 @ V2) @ V0) @ V1))))))))))
(TList.list_all2_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq))) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ cHOL.eq))) @ cList.list_all2) @ cList.list_all2))))))
(TList.list_case_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ V0))) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V1)) @ V0))) @ cList.list.list_case) @ cList.list.list_case))))))
(TList.list_eq_iff_nth_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ ((cList.nth @ V0) @ V2)) @ ((cList.nth @ V1) @ V2))))))))))))
(TList.list_eq_iff_zip_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cSet.Ball @ (cList.set @ ((cList.zip @ V0) @ V1))) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.eq @ V2) @ V3))))))))))))
(TList.list_update_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_update @ ((cList.append @ V0) @ V1)) @ V2) @ V3)) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cList.append @ (((cList.list_update @ V0) @ V2) @ V3)) @ V1)) @ ((cList.append @ V0) @ (((cList.list_update @ V1) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ (cNat.size_class.size @ V0))) @ V3)))))))))))))
(TList.list_update_beyond,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ V1)) @ ((cHOL.eq @ (((cList.list_update @ V0) @ V1) @ V2)) @ V0)))))))))
(TList.list_update_length,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_update @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (cNat.size_class.size @ V0)) @ V3)) @ ((cList.append @ V0) @ ((cList.list.Cons @ V3) @ V2))))))))))))
(TList.listsum_update_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ (((cList.list_update @ V1) @ V0) @ V2))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ (cList.monoid_add_class.listsum @ V1)) @ V2)) @ ((cList.nth @ V1) @ V0)))))))))))
(TList.map_eq_map_tailrec,((cHOL.eq @ cList.map) @ cList.map_tailrec))
(TList.minus_coset_filter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ (cList.coset @ V1))) @ (cList.set @ ((cList.filter @ (^[V2]: ((cSet.member @ V2) @ V0))) @ V1))))))))
(TList.notin_set_sublistI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ ((cList.sublist @ V1) @ V2))))))))))))
(TList.nth_equal_first_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V1)) @ V2)) @ V0)) @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)))))))))))
(TList.nth_list_update_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.nth @ (((cList.list_update @ V1) @ V0) @ V2)) @ V0)) @ V2)))))))))
(TList.partition_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cLifting_Product.prod_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0)))) @ cList.partition) @ cList.partition))))
(TList.remdups_adj.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V2]: (V0 @ ((cList.list.Cons @ V2) @ cList.list.Nil))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ (V0 @ ((cList.list.Cons @ V2) @ V4)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ (V0 @ ((cList.list.Cons @ V3) @ V4)))) @ (V0 @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4)))))))))))) @ (V0 @ V1)))))))))
(TList.remdups_adj.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cList.remdups_adj @ V0)) @ V1)) @ ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ V0)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ cList.list.Nil)) @ V2)))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ cList.list.Nil))) @ ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ ((cList.list.Cons @ V3) @ cList.list.Nil))) @ V2)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V3) @ V4)) @ (cList.remdups_adj @ ((cList.list.Cons @ V3) @ V5))) @ ((cList.list.Cons @ V3) @ (cList.remdups_adj @ ((cList.list.Cons @ V4) @ V5)))))) @ ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ V2)))))))))) @ V2))))))))))))
(TList.remdups_adj.psimps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ ((cHOL.eq @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V1)) @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ V2))) @ ((cList.list.Cons @ V0) @ (cList.remdups_adj @ ((cList.list.Cons @ V1) @ V2)))))))))))))
(TList.remdups_adj.psimps_2,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ ((cList.list.Cons @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ cList.list.Nil))) @ ((cList.list.Cons @ V0) @ cList.list.Nil))))))
(TList.remdups_adj.psimps_1,((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ cList.list.Nil)) @ ((cHOL.eq @ (cList.remdups_adj @ cList.list.Nil)) @ cList.list.Nil)))
(TList.remdups_adj_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.remdups_adj @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ ((cList.append @ (cList.remdups_adj @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))) @ (cList.tl @ (cList.remdups_adj @ ((cList.list.Cons @ V1) @ V2))))))))))))
(TList.remdups_adj_length,(call @ (^[V0]: ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ (cList.remdups_adj @ V0))) @ (cNat.size_class.size @ V0)))))
(TList.remdups_eq_nil_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.remdups @ V0)) @ cList.list.Nil)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.remove1_filter_not,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ (V0 @ V1))) @ ((cHOL.eq @ ((cList.remove1 @ V1) @ ((cList.filter @ V0) @ V2))) @ ((cList.filter @ V0) @ V2))))))))))
(TList.removeAll_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.removeAll) @ cList.removeAll)))))
(TList.replicate_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ V0) @ (cList.list_all2 @ V0))) @ cList.replicate) @ cList.replicate))))
(TList.rev_singleton_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cList.rev @ V0)) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil))))))))
(TList.rotate_is_Nil_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.rotate @ V0) @ V1)) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil)))))))
(TList.set_remove1_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cList.set @ ((cList.remove1 @ V0) @ V1))) @ (cList.set @ V1)))))))
(TList.set_sublist_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cList.set @ ((cList.sublist @ V0) @ V1))) @ (cList.set @ V0)))))))
(TList.set_update_subsetI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ (cList.set @ V0)) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.set @ (((cList.list_update @ V0) @ V3) @ V2))) @ V1))))))))))))
(TList.singleton_rev_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ cList.list.Nil)) @ (cList.rev @ V1))) @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V0) @ cList.list.Nil))))))))
(TList.splice.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V2) @ V4)) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V1) @ V2)) @ ((cList.list.Cons @ V3) @ V4)))) @ V0)))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cList.splice_rel) @ V1))))))))
(TList.splice_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.splice_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V4))) @ ((c==> @ ((cHOL.eq @ V1) @ V4)) @ V2))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V5))) @ V2))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V6) @ V7)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V6) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))))) @ ((c==> @ ((cList.splice_graph @ ((cProduct_Type.Pair @ V5) @ V7)) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))) @ V2)))))))))))))) @ V2)))))))))))
(TList.splice_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.splice_graph @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V3))) @ ((cHOL.eq @ V1) @ V3))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ cList.list.Nil))) @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ V4)))))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V5) @ (V2 @ ((cProduct_Type.Pair @ V4) @ V6)))))) @ ((cList.splice_graph @ ((cProduct_Type.Pair @ V4) @ V6)) @ (V2 @ ((cProduct_Type.Pair @ V4) @ V6)))))))))))))))))))))))
(TList.splice_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.splice_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V4) @ V6)) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ ((cList.list.Cons @ V5) @ V6)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TList.takeWhile_not_last,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ ((cList.takeWhile @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V1) @ (cList.last @ V0))))) @ V0)) @ (cList.butlast @ V0))))))
(TList.takeWhile_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0))) @ cList.takeWhile) @ cList.takeWhile))))
(TList.trancl_set_ntrancl,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.trancl @ (cList.set @ V0))) @ ((cTransitive_Closure.ntrancl @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ (cList.set @ V0))) @ cNat.one_nat_inst.one_nat)) @ (cList.set @ V0))))))
(TList.transpose_sumC_def,((c== @ cList.transpose_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cList.transpose_graph @ V0) @ V1))))))
(TList.union_coset_filter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cList.coset @ V0)) @ V1)) @ (cList.coset @ ((cList.filter @ (^[V2]: (cHOL.Not @ ((cSet.member @ V2) @ V1)))) @ V0))))))))
(TList.upto_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.upto_graph @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((V2 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V5)) @ ((cList.list.Cons @ V4) @ (V3 @ ((cProduct_Type.Pair @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)) @ V5)))) @ cList.list.Nil))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TMain.random_sumbool_def,(call @ (^[V0]: ((cHOL.eq @ (cMain.random_sumbool_inst.random_sumbool @ V0)) @ ((cMain.random_aux_sumbool @ V0) @ V0)))))
(TMap.finite_range_map_of,(call @ (^[V0]: (cFinite_Set.finite @ ((cSet.image @ (cMap.map_of @ V0)) @ cOrderings.top_class.top)))))
(TMap.map_of_map_restrict,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cMap.map_of @ ((cList.map @ (^[V2]: ((cProduct_Type.Pair @ V2) @ (V0 @ V2)))) @ V1))) @ ((cMap.restrict_map @ ((cFun.comp @ cOption.option.Some) @ V0)) @ (cList.set @ V1))))))))
(TMap.map_upd_Some_unfold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cHOL.eq @ ((((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2)) @ V3)) @ (cOption.option.Some @ V4))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V1)) @ ((cHOL.eq @ V2) @ V4))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V3) @ V1))) @ ((cHOL.eq @ (V0 @ V3)) @ (cOption.option.Some @ V4))))))))))))))))
(TMap.restrict_map_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cMap.restrict_map @ V0) @ ((cSet.insert @ V1) @ V2))) @ (((cFun.fun_upd @ ((cMap.restrict_map @ V0) @ V2)) @ V1) @ (V0 @ V1))))))))))
(TNat.Nat_Abs_Nat_inverse,(call @ (^[V0]: ((c==> @ (cNat.Nat @ V0)) @ ((cHOL.eq @ (cNat.Rep_Nat @ (cNat.Abs_Nat @ V0))) @ V0)))))
(TNat.Suc_mult_le_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V2))) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)))))))))
(TNat.arity_order_bot_nat,(cOrderings.order_bot_class @ cTYPE))
(TNat.arity_wellorder_nat,(cOrderings.wellorder_class @ cTYPE))
(TNat.dvd.dual_order.asym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))) @ cHOL.False)))))))
(TNat.dvd.dual_order.refl,(call @ (^[V0]: ((cRings.dvd_class.dvd @ V0) @ V0))))
(TNat.dvd.less_imp_not_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ cHOL.False)))))))
(TNat.dvd.ord_eq_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TNat.dvd.ord_le_eq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TNat.dvd.preorder_axioms,((cOrderings.class.preorder @ cRings.dvd_class.dvd) @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))
(TNat.dvd.strict_mono_def,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.order.strict_mono @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))))) @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat.le_add_diff_inverse,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ V1)))))))
(TNat.le_neq_implies_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))))))))
(TNat.measure_induct_rule,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V4)) @ (V0 @ V3))) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2)))))))))
(TNat.nat.Abs_Nat_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ (^[V1]: (cNat.Nat @ V1))))) @ ((cHOL.eq @ (cNat.Rep_Nat @ (cNat.Abs_Nat @ V0))) @ V0)))))
(TNat.nat.Rep_Nat_inverse,(call @ (^[V0]: ((cHOL.eq @ (cNat.Abs_Nat @ (cNat.Rep_Nat @ V0))) @ V0))))
(TNat.nat.nat_rec_set_def,((c== @ cNat.nat.nat_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V4) @ V0))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cNat.Suc @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((V1 @ V5) @ V6))) @ ((V2 @ V5) @ V6))))))))))))))))
(TNat.nat_0_less_mult_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1))))))))
(TNat.nat_add_left_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2)))))))))
(TNat.semiring_1.Nats_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))) @ ((c==> @ ((cSet.member @ V5) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))) @ ((cSet.member @ ((V2 @ V4) @ V5)) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))))))))))))))))))
(TNat.semiring_1.Nats_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3)) @ ((cSet.image @ (((cNat.semiring_1.of_nat @ V0) @ V2) @ V3)) @ cOrderings.top_class.top))))))))))))
(TNat.semiring_1.of_nat_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ cNat.zero_nat_inst.zero_nat)) @ V3)))))))))))
(TNat.semiring_1.of_nat_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ cNat.one_nat_inst.one_nat)) @ V0)))))))))))
(TNat.type_definition_nat,(((cTypedef.type_definition @ cNat.Rep_Nat) @ cNat.Abs_Nat) @ (cSet.Collect @ (^[V0]: (cNat.Nat @ V0)))))
(TNat_Transfer.is_nat_def,(call @ (^[V0]: ((cHOL.eq @ (cNat_Transfer.is_nat @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)))))
(TNitpick.arity_type_word,(cHOL.type_class @ cTYPE))
(TNitpick.fold_graph'_def,((c== @ cNitpick.fold_graph') @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V6)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V4) @ V6))))))))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V7)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V8)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V6)) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((V7 @ V5) @ V9))) @ ((cHOL.conj @ ((cSet.member @ V5) @ V6)) @ ((((V0 @ V7) @ V8) @ ((cGroups.minus_class.minus @ V6) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ V9)))))))))))))))))))))))))
(TNitpick.fun_box.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TNitpick.fun_box.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.fun_box.FunBox @ V2))) @ V1)))) @ V1))))))
(TNitpick.fun_box.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cNitpick.fun_box.FunBox @ V2))))) @ (V0 @ V1)))))))
(TNitpick.nat_case_unfold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cNat.nat.nat_case @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ V0) @ (V1 @ ((cNat.minus_nat_inst.minus_nat @ V2) @ cNat.one_nat_inst.one_nat)))))))))))
(TNitpick.nat_gcd.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cNitpick.nat_gcd_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cNitpick.nat_gcd_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))) @ ((V2 @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.nat_gcd_rel_def,((c== @ cNitpick.nat_gcd_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))))))))))))))
(TNitpick.norm_frac.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TNitpick.norm_frac.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cNitpick.norm_frac @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V4) @ V5)) @ (^[V6]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V4) @ V6)) @ ((cDivides.div_int_inst.div_int @ V5) @ V6)))))))) @ V3)))))))) @ V3)))))))))))
(TNitpick.norm_frac.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.norm_frac @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V0) @ V1)) @ (^[V2]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V0) @ V2)) @ ((cDivides.div_int_inst.div_int @ V1) @ V2))))))))))))
(TNitpick.pair_box.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cNitpick.pair_box.PairBox @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TNitpick.pair_box.inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cNitpick.pair_box.PairBox @ V0) @ V1)) @ ((cNitpick.pair_box.PairBox @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TNitpick.pair_box.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.pair_box.pair_box_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cNitpick.pair_box.PairBox @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TNitpick.pair_box.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.pair_box.pair_box_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cNitpick.pair_box.PairBox @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TNitpick.random_word_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cNitpick.random_aux_word @ V0) @ V0)))))
(TNitpick.rtranclp_unfold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ V2)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2))))))))))
(TNitpick.uminus_frac_def,(call @ (^[V0]: ((c== @ (cNitpick.uminus_frac @ V0)) @ (cNitpick.Abs_Frac @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ (cNitpick.num @ V0))) @ (cNitpick.denom @ V0)))))))
(TNum.class.numeral.intro,(call @ (^[V0]: ((c==> @ (cGroups.class.semigroup_add @ V0)) @ (cNum.class.numeral @ V0)))))
(TNum.neg_numeral.dbl_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cNum.neg_numeral.dbl @ V1) @ V4)) @ ((V1 @ V4) @ V4))))))))))))))
(TNum.neg_numeral.sub_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ V6)) @ ((V0 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5)) @ (((cNum.numeral.numeral @ V4) @ V1) @ V6)))))))))))))))))))
(TNum.num.Abs_num_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNum.num.num_rep_set))) @ ((cHOL.eq @ (cNum.Rep_num @ (cNum.Abs_num @ V0))) @ V0)))))
(TNum.num.Rep_num_inverse,(call @ (^[V0]: ((cHOL.eq @ (cNum.Abs_num @ (cNum.Rep_num @ V0))) @ V0))))
(TNum.num.num_rec_set_def,((c== @ cNum.num.num_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (cInductive.complete_lattice_class.lfp @ (^[V3]: (^[V4]: (^[V5]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cNum.num.One)) @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cNum.num.Bit0 @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ ((V1 @ V6) @ V7))) @ ((V3 @ V6) @ V7)))))))) @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cNum.num.Bit1 @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ ((V2 @ V6) @ V7))) @ ((V3 @ V6) @ V7))))))))))))))))))
(TNum.num.num_rep_set_def,((c== @ cNum.num.num_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ V2)))) @ (V0 @ V2))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ V2)))) @ (V0 @ V2)))))))))))
(TNum.numeral.numeral_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ ((cNum.plus_num_inst.plus_num @ V2) @ V3))) @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (((cNum.numeral.numeral @ V1) @ V0) @ V3)))))))))))))
(TNum.numeral.numeral_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.class.numeral @ V0)) @ ((c== @ ((cNum.numeral.numeral @ V1) @ V0)) @ (^[V2]: ((((cNum.num.num_rec @ V1) @ (^[V3]: (^[V4]: ((V0 @ V4) @ V4)))) @ (^[V3]: (^[V4]: ((V0 @ ((V0 @ V4) @ V4)) @ V1)))) @ V2)))))))))
(TNum.numeral.numeral_inc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.inc @ V2))) @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ V1))))))))))
(TNum.numeral.one_add_one,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V1)) @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TNum.numeral_class.intro,((c==> @ (cGroups.one_class @ cTYPE)) @ ((c==> @ (cGroups.semigroup_add_class @ cTYPE)) @ (cNum.numeral_class @ cTYPE))))
(TNum.numeral_class.super_2,((c==> @ (cNum.numeral_class @ cTYPE)) @ (cGroups.semigroup_add_class @ cTYPE)))
(TNum.numeral_class.super_1,((c==> @ (cNum.numeral_class @ cTYPE)) @ (cGroups.one_class @ cTYPE)))
(TNum.ring_1.not_iszero_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cNum.ring_1.iszero @ V3) @ V0))))))))))))))))
(TNum.type_definition_num,(((cTypedef.type_definition @ cNum.Rep_num) @ cNum.Abs_num) @ (cSet.Collect @ cNum.num.num_rep_set)))
(TOption.UNIV_option_conv,((cHOL.eq @ cOrderings.top_class.top) @ ((cSet.insert @ cOption.option.None) @ ((cSet.image @ cOption.option.Some) @ cOrderings.top_class.top))))
(TOption.equal_option_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TOption.option.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cOption.option.None)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ (cOption.option.Some @ V6))) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ (((cOption.option.option_case @ V2) @ V4) @ V0)) @ (((cOption.option.option_case @ V3) @ V5) @ V1))))))))))))))))))
(TOption.option.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cOption.option.option_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cOption.option.None)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cOption.option.Some @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TOption.split_option_all,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ ((cHOL.conj @ (V0 @ cOption.option.None)) @ (cHOL.All @ (^[V1]: (V0 @ (cOption.option.Some @ V1)))))))))
(TOrderings.arity_bot_fun,(cOrderings.bot_class @ cTYPE))
(TOrderings.arity_ord_fun,(cOrderings.ord_class @ cTYPE))
(TOrderings.arity_top_fun,(cOrderings.top_class @ cTYPE))
(TOrderings.bot_class_def,((c== @ (cOrderings.bot_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TOrderings.less_bool_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_bool_inst.less_bool @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ V1)))))))
(TOrderings.linorder.neqE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((V1 @ V2) @ V3)) @ V4)) @ ((c==> @ ((c==> @ ((V1 @ V3) @ V2)) @ V4)) @ V4)))))))))))))))
(TOrderings.linorder_neqE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)) @ V2))))))))))
(TOrderings.ord.Least_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord.Least @ V0) @ V1)) @ (cHOL.The @ (^[V2]: ((cHOL.conj @ (V1 @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ ((V0 @ V2) @ V3)))))))))))))
(TOrderings.ord_class_def,((c== @ (cOrderings.ord_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TOrderings.order.antisym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.order.le_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ ((cHOL.disj @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.order.less_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))))))))))))))
(TOrderings.order_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_eq_refl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TOrderings.order_le_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_less_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TOrderings.ordering.asym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V2)) @ cHOL.False))))))))))))
(TOrderings.ordering.refl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((V0 @ V2) @ V2)))))))))
(TOrderings.top_class_def,((c== @ (cOrderings.top_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TPower.power.power.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNat.Suc @ V3))) @ ((V1 @ V2) @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3))))))))))))
(TPower.power.power.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))))
(TPower.power_class.intro,((c==> @ (cGroups.one_class @ cTYPE)) @ ((c==> @ (cGroups.times_class @ cTYPE)) @ (cPower.power_class @ cTYPE))))
(TPower.power_class.super_2,((c==> @ (cPower.power_class @ cTYPE)) @ (cGroups.times_class @ cTYPE)))
(TPower.power_class.super_1,((c==> @ (cPower.power_class @ cTYPE)) @ (cGroups.one_class @ cTYPE)))
(TPower.power_power_power,((cHOL.eq @ cPower.power_class.power) @ ((cPower.power.power @ cGroups.one_class.one) @ cGroups.times_class.times)))
(TPredicate.adjunct.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.adjunct @ V0) @ ((cPredicate.seq.Join @ V1) @ V2))) @ ((cPredicate.seq.Join @ V1) @ ((cPredicate.adjunct @ V0) @ V2))))))))))
(TPredicate.adjunct.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.adjunct @ V0) @ ((cPredicate.seq.Insert @ V1) @ V2))) @ ((cPredicate.seq.Insert @ V1) @ ((cLattices.sup_class.sup @ V2) @ V0))))))))))
(TPredicate.adjunct.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.adjunct @ V0) @ cPredicate.seq.Empty)) @ ((cPredicate.seq.Join @ V0) @ cPredicate.seq.Empty)))))
(TPredicate.contained_def,((c== @ cPredicate.contained) @ (^[V0]: ((((cPredicate.seq.seq_rec @ (^[V1]: cHOL.True)) @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.conj @ ((cPredicate.eval @ V3) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V3)))))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V1) @ V4)) @ (V3 @ V4))))))) @ V0))))
(TPredicate.equal_seq_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.holds_if_pred,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.holds @ (cPredicate.if_pred @ V0))) @ V0))))
(TPredicate.if_pred_holds,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.if_pred @ (cPredicate.holds @ V0))) @ V0))))
(TPredicate.is_empty_code,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.is_empty @ (cPredicate.Seq @ V0))) @ (cPredicate.null @ (V0 @ cProduct_Type.Unity))))))
(TPredicate.less_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1))))))))
(TPredicate.null_is_empty,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.null @ V0)) @ (cPredicate.is_empty @ (cPredicate.pred_of_seq @ V0))))))
(TPredicate.pred.Pred_def,(call @ (^[V0]: ((c== @ (cPredicate.pred.Pred @ V0)) @ (cPredicate.Abs_pred @ (cDatatype.Leaf @ V0))))))
(TPredicate.pred.Rep_pred,(call @ (^[V0]: ((cSet.member @ (cPredicate.Rep_pred @ V0)) @ (cSet.Collect @ cPredicate.pred.pred_rep_set)))))
(TPredicate.pred.eq.simps,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cPredicate.pred.Pred @ V0)) @ (cPredicate.pred.Pred @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.pred.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cPredicate.pred.Pred @ V1)))))))
(TPredicate.seq.Empty_def,((c== @ cPredicate.seq.Empty) @ (cPredicate.Abs_seq @ (cDatatype.In0 @ cHOL.undefined))))
(TPredicate.seq.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cPredicate.seq.Empty)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V1) @ ((cPredicate.seq.Insert @ V8) @ V9))) @ ((cHOL.eq @ ((V4 @ V8) @ V9)) @ ((V5 @ V8) @ V9)))))))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V1) @ ((cPredicate.seq.Join @ V8) @ V9))) @ ((cHOL.eq @ ((V6 @ V8) @ V9)) @ ((V7 @ V8) @ V9)))))))) @ ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V2) @ V4) @ V6) @ V0)) @ ((((cPredicate.seq.seq_case @ V3) @ V5) @ V7) @ V1)))))))))))))))))))))))
(TPredicate.seq.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cPredicate.seq.seq_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cPredicate.seq.Empty)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Insert @ V5) @ V6))) @ (cHOL.Not @ (V0 @ ((V2 @ V5) @ V6))))))))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Join @ V5) @ V6))) @ (cHOL.Not @ (V0 @ ((V3 @ V5) @ V6)))))))))))))))))))))))
(TPredicate.singleton_bot,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.singleton @ V0) @ cOrderings.bot_class.bot)) @ (V0 @ cProduct_Type.Unity)))))
(TPredicate.singleton_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.singleton @ V0) @ V1)) @ (((cHOL.If @ (cHOL.Ex1 @ (^[V2]: ((cPredicate.eval @ V1) @ V2)))) @ (cHOL.The @ (^[V2]: ((cPredicate.eval @ V1) @ V2)))) @ (V0 @ cProduct_Type.Unity))))))))
(TPredicate.singleton_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Ex1 @ (^[V3]: ((cPredicate.eval @ V0) @ V3)))) @ ((c==> @ ((cPredicate.eval @ V0) @ V1)) @ ((cHOL.eq @ ((cPredicate.singleton @ V2) @ V0)) @ V1))))))))))
(TPredicate.singleton_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.singleton @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ ((cPredicate.singleton @ V0) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)) @ ((cPredicate.singleton @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ ((cPredicate.singleton @ V0) @ V1)) @ ((cPredicate.singleton @ V0) @ V2))) @ ((cPredicate.singleton @ V0) @ V1)) @ (V0 @ cProduct_Type.Unity))))))))))))
(TPresburger.conj_le_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ V2)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ V3)))))))))))))
(TPresburger.plusinfinity,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ (V1 @ V3)) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V3) @ ((cInt.times_int_inst.times_int @ V4) @ V0))))))))) @ ((c==> @ (cHOL.Ex @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cHOL.eq @ (V2 @ V4)) @ (V1 @ V4)))))))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V3]: (V1 @ V3)))) @ (cHOL.Ex @ (^[V3]: (V2 @ V3))))))))))))))
(TPresburger.simp_from_to,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ V0)) @ cOrderings.bot_class.bot) @ ((cSet.insert @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)))))))))
(TProduct_Type.Pair_scomp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.scomp @ (cProduct_Type.Pair @ V0)) @ V1)) @ (V1 @ V0)))))))
(TProduct_Type.Sigma_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cProduct_Type.Sigma @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TProduct_Type.Sigma_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cOrderings.ord_class.less_eq @ ((cProduct_Type.Sigma @ V0) @ V2)) @ ((cProduct_Type.Sigma @ V1) @ V3)))))))))))))
(TProduct_Type.apfst_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.apfst @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((cProduct_Type.Pair @ (V0 @ V1)) @ V2)))))))))
(TProduct_Type.apsnd_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.apsnd @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((cProduct_Type.Pair @ V1) @ (V0 @ V2))))))))))
(TProduct_Type.bool.cases_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_case @ V0) @ V1) @ cHOL.False)) @ V1))))))
(TProduct_Type.bool.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_case @ V0) @ V1) @ cHOL.True)) @ V0))))))
(TProduct_Type.bool.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_rec @ V0) @ V1) @ cHOL.False)) @ V1))))))
(TProduct_Type.bool.simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_rec @ V0) @ V1) @ cHOL.True)) @ V0))))))
(TProduct_Type.bool.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_case @ V0) @ V1) @ cHOL.False)) @ V1))))))
(TProduct_Type.bool.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cProduct_Type.bool.bool_case @ V0) @ V1) @ cHOL.True)) @ V0))))))
(TProduct_Type.bool.simps_2,(cHOL.Not @ ((cHOL.eq @ cHOL.False) @ cHOL.True)))
(TProduct_Type.bool.simps_1,(cHOL.Not @ ((cHOL.eq @ cHOL.True) @ cHOL.False)))
(TProduct_Type.bool.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cProduct_Type.bool.bool_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cHOL.True)) @ (V0 @ V1))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cHOL.False)) @ (V0 @ V2)))))))))))))
(TProduct_Type.curry_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cProduct_Type.curry @ V0) @ V1) @ V2)) @ (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TProduct_Type.mem_splitE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cSet.member @ V0) @ ((V1 @ V4) @ V5))) @ V3))))))) @ V3)))))))))))
(TProduct_Type.mem_splitI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((V1 @ V2) @ V3))) @ ((cSet.member @ V0) @ ((cProduct_Type.prod.prod_case @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))))))))))))
(TProduct_Type.prod.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.prod.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_rec @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.prod.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.prod.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TProduct_Type.prod.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TProduct_Type.prod_caseE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cProduct_Type.prod.prod_case @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((V0 @ V3) @ V4)) @ V2))))))) @ V2)))))))))
(TProduct_Type.prod_caseI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TProduct_Type.scomp_Pair,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.scomp @ V0) @ cProduct_Type.Pair)) @ V0))))
(TProduct_Type.split_Pair,((cHOL.eq @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cProduct_Type.Pair @ V0) @ V1))))) @ cFun.id))
(TProduct_Type.split_beta,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((V0 @ V2) @ V3)))) @ V1)) @ ((V0 @ (cProduct_Type.fst @ V1)) @ (cProduct_Type.snd @ V1))))))))
(TProduct_Type.split_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ ((cFun.comp @ V0) @ V1)) @ V2)) @ ((V0 @ (V1 @ (cProduct_Type.fst @ V2))) @ (cProduct_Type.snd @ V2))))))))))
(TProduct_Type.split_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.split_part,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ V0) @ ((V1 @ V2) @ V3)))))) @ (^[V2]: ((cHOL.conj @ V0) @ ((cProduct_Type.prod.prod_case @ V1) @ V2)))))))))
(TProduct_Type.unit.cases,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.unit.unit_case @ V0) @ cProduct_Type.Unity)) @ V0))))
(TProduct_Type.unit.simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.unit.unit_rec @ V0) @ cProduct_Type.Unity)) @ V0))))
(TProduct_Type.unit.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.unit.unit_case @ V0) @ cProduct_Type.Unity)) @ V0))))
(TProduct_Type.unit.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.unit.unit_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cProduct_Type.Unity)) @ (V0 @ V1))))))))))
(TPure.sort_constraint_eq,(call @ (^[V0]: ((c== @ ((c==> @ (cPure.sort_constraint @ cTYPE)) @ V0)) @ V0))))
(TQuotient.Quotient3_symp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ (cRelation.symp @ V0)))))))))
(TQuotient.ball_reg_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.implies @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cHOL.implies @ (cHOL.All @ V1)) @ ((cSet.Ball @ V0) @ V2))))))))))
(TQuotient.bex1_bexeq_reg,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.implies @ (cHOL.Ex1 @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ (cLifting.Respects @ V0))) @ (V1 @ V2))))) @ ((cQuotient.Bex1_rel @ V0) @ (^[V2]: (V1 @ V2)))))))))
(TRandom.iterate_sumC_def,((c== @ cRandom.iterate_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cRandom.iterate_graph @ V0) @ V1))))))
(TRandom.log_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.log_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)))) @ ((cRandom.log_graph @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom.log_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V0)))) @ ((cRandom.log_graph @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ V0))) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ V0)))))) @ ((cRandom.log_graph @ ((cProduct_Type.Pair @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V0))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.div_natural_inst.div_natural @ V1) @ V0))))))))))))))
(TRandom_Pred.iter'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))) @ V1)))))))))) @ V1))))))
(TRandom_Pred.iter'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ ((((cRandom_Pred.iter' @ V0) @ V1) @ V2) @ V3)) @ V4)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V0) @ V6)) @ ((c==> @ ((cHOL.eq @ V1) @ V7)) @ ((c==> @ ((cHOL.eq @ V2) @ V8)) @ ((c==> @ ((cHOL.eq @ V3) @ V9)) @ ((c==> @ ((cHOL.eq @ V4) @ (((cHOL.If @ ((cHOL.eq @ V7) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V8) @ V9)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V10]: (^[V11]: (^[V12]: (cPredicate.Seq @ (^[V13]: ((cPredicate.seq.Insert @ V10) @ ((((cRandom_Pred.iter' @ V6) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V7) @ cCode_Numeral.one_natural_inst.one_natural)) @ V8) @ V12))))))))))))) @ V5)))))))))))))) @ V5)))))))))))))))
(TRandom_Pred.iter'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cRandom_Pred.iter' @ V0) @ V1) @ V2) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V2) @ V3)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (^[V6]: (cPredicate.Seq @ (^[V7]: ((cPredicate.seq.Insert @ V4) @ ((((cRandom_Pred.iter' @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2) @ V6)))))))))))))))))))))
(TRandom_Sequence.map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.map @ V0) @ V1)) @ ((cRandom_Sequence.bind @ V1) @ ((cFun.comp @ cRandom_Sequence.single) @ V0))))))))
(TRecord.iso_tuple_UNIV_I,(call @ (^[V0]: ((c== @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ cHOL.True))))
(TRelation.Domain.DomainI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ V0) @ (cRelation.Domain @ V2))))))))))
(TRelation.Domain.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cRelation.Domain @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ (V2 @ V3))))))) @ (V2 @ V0))))))))))
(TRelation.Domainp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Domainp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ (V2 @ V3))))))) @ (V2 @ V1))))))))))
(TRelation.Domainp.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cRelation.Domainp @ V0) @ V1)))))))))
(TRelation.Field_converse,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Field @ (cRelation.converse @ V0))) @ (cRelation.Field @ V0)))))
(TRelation.Range_converse,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Range @ (cRelation.converse @ V0))) @ (cRelation.Domain @ V0)))))
(TRelation.Rangep.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Rangep @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ (V2 @ V4))))))) @ (V2 @ V1))))))))))
(TRelation.antisym_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cRelation.antisym @ V1)) @ (cRelation.antisym @ V0))))))))
(TRelation.converse.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ V3)))))))) @ V3)))))))))))
(TRelation.converse.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ V2))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V2)))))))))))))))
(TRelation.converse_INTER,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.converse @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (cRelation.converse @ (V1 @ V2))))))))))
(TRelation.converse_Id_on,(call @ (^[V0]: ((cHOL.eq @ (cRelation.converse @ (cRelation.Id_on @ V0))) @ (cRelation.Id_on @ V0)))))
(TRelation.converse_UNION,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.converse @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (cRelation.converse @ (V1 @ V2))))))))))
(TRelation.converse_empty,((cHOL.eq @ (cRelation.converse @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TRelation.conversep_mono,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cRelation.conversep @ V0)) @ (cRelation.conversep @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TRelation.inv_imagep_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.inv_imagep @ V0) @ V1)) @ (^[V2]: (^[V3]: ((V0 @ (V1 @ V2)) @ (V1 @ V3))))))))))
(TRelation.irrefl_diff_Id,(call @ (^[V0]: (cRelation.irrefl @ ((cGroups.minus_class.minus @ V0) @ cRelation.Id)))))
(TRelation.pred_equals_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1)))) @ ((cHOL.eq @ V0) @ V1)))))))
(TRelation.pred_subset_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (^[V2]: ((cSet.member @ V2) @ V0))) @ (^[V2]: ((cSet.member @ V2) @ V1)))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TRelation.relcomp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cRelation.relcomp @ V2) @ V3))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ V3)) @ ((V4 @ V5) @ V7)))))))))) @ ((V4 @ V0) @ V1))))))))))))))
(TRelation.relcomp.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V4)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ ((cRelation.relcomp @ V2) @ V4)))))))))))))))
(TRelation.relcomp_empty1,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcomp @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TRelation.relcomp_empty2,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcomp @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TRelation.relcomp_unfold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcomp @ V0) @ V1)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V4)) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1))))))))))))))
(TRelation.relcompp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRelation.relcompp @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V2) @ V5)) @ ((c==> @ ((cHOL.eq @ V3) @ V7)) @ ((c==> @ ((V0 @ V5) @ V6)) @ ((c==> @ ((V1 @ V6) @ V7)) @ V4))))))))))) @ V4)))))))))))))
(TRelation.relcompp.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cRelation.relcompp @ V0) @ V1) @ V2) @ V3)) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V6)) @ ((cHOL.conj @ ((V0 @ V4) @ V5)) @ ((V1 @ V5) @ V6))))))))))))))))))))
(TRelation.relcompp_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcompp @ ((cRelation.relcompp @ V0) @ V1)) @ V2)) @ ((cRelation.relcompp @ V0) @ ((cRelation.relcompp @ V1) @ V2))))))))))
(TRelation.single_valuedD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRelation.single_valued @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V0)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TRelation.single_valuedI,(call @ (^[V0]: ((c==> @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V0)) @ ((cHOL.eq @ V2) @ V3)))))))))) @ (cRelation.single_valued @ V0)))))
(TRelation.total_on_empty,(call @ (^[V0]: ((cRelation.total_on @ cOrderings.bot_class.bot) @ V0))))
(TRelation.trans_O_subset,(call @ (^[V0]: ((c==> @ (cRelation.trans @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ V0) @ V0)) @ V0)))))
(TRelation.trans_converse,(call @ (^[V0]: ((cHOL.eq @ (cRelation.trans @ (cRelation.converse @ V0))) @ (cRelation.trans @ V0)))))
(TRings.class.idom.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cRings.class.no_zero_divisors @ V0) @ V3)))))))))))))))
(TRings.class.idom.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))
(TRings.class.ring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cRings.class.semiring @ V0) @ V4)))))))))))))
(TRings.class.ring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)))))))))))))
(TRings.dvd_class.dvd_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TSMT.arity_equal_pattern,(cHOL.equal_class @ cTYPE))
(TSMT.pattern.Pattern_def,((c== @ cSMT.pattern.Pattern) @ (cSMT.Abs_pattern @ cHOL.undefined)))
(TSMT.pattern.Rep_pattern,(call @ (^[V0]: ((cSet.member @ (cSMT.Rep_pattern @ V0)) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set)))))
(TSMT.typerep_pattern_def,(call @ (^[V0]: ((cHOL.eq @ (cSMT.typerep_pattern_inst.typerep_pattern @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))) @ cList.list.Nil)))))
(TSet.Int_insert_left_if0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet.insert @ V0) @ V2)) @ V1)) @ ((cLattices.inf_class.inf @ V2) @ V1))))))))))
(TSet.Int_insert_left_if1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet.insert @ V0) @ V2)) @ V1)) @ ((cSet.insert @ V0) @ ((cLattices.inf_class.inf @ V2) @ V1)))))))))))
(TSet.bex_triv_one_point1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V2]: ((cHOL.eq @ V2) @ V1)))) @ ((cSet.member @ V1) @ V0)))))))
(TSet.bex_triv_one_point2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ V0) @ (^[V2]: ((cHOL.eq @ V1) @ V2)))) @ ((cSet.member @ V1) @ V0)))))))
(TSet.image_constant_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ (^[V2]: V0)) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))))
(TSet.image_vimage_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ ((cSet.vimage @ V0) @ V1))) @ V1))))))
(TSet.insert_inter_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet.insert @ V0) @ V1)) @ ((cSet.insert @ V0) @ V2))) @ ((cSet.insert @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TSet.nonempty_bind_const,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cSet.bind @ V0) @ (^[V2]: V1))) @ V1)))))))
(TSet.vimage_singleton_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.vimage @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ ((cHOL.eq @ (V1 @ V0)) @ V2)))))))))
(TSet_Interval.atMost_Suc,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ (cNat.Suc @ V0))) @ ((cSet.insert @ (cNat.Suc @ V0)) @ (cSet_Interval.ord_class.atMost @ V0))))))
(TSet_Interval.ivl_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))))
(TSet_Interval.lessThan_0,((cHOL.eq @ (cSet_Interval.ord_class.lessThan @ cNat.zero_nat_inst.zero_nat)) @ cOrderings.bot_class.bot))
(TString.arity_equal_char,(cHOL.equal_class @ cTYPE))
(TString.card_UNIV_nibble,((cHOL.eq @ (cFinite_Set.card @ cOrderings.top_class.top)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.enum_ex_char_def,(call @ (^[V0]: ((cHOL.eq @ (cString.enum_char_inst.enum_ex_char @ V0)) @ ((cList.list_ex @ V0) @ cString.enum_char_inst.enum_char)))))
(TString.equal_nibble_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.nat_of_char_Char,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ (cString.nat_of_nibble @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))) @ (cString.nat_of_nibble @ V1))))))))
(TString.nibble.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: (call @ (^[V18]: (call @ (^[V19]: (call @ (^[V20]: (call @ (^[V21]: (call @ (^[V22]: (call @ (^[V23]: (call @ (^[V24]: (call @ (^[V25]: (call @ (^[V26]: (call @ (^[V27]: (call @ (^[V28]: (call @ (^[V29]: (call @ (^[V30]: (call @ (^[V31]: (call @ (^[V32]: (call @ (^[V33]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble0)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble1)) @ ((cHOL.eq @ V4) @ V5))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble2)) @ ((cHOL.eq @ V6) @ V7))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble3)) @ ((cHOL.eq @ V8) @ V9))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble4)) @ ((cHOL.eq @ V10) @ V11))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble5)) @ ((cHOL.eq @ V12) @ V13))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble6)) @ ((cHOL.eq @ V14) @ V15))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble7)) @ ((cHOL.eq @ V16) @ V17))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble8)) @ ((cHOL.eq @ V18) @ V19))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.Nibble9)) @ ((cHOL.eq @ V20) @ V21))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.NibbleA)) @ ((cHOL.eq @ V22) @ V23))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.NibbleB)) @ ((cHOL.eq @ V24) @ V25))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.NibbleC)) @ ((cHOL.eq @ V26) @ V27))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.NibbleD)) @ ((cHOL.eq @ V28) @ V29))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.NibbleE)) @ ((cHOL.eq @ V30) @ V31))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cString.nibble.NibbleF)) @ ((cHOL.eq @ V32) @ V33))) @ ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V2) @ V4) @ V6) @ V8) @ V10) @ V12) @ V14) @ V16) @ V18) @ V20) @ V22) @ V24) @ V26) @ V28) @ V30) @ V32) @ V0)) @ (((((((((((((((((cString.nibble.nibble_case @ V3) @ V5) @ V7) @ V9) @ V11) @ V13) @ V15) @ V17) @ V19) @ V21) @ V23) @ V25) @ V27) @ V29) @ V31) @ V33) @ V1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TString.nibble.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: ((cHOL.eq @ (V0 @ (((((((((((((((((cString.nibble.nibble_case @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble0)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble1)) @ (cHOL.Not @ (V0 @ V2)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble2)) @ (cHOL.Not @ (V0 @ V3)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble3)) @ (cHOL.Not @ (V0 @ V4)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble4)) @ (cHOL.Not @ (V0 @ V5)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble5)) @ (cHOL.Not @ (V0 @ V6)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble6)) @ (cHOL.Not @ (V0 @ V7)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble7)) @ (cHOL.Not @ (V0 @ V8)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble8)) @ (cHOL.Not @ (V0 @ V9)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble9)) @ (cHOL.Not @ (V0 @ V10)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleA)) @ (cHOL.Not @ (V0 @ V11)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleB)) @ (cHOL.Not @ (V0 @ V12)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleC)) @ (cHOL.Not @ (V0 @ V13)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleD)) @ (cHOL.Not @ (V0 @ V14)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleE)) @ (cHOL.Not @ (V0 @ V15)))) @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleF)) @ (cHOL.Not @ (V0 @ V16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TString.size_literal_def,(call @ (^[V0]: ((cHOL.eq @ (cString.size_literal_inst.size_literal @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TSum_Type.Inl_Rep_inject,(call @ (^[V0]: ((cFun.inj_on @ cSum_Type.Inl_Rep) @ V0))))
(TSum_Type.Inr_Rep_inject,(call @ (^[V0]: ((cFun.inj_on @ cSum_Type.Inr_Rep) @ V0))))
(TSum_Type.UNIV_Plus_UNIV,((cHOL.eq @ ((cSum_Type.Plus @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(TSum_Type.arity_type_sum,(cHOL.type_class @ cTYPE))
(TSum_Type.inj_on_Abs_sum,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cSum_Type.sum)) @ ((cFun.inj_on @ cSum_Type.Abs_sum) @ V0)))))
(TSum_Type.surjective_sum,(call @ (^[V0]: ((cHOL.eq @ ((cSum_Type.sum.sum_case @ (^[V1]: (V0 @ (cSum_Type.Inl @ V1)))) @ (^[V1]: (V0 @ (cSum_Type.Inr @ V1))))) @ V0))))
(TTransfer.fun_rel_eq_rel,(call @ (^[V0]: ((cHOL.eq @ ((cTransfer.fun_rel @ cHOL.eq) @ V0)) @ (^[V1]: (^[V2]: (cHOL.All @ (^[V3]: ((V0 @ (V1 @ V3)) @ (V2 @ V3))))))))))
(TTransfer.is_equality_eq,(cTransfer.is_equality @ cHOL.eq))
(TTransfer.reflp_transfer_5,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ cTransfer.rev_implies) @ cRelation.reflp) @ cRelation.reflp)))))
(TTransfer.reflp_transfer_4,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cTransfer.rev_implies))) @ cTransfer.rev_implies) @ cRelation.reflp) @ cRelation.reflp)))))
(TTransfer.reflp_transfer_3,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ cHOL.implies) @ cRelation.reflp) @ cRelation.reflp)))))
(TTransfer.reflp_transfer_2,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.implies))) @ cHOL.implies) @ cRelation.reflp) @ cRelation.reflp)))))
(TTransfer.reflp_transfer_1,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ cHOL.eq) @ cRelation.reflp) @ cRelation.reflp)))))
(TTransfer.right_total_OO,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_total @ V0)) @ ((c==> @ (cTransfer.right_total @ V1)) @ (cTransfer.right_total @ ((cRelation.relcompp @ V0) @ V1)))))))))
(TTransfer.right_total_eq,(cTransfer.right_total @ cHOL.eq))
(TTransfer.transfer_start,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ (((cTransfer.Rel @ cHOL.eq) @ V0) @ V1)) @ V1)))))))
(TTyperep.typerep.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TTyperep.typerep.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cTyperep.typerep.Typerep @ V2) @ V3))) @ V1)))))) @ V1))))))
(TTyperep.typerep.inducts_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V1 @ ((cTyperep.typerep.Typerep @ V3) @ V4)))))))) @ ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V1 @ V3)) @ ((c==> @ (V0 @ V4)) @ (V0 @ ((cList.list.Cons @ V3) @ V4))))))))) @ (V0 @ V2)))))))))))
(TTyperep.typerep.inducts_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V1 @ ((cTyperep.typerep.Typerep @ V3) @ V4)))))))) @ ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V1 @ V3)) @ ((c==> @ (V0 @ V4)) @ (V0 @ ((cList.list.Cons @ V3) @ V4))))))))) @ (V1 @ V2)))))))))))
(TTyperep.typerep_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TTyperep.typerep_int_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_int_inst.typerep_int @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_nat_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_nat_inst.typerep_nat @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_num_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_num_inst.typerep_num @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_set_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TTyperep.typerep_sum_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TWellfounded.acc.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1)) @ ((cSet.member @ V4) @ (cWellfounded.acc @ V1)))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V0))))))))))
(TWellfounded.accp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ ((cWellfounded.accp @ V0) @ V4))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V1))))))))))
(TWellfounded.accp.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((V0 @ V2) @ V1)) @ ((cWellfounded.accp @ V0) @ V2))))) @ ((cWellfounded.accp @ V0) @ V1)))))))
(TWellfounded.accp_acc_eq,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.accp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: ((cSet.member @ V1) @ (cWellfounded.acc @ V0)))))))
(TWellfounded.accp_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ V0) @ V3)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V4) @ V3)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V1))))))))))
(TWellfounded.accp_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cWellfounded.accp @ V1)) @ (cWellfounded.accp @ V0))))))))
(TWellfounded.in_lex_prod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cWellfounded.lex_prod @ V4) @ V5))) @ ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V5)))))))))))))))))
(TWellfounded.max_ext_def,((c== @ cWellfounded.max_ext) @ (^[V0]: (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (((cWellfounded.max_extp @ (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)))) @ V1) @ V2))))))))
(TWellfounded.measure_def,((cHOL.eq @ cWellfounded.measure) @ (cRelation.inv_image @ cWellfounded.less_than)))
(TWellfounded.min_ext_def,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.min_ext @ V0)) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cSet.Ball @ V3) @ (^[V4]: ((cSet.Bex @ V2) @ (^[V5]: ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V4)) @ V0)))))))))))))))))
(TWellfounded.wf_lex_prod,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (cWellfounded.wf @ V1)) @ (cWellfounded.wf @ ((cWellfounded.lex_prod @ V0) @ V1)))))))))
(TWellfounded.wf_not_refl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ V0))))))))
(TWellfounded.wf_pred_nat,(cWellfounded.wf @ cWellfounded.pred_nat))
(TBig_Operators.dvd_setsum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cRings.dvd_class.dvd @ V1) @ (V2 @ V3)))))) @ ((cRings.dvd_class.dvd @ V1) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))
(TBig_Operators.setprod_1',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ cGroups.one_class.one)))))))
(TBig_Operators.setprod_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1))))))))))))))
(TBig_Operators.setsum_Un2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1))))))))))))
(TBig_Operators.setsum_abs,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cGroups.abs_class.abs @ (V0 @ V2)))) @ V1)))))))
(TCode_Evaluation.Free_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Evaluation.Free @ V0) @ V1)) @ cCode_Evaluation.term.dummy_term))))))
(TCode_Generator.holds_def,((c== @ cCode_Generator.holds) @ ((c== @ (^[V0]: V0)) @ (^[V0]: V0))))
(TCode_Numeral.integer_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TCode_Numeral.natural_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TComplete_Lattices.INF1_D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V1 @ V4))) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((V1 @ V3) @ V2))))))))))))
(TComplete_Lattices.INF1_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V5]: (V1 @ V5))) @ V2)) @ ((c==> @ ((c==> @ ((V1 @ V3) @ V2)) @ V4)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V3) @ V0))) @ V4)) @ V4))))))))))))))
(TComplete_Lattices.INF1_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((V1 @ V3) @ V2))))) @ (((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3))) @ V2)))))))))
(TComplete_Lattices.INF2_D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V5]: (V1 @ V5))) @ V2) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ V0)) @ (((V1 @ V4) @ V2) @ V3))))))))))))))
(TComplete_Lattices.INF2_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V6]: (V1 @ V6))) @ V2) @ V3)) @ ((c==> @ ((c==> @ (((V1 @ V4) @ V2) @ V3)) @ V5)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V4) @ V0))) @ V5)) @ V5))))))))))))))))
(TComplete_Lattices.INF2_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ (((V1 @ V4) @ V2) @ V3))))) @ ((((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V1 @ V4))) @ V2) @ V3)))))))))))
(TComplete_Lattices.INT_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.InterD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TComplete_Lattices.InterE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V1))) @ V3)) @ ((c==> @ ((c==> @ ((cSet.member @ V0) @ V2)) @ V3)) @ V3))))))))))))
(TComplete_Lattices.InterI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V1) @ V2))))) @ ((cSet.member @ V1) @ (cComplete_Lattices.Inf_class.Inf @ V0))))))))
(TComplete_Lattices.SUP1_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V1 @ V4))) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((c==> @ ((V1 @ V4) @ V2)) @ V3))))) @ V3)))))))))))
(TComplete_Lattices.SUP1_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((V2 @ V0) @ V3)) @ (((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V2 @ V4))) @ V3))))))))))))
(TComplete_Lattices.SUP2_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V5]: (V1 @ V5))) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V0)) @ ((c==> @ (((V1 @ V5) @ V2) @ V3)) @ V4))))) @ V4)))))))))))))
(TComplete_Lattices.SUP2_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ (((V2 @ V0) @ V3) @ V4)) @ ((((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V5]: (V2 @ V5))) @ V3) @ V4))))))))))))))
(TComplete_Lattices.UN_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cSet.Bex @ V1) @ (^[V3]: ((cSet.member @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.UnionE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V3)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ V2))))) @ V2)))))))))
(TComplete_Lattices.UnionI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ (cComplete_Lattices.Sup_class.Sup @ V1)))))))))))
(TComplete_Lattices.bex_UN,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Bex @ V0) @ (^[V3]: ((cSet.Bex @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))))))))))
(TDatatype.arity_type_node,(cHOL.type_class @ cTYPE))
(TDatatype.ntrunc_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((cDatatype.ntrunc @ V2) @ V0)) @ ((cDatatype.ntrunc @ V2) @ V1))))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDivides.Suc_times_mod_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.one_nat_inst.one_nat) @ V0)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ V0)) @ cNat.one_nat_inst.one_nat)))))))
(TDivides.divmod_int_rel_0,(call @ (^[V0]: (((cDivides.divmod_int_rel @ cInt.zero_int_inst.zero_int) @ V0) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)))))
(TDivides.mod_less_divisor,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0)) @ V0)))))))
(TDivides.nat_mod_eq_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ V2) @ V1))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V0)) @ (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ ((cNat.times_nat_inst.times_nat @ V1) @ V3))))))))))))))
(TDivides.negDivAlg.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V0 @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TDivides.negDivAlg.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDivides.negDivAlg @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cDivides.negDivAlg_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cDivides.adjust @ V5) @ ((cDivides.negDivAlg @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((c==> @ ((cWellfounded.accp @ cDivides.negDivAlg_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TDivides.negDivAlg.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cDivides.negDivAlg_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cDivides.negDivAlg @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cDivides.adjust @ V1) @ ((cDivides.negDivAlg @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))))))))))
(TDivides.negDivAlg_minus1,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.negDivAlg @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int))))))
(TDivides.posDivAlg.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V0 @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TDivides.posDivAlg.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cDivides.posDivAlg @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cDivides.posDivAlg_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cDivides.adjust @ V5) @ ((cDivides.posDivAlg @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((c==> @ ((cWellfounded.accp @ cDivides.posDivAlg_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TDivides.posDivAlg.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cDivides.posDivAlg_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cDivides.posDivAlg @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cDivides.adjust @ V1) @ ((cDivides.posDivAlg @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))))))))))
(TDivides.unique_remainder,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.eq @ V3) @ V5))))))))))))))))
(TDivides.zdiff_zmod_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ V0) @ ((cDivides.div_int_inst.mod_int @ V1) @ V2))) @ V2)) @ ((cDivides.div_int_inst.mod_int @ ((cInt.minus_int_inst.minus_int @ V0) @ V1)) @ V2)))))))))
(TDivides.zdiv_mono2_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V2)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V3) @ V4)) @ V5))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V3) @ V4)) @ V5))) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V5) @ V3)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V3)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V4))))))))))))))))))))
(TDivides.zmult_div_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ V0) @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ ((cInt.minus_int_inst.minus_int @ V1) @ ((cDivides.div_int_inst.mod_int @ V1) @ V0))))))))
(TEnum.arity_enum_finite_1,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_finite_2,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_finite_3,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_finite_4,(cEnum.enum_class @ cTYPE))
(TEnum.arity_enum_finite_5,(cEnum.enum_class @ cTYPE))
(TEnum.arity_type_finite_1,(cHOL.type_class @ cTYPE))
(TEnum.arity_type_finite_2,(cHOL.type_class @ cTYPE))
(TEnum.arity_type_finite_3,(cHOL.type_class @ cTYPE))
(TEnum.arity_type_finite_4,(cHOL.type_class @ cTYPE))
(TEnum.arity_type_finite_5,(cHOL.type_class @ cTYPE))
(TEnum.enum_all_option_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_all @ V0)) @ ((cHOL.conj @ (V0 @ cOption.option.None)) @ (cEnum.enum_class.enum_all @ (^[V1]: (V0 @ (cOption.option.Some @ V1)))))))))
(TEnum.enum_class.enum_all,((cHOL.eq @ cEnum.enum_class.enum_all) @ cHOL.All))
(TEnum.rtranclp_rtrancl_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cTransitive_Closure.rtrancl @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4)))))))))))))))
(TExtraction.exE_realizer',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ (cProduct_Type.snd @ V1)) @ (cProduct_Type.fst @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ V2)))))) @ V2)))))))))
(TExtraction.sumbool.cases_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_case @ V0) @ V1) @ cExtraction.sumbool.Right)) @ V1))))))
(TExtraction.sumbool.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_case @ V0) @ V1) @ cExtraction.sumbool.Left)) @ V0))))))
(TExtraction.sumbool.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_rec @ V0) @ V1) @ cExtraction.sumbool.Right)) @ V1))))))
(TExtraction.sumbool.simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_rec @ V0) @ V1) @ cExtraction.sumbool.Left)) @ V0))))))
(TExtraction.sumbool.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_case @ V0) @ V1) @ cExtraction.sumbool.Right)) @ V1))))))
(TExtraction.sumbool.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cExtraction.sumbool.sumbool_case @ V0) @ V1) @ cExtraction.sumbool.Left)) @ V0))))))
(TExtraction.sumbool.simps_2,(cHOL.Not @ ((cHOL.eq @ cExtraction.sumbool.Right) @ cExtraction.sumbool.Left)))
(TExtraction.sumbool.simps_1,(cHOL.Not @ ((cHOL.eq @ cExtraction.sumbool.Left) @ cExtraction.sumbool.Right)))
(TExtraction.sumbool.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cExtraction.sumbool.sumbool_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Left)) @ (V0 @ V1))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Right)) @ (V0 @ V2)))))))))))))
(TFields.class.field.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((((cFields.class.field_axioms @ V6) @ V7) @ V0) @ V1) @ V3)) @ ((((((((cFields.class.field @ V6) @ V7) @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))))))
(TFields.field.add_frac_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V4 @ ((V1 @ V10) @ V8)) @ ((V1 @ V11) @ V9))) @ ((V1 @ ((V4 @ ((V2 @ V10) @ V9)) @ ((V2 @ V11) @ V8))) @ ((V2 @ V8) @ V9)))))))))))))))))))))))))))))))
(TFields.field.inverse_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V4 @ (V0 @ V8)) @ (V0 @ V9))) @ ((V2 @ ((V2 @ ((V4 @ V8) @ V9)) @ (V0 @ V8))) @ (V0 @ V9)))))))))))))))))))))))))))
(TFields.field_class.intro,((c==> @ (cFields.inverse_class @ cTYPE)) @ ((c==> @ (cRings.comm_ring_1_class @ cTYPE)) @ ((c==> @ (((((cFields.class.field_axioms @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.zero_class.zero)) @ (cFields.field_class @ cTYPE)))))
(TFields.field_class.super_2,((c==> @ (cFields.field_class @ cTYPE)) @ (cRings.comm_ring_1_class @ cTYPE)))
(TFields.field_class.super_1,((c==> @ (cFields.field_class @ cTYPE)) @ (cFields.inverse_class @ cTYPE)))
(TFields.inverse_class_def,((c== @ (cFields.inverse_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TFinite_Set.card.infinite,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TFinite_Set.card_Diff1_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ (cFinite_Set.card @ V0))))))))
(TFinite_Set.card_eq_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ (cFinite_Set.finite @ V0)))))))
(TFinite_Set.card_gt_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cFinite_Set.card @ V0))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ (cFinite_Set.finite @ V0))))))
(TFinite_Set.card_image_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ ((cSet.image @ V1) @ V0))) @ (cFinite_Set.card @ V0))))))))
(TFinite_Set.card_infinite,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TFinite_Set.dvd_partition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cRings.dvd_class.dvd @ V1) @ (cFinite_Set.card @ V2))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))) @ ((cRings.dvd_class.dvd @ V1) @ (cFinite_Set.card @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))))))
(TFinite_Set.endo_inj_surj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V1) @ V0)) @ V0)) @ ((c==> @ ((cFun.inj_on @ V1) @ V0)) @ ((cHOL.eq @ ((cSet.image @ V1) @ V0)) @ V0)))))))))
(TFinite_Set.finite.emptyI,(cFinite_Set.finite @ cOrderings.bot_class.bot))
(TFinite_Set.finite.finite,(call @ (^[V0]: ((c==> @ (cFinite_Set.class.finite @ cTYPE)) @ (cFinite_Set.finite @ V0)))))
(TFinite_Set.finite.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (V1 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ ((cSet.insert @ V3) @ V2))))))))) @ (V1 @ V0)))))))))
(TFinite_Set.finite.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ ((cSet.insert @ V1) @ V0))))))))
(TFinite_Set.finite.intros_1,(cFinite_Set.finite @ cOrderings.bot_class.bot))
(TFinite_Set.finite_SigmaI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (cFinite_Set.finite @ (V1 @ V2)))))) @ (cFinite_Set.finite @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: (V1 @ V2)))))))))))
(TFinite_Set.finite_UnionD,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ (cFinite_Set.finite @ V0)))))
(TFinite_Set.finite_imageD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cSet.image @ V0) @ V1))) @ ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.finite_imageI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ ((cSet.image @ V1) @ V0))))))))
(TFinite_Set.finite_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (V1 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cSet.insert @ V2) @ V3)))))))))) @ (V1 @ V0)))))))))
(TFinite_Set.finite_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.finite @ ((cSet.insert @ V0) @ V1))) @ (cFinite_Set.finite @ V1)))))))
(TFinite_Set.finite_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ V0))))))))
(TFinite_Set.fold_infinite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ (((cFinite_Set.fold @ V1) @ V2) @ V0)) @ V2)))))))))
(TFinite_Set.folding.empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((cHOL.eq @ (((cFinite_Set.folding.F @ V0) @ V1) @ cOrderings.bot_class.bot)) @ V1)))))))
(TFinite_Set.folding.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V2))) @ ((cFun.comp @ (V0 @ V2)) @ (V0 @ V1)))))))) @ (cFinite_Set.folding @ V0)))))
(TFun.bij_betw_UNION_chain,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((c==> @ ((cSet.member @ V5) @ V0)) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5))) @ ((cOrderings.ord_class.less_eq @ (V1 @ V5)) @ (V1 @ V4)))))))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ (((cFun.bij_betw @ V2) @ (V1 @ V4)) @ (V3 @ V4)))))) @ (((cFun.bij_betw @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V1 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V3 @ V4)))))))))))))))
(TFun.inj_image_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TFun.inj_on_strict_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((cOrderings.ord_class.less @ ((cSet.image @ V0) @ V2)) @ ((cSet.image @ V0) @ V1)))))))))))
(TFun.inj_vimage_singleton,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cOrderings.ord_class.less_eq @ ((cSet.vimage @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet.insert @ (cHOL.The @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ V1)))) @ cOrderings.bot_class.bot))))))))
(TFun.override_on_apply_in,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((((cFun.override_on @ V2) @ V3) @ V1) @ V0)) @ (V3 @ V0))))))))))))
(TFun.override_on_emptyset,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cFun.override_on @ V0) @ V1) @ cOrderings.bot_class.bot)) @ V0))))))
(TFun.set.compositionality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cSet.vimage @ V1) @ V2))) @ ((cSet.vimage @ ((cFun.comp @ V1) @ V0)) @ V2)))))))))
(TFun.surj_image_vimage_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cSet.vimage @ V0) @ V1))) @ V1)))))))
(TFunDef.is_measure.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFunDef.is_measure @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ V2)))) @ (V1 @ V0))))))))
(TFunDef.is_measure.intros,(call @ (^[V0]: (cFunDef.is_measure @ V0))))
(TFunDef.union_comp_emptyL,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cRelation.relcomp @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((c==> @ ((cHOL.eq @ ((cRelation.relcomp @ V2) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cRelation.relcomp @ ((cLattices.sup_class.sup @ V0) @ V2)) @ V1)) @ cOrderings.bot_class.bot))))))))))
(TFunDef.union_comp_emptyR,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cRelation.relcomp @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((c==> @ ((cHOL.eq @ ((cRelation.relcomp @ V0) @ V2)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cRelation.relcomp @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))))
(TGroebner_Basis.nnf_simps_5,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(TGroebner_Basis.nnf_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1)))))))))
(TGroebner_Basis.nnf_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.implies @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)))))))
(TGroebner_Basis.nnf_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.conj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(TGroebner_Basis.nnf_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.disj @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))))))))
(TGroups.comm_monoid.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.abel_semigroup @ V0)) @ ((c==> @ ((cGroups.comm_monoid_axioms @ V0) @ V1)) @ ((cGroups.comm_monoid @ V0) @ V1))))))))
(TGroups.minus_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TGroups.minus_class.super,((c==> @ (cGroups.minus_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TGroups.monoid_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.monoid_axioms @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2))))))))))
(TGroups.sgn_if_class.sgn0,((cHOL.eq @ (cGroups.sgn_class.sgn @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TGroups.times_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.times_class @ cTYPE)))
(TGroups.times_class.super,((c==> @ (cGroups.times_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THOL.bool.arity_size_bool,(cNat.size_class @ cTYPE))
(THOL.equal_class.eq_equal,((c== @ cHOL.eq) @ cHOL.eq))
(THOL.equal_class.equal_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(THilbert_Choice.Eps_split,(call @ (^[V0]: ((cHOL.eq @ (cHilbert_Choice.Eps @ (cProduct_Type.prod.prod_case @ V0))) @ (cHilbert_Choice.Eps @ (^[V1]: ((V0 @ (cProduct_Type.fst @ V1)) @ (cProduct_Type.snd @ V1))))))))
(THilbert_Choice.GreatestI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V0 @ V3)) @ ((cNat.ord_nat_inst.less_nat @ V3) @ V2))))) @ (V0 @ (cHilbert_Choice.Greatest @ (^[V3]: (V0 @ V3)))))))))))))
(THilbert_Choice.bacc_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cHilbert_Choice.bacc @ V2) @ V0)) @ ((cHilbert_Choice.bacc @ V2) @ V1))))))))))
(THilbert_Choice.someI2_ex,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))) @ (V1 @ (cHilbert_Choice.Eps @ (^[V2]: (V0 @ V2)))))))))))
(TInductive.coinduct_lemma,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ ((cLattices.sup_class.sup @ V0) @ (cInductive.complete_lattice_class.gfp @ V1))))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ (cInductive.complete_lattice_class.gfp @ V1))) @ (V1 @ ((cLattices.sup_class.sup @ V0) @ (cInductive.complete_lattice_class.gfp @ V1)))))))))))
(TInductive.def_gfp_unfold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.gfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((cHOL.eq @ V0) @ (V1 @ V0)))))))))
(TInductive.def_lfp_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.lfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V1 @ ((cLattices.inf_class.inf @ V0) @ V2))) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2)))))))))))
(TInductive.def_lfp_unfold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.lfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((cHOL.eq @ V0) @ (V1 @ V0)))))))))
(TInductive.gfp_upperbound,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V0))) @ ((cOrderings.ord_class.less_eq @ V0) @ (cInductive.complete_lattice_class.gfp @ V1))))))))
(TInductive.lfp_induct_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cInductive.complete_lattice_class.lfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (V1 @ ((cLattices.inf_class.inf @ (cInductive.complete_lattice_class.lfp @ V1)) @ (cSet.Collect @ (^[V4]: (V2 @ V4))))))) @ (V2 @ V3))))) @ (V2 @ V0)))))))))))
(TInt.Ints_double_eq_0_iff,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))))))
(TInt.Suc_nat_eq_nat_zadd1,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ (cNat.Suc @ (cInt.nat @ V0))) @ (cInt.nat @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ V0)))))))
(TInt.abs_int_inst.abs_int,((c== @ cInt.abs_int_inst.abs_int) @ cInt.abs_int_inst.abs_int))
(TInt.distrib_left_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))))))))))
(TInt.divide_eq_eq_numeral_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1))) @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ cGroups.zero_class.zero))))))))))
(TInt.divide_eq_eq_numeral_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1))) @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V2)) @ cGroups.zero_class.zero))))))))))
(TInt.divide_le_eq_numeral_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V2))))))))))))
(TInt.divide_le_eq_numeral_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V2))))))))))))
(TInt.eq_divide_eq_numeral_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2)) @ V1)) @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))))))))
(TInt.eq_divide_eq_numeral_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2)) @ V1)) @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero))))))))))
(TInt.equation_minus_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cGroups.uminus_class.uminus @ V0))) @ ((cHOL.eq @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))))))
(TInt.finite_interval_int1,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ V2) @ V1))))))))))
(TInt.finite_interval_int2,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V2)) @ ((cInt.ord_int_inst.less_int @ V2) @ V1))))))))))
(TInt.finite_interval_int3,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V0) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ V2) @ V1))))))))))
(TInt.finite_interval_int4,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V0) @ V2)) @ ((cInt.ord_int_inst.less_int @ V2) @ V1))))))))))
(TInt.inf_int_inst.inf_int,((c== @ cInt.inf_int_inst.inf_int) @ cInt.inf_int_inst.inf_int))
(TInt.int_ge_less_than_def,(call @ (^[V0]: ((cHOL.eq @ (cInt.int_ge_less_than @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)) @ ((cInt.ord_int_inst.less_int @ V1) @ V2))))))))))
(TInt.le_divide_eq_numeral_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.le_divide_eq_numeral_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.le_minus_iff_numeral_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V0)))))))))
(TInt.le_minus_iff_numeral_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0)))))))))
(TInt.less_eq_int.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ ((cTransfer.fun_rel @ cInt.cr_int) @ cHOL.eq)) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))) @ cInt.ord_int_inst.less_eq_int))
(TInt.measure_function_int,(cFunDef.is_measure @ ((cFun.comp @ cInt.nat) @ cInt.abs_int_inst.abs_int)))
(TInt.minus_equation_iff_1,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))))))
(TInt.minus_le_iff_numeral_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V0)))))))
(TInt.minus_le_iff_numeral_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V1))) @ V0)))))))
(TInt.nat_abs_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)))) @ ((cNat.times_nat_inst.times_nat @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V0))) @ (cInt.nat @ (cInt.abs_int_inst.abs_int @ V1)))))))))
(TInt.nat_intermed_int_val,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V4)) @ ((cNat.ord_nat_inst.less_nat @ V4) @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ (cInt.abs_int_inst.abs_int @ ((cInt.minus_int_inst.minus_int @ (V2 @ ((cNat.plus_nat_inst.plus_nat @ V4) @ cNat.one_nat_inst.one_nat))) @ (V2 @ V4)))) @ cInt.one_int_inst.one_int))))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ (V2 @ V0)) @ V3)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ (V2 @ V1))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V4)) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ V3))))))))))))))))))
(TInt.nat_mult_distrib_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ (cInt.nat @ ((cInt.times_int_inst.times_int @ V0) @ V1))) @ ((cNat.times_nat_inst.times_nat @ (cInt.nat @ (cInt.uminus_int_inst.uminus_int @ V0))) @ (cInt.nat @ (cInt.uminus_int_inst.uminus_int @ V1))))))))))
(TInt.negative_eq_positive,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TInt.one_int_inst.one_int,((c== @ cInt.one_int_inst.one_int) @ cInt.one_int_inst.one_int))
(TInt.ring_1.of_int.abs_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ (cInt.Abs_Integ @ V6))) @ ((cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: ((V4 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V7)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V8))))) @ V6))))))))))))))))))
(TInt.ring_1.of_int.rep_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c== @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ ((cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: ((V4 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V7)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V8))))) @ (cInt.Rep_Integ @ V6)))))))))))))))))))
(TInt.ring_1.of_int_of_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V6) @ cInt.zero_int_inst.zero_int)) @ (V5 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ (cInt.nat @ (cInt.uminus_int_inst.uminus_int @ V6))))) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ (cInt.nat @ V6))))))))))))))))))))
(TInt.sgn_int_inst.sgn_int,((c== @ cInt.sgn_int_inst.sgn_int) @ cInt.sgn_int_inst.sgn_int))
(TInt.sup_int_inst.sup_int,((c== @ cInt.sup_int_inst.sup_int) @ cInt.sup_int_inst.sup_int))
(TInt.wf_int_ge_less_than2,(call @ (^[V0]: (cWellfounded.wf @ (cInt.int_ge_less_than2 @ V0)))))
(TInt.zero_less_imp_eq_int,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V1)))))))))
(TLattices.arity_minus_fun,(cGroups.minus_class @ cTYPE))
(TLattices.inf_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cLattices.inf_class @ cTYPE)))
(TLattices.inf_class.super,((c==> @ (cLattices.inf_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TLattices.semilattice_def,(call @ (^[V0]: ((c== @ (cLattices.semilattice @ V0)) @ ((cHOL.conj @ (cGroups.abel_semigroup @ V0)) @ (cLattices.semilattice_axioms @ V0))))))
(TLattices.sup_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cLattices.sup_class @ cTYPE)))
(TLattices.sup_class.super,((c==> @ (cLattices.sup_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TLazy_Sequence.append_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.append @ V0) @ V1)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ ((cList.append @ (cLazy_Sequence.list_of_lazy_sequence @ V0)) @ (cLazy_Sequence.list_of_lazy_sequence @ V1)))))))))
(TLazy_Sequence.empty_code,((cHOL.eq @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V0]: cOption.option.None))))
(TLazy_Sequence.hb_map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.hb_map @ V0) @ V1)) @ ((cLazy_Sequence.map @ (cOption.map @ V0)) @ V1)))))))
(TLazy_Sequence.if_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.if_seq @ V0)) @ (((cHOL.If @ V0) @ (cLazy_Sequence.single @ cProduct_Type.Unity)) @ cLazy_Sequence.empty)))))
(TLazy_Sequence.single_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.single @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ ((cList.list.Cons @ V0) @ cList.list.Nil))))))
(TLifting.Quotient_abs_rep,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V1 @ (V2 @ V4))) @ V4)))))))))))))
(TLifting.Quotient_alt_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V3 @ V4) @ V5)) @ ((cHOL.eq @ (V1 @ V4)) @ V5))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((V3 @ (V2 @ V4)) @ V4)))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((cHOL.conj @ ((V3 @ V4) @ (V1 @ V4))) @ ((cHOL.conj @ ((V3 @ V5) @ (V1 @ V5))) @ ((cHOL.eq @ (V1 @ V4)) @ (V1 @ V5)))))))))))))))))))))
(TLifting.Quotient_compose,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cLifting.Quotient @ V4) @ V5) @ V6) @ V7)) @ ((((cLifting.Quotient @ ((cRelation.relcompp @ V3) @ ((cRelation.relcompp @ V4) @ (cRelation.conversep @ V3)))) @ ((cFun.comp @ V5) @ V1)) @ ((cFun.comp @ V2) @ V6)) @ ((cRelation.relcompp @ V3) @ V7)))))))))))))))))))))
(TLifting.Quotient_rel_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((cHOL.eq @ (V1 @ V4)) @ (V1 @ V5)))))))))))))))))
(TLifting.Quotient_rel_rep,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ (V2 @ V4)) @ (V2 @ V5))) @ ((cHOL.eq @ V4) @ V5))))))))))))))))
(TLifting.Quotient_rep_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V4)) @ ((V0 @ (V2 @ (V1 @ V4))) @ V4))))))))))))))
(TLifting_Set.Bex_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq)) @ cSet.Bex) @ cSet.Bex))))
(TLifting_Set.Pow_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ (cLifting_Set.set_rel @ V0))) @ cSet.Pow) @ cSet.Pow))))
(TLifting_Set.Quotient_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((((cLifting.Quotient @ (cLifting_Set.set_rel @ V0)) @ (cSet.image @ V1)) @ (cSet.image @ V2)) @ (cLifting_Set.set_rel @ V3))))))))))))
(TLifting_Set.set_rel_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V1))))))))
(TLifting_Sum.Inl_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cLifting_Sum.sum_rel @ V0) @ V1)) @ cSum_Type.Inl) @ cSum_Type.Inl))))))
(TLifting_Sum.Inr_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cLifting_Sum.sum_rel @ V1) @ V0)) @ cSum_Type.Inr) @ cSum_Type.Inr))))))
(TLifting_Sum.Quotient_sum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cLifting.Quotient @ V4) @ V5) @ V6) @ V7)) @ ((((cLifting.Quotient @ ((cLifting_Sum.sum_rel @ V0) @ V4)) @ ((cSum_Type.sum_map @ V1) @ V5)) @ ((cSum_Type.sum_map @ V2) @ V6)) @ ((cLifting_Sum.sum_rel @ V3) @ V7)))))))))))))))))))))
(TLifting_Sum.sum_rel_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLifting_Sum.sum_rel @ V0) @ V2)) @ ((cLifting_Sum.sum_rel @ V1) @ V3)))))))))))))
(TLimited_Sequence.map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.map @ V0) @ V1)) @ (^[V2]: (^[V3]: (((cOption.option.option_case @ cOption.option.None) @ (^[V4]: (cOption.option.Some @ ((cLazy_Sequence.map @ V0) @ V4)))) @ ((V1 @ V2) @ V3))))))))))
(TList.Cons_eq_append_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ ((cList.append @ V2) @ V3))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V1)) @ V3))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ ((cList.list.Cons @ V0) @ V4)) @ V2)) @ ((cHOL.eq @ V1) @ ((cList.append @ V4) @ V3))))))))))))))))
(TList.all_nth_imp_all_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V0))) @ (V1 @ ((cList.nth @ V0) @ V3)))))) @ ((c==> @ ((cSet.member @ V2) @ (cList.set @ V0))) @ (V1 @ V2))))))))))
(TList.append_eq_Cons_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V2) @ V3)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V4))) @ ((cHOL.eq @ ((cList.append @ V4) @ V1)) @ V3)))))))))))))))
(TList.append_eq_conv_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.take @ (cNat.size_class.size @ V0)) @ V2))) @ ((cHOL.eq @ V1) @ ((cList.drop @ (cNat.size_class.size @ V0)) @ V2)))))))))))
(TList.append_take_drop_id,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.append @ ((cList.take @ V0) @ V1)) @ ((cList.drop @ V0) @ V1))) @ V1))))))
(TList.atLeastLessThan_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ (cList.set @ ((cList.upt @ V0) @ V1))))))))
(TList.bi_unique_list_all2,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ (cTransfer.bi_unique @ (cList.list_all2 @ V0))))))
(TList.butlast_list_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.butlast @ (((cList.list_update @ V0) @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.size_class.size @ V0)) @ cNat.one_nat_inst.one_nat))) @ (cList.butlast @ V0)) @ (((cList.list_update @ (cList.butlast @ V0)) @ V1) @ V2))))))))))
(TList.distinct_remdups_id,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ (cList.remdups @ V0)) @ V0)))))
(TList.elem_le_listsum_nat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cList.nth @ V1) @ V0)) @ (cList.monoid_add_class.listsum @ V1))))))))
(TList.in_set_enumerate_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ ((cList.enumerate @ V1) @ V2)))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ (cProduct_Type.fst @ V0))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ (cProduct_Type.fst @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ V2)) @ V1))) @ ((cHOL.eq @ ((cList.nth @ V2) @ ((cNat.minus_nat_inst.minus_nat @ (cProduct_Type.fst @ V0)) @ V1))) @ (cProduct_Type.snd @ V0))))))))))))
(TList.infinite_UNIV_listI,(cHOL.Not @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TList.length_dropWhile_le,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ ((cList.dropWhile @ V0) @ V1))) @ (cNat.size_class.size @ V1)))))))
(TList.length_n_lists_elem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ ((cList.n_lists @ V1) @ V2)))) @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ V1)))))))))
(TList.length_takeWhile_le,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ ((cList.takeWhile @ V0) @ V1))) @ (cNat.size_class.size @ V1)))))))
(TList.lexord_append_leftD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.append @ V0) @ V1)) @ ((cList.append @ V0) @ V2))) @ (cList.lexord @ V3))) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V4)) @ V3))))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.lexord @ V3)))))))))))))
(TList.lexord_append_leftI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.lexord @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.append @ V3) @ V0)) @ ((cList.append @ V3) @ V1))) @ (cList.lexord @ V2))))))))))))
(TList.linorder.set_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cList.set @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4))) @ ((cSet.insert @ V3) @ (cList.set @ V4)))))))))))))))
(TList.linorder.sorted.Nil,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cList.linorder.sorted @ V0) @ cList.list.Nil)))))))
(TList.linorder.sorted_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c== @ (cList.linorder.sorted @ V0)) @ (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: ((cHOL.disj @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V5) @ V4))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: ((V0 @ V5) @ V6)))) @ (V2 @ V4))))))))))))))))))
(TList.list.Abs_list_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cList.Abs_list @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cList.list.list_rep_set))) @ V1))))) @ V1))))))
(TList.list.Rep_list_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cList.list.list_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cList.Rep_list @ V2))) @ V1)))) @ V1)))))))
(TList.list.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cList.list.list_case @ V2) @ V3) @ V0)) @ (((cList.list.list_case @ V2) @ V3) @ V1))))))))))))
(TList.list_size_pointwise,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ ((cNat.ord_nat_inst.less_eq_nat @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cList.list.list_size @ V1) @ V0)) @ ((cList.list.list_size @ V2) @ V0))))))))))
(TList.list_update_append1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (((cList.list_update @ ((cList.append @ V1) @ V2)) @ V0) @ V3)) @ ((cList.append @ (((cList.list_update @ V1) @ V0) @ V3)) @ V2))))))))))))
(TList.listrel1_iff_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel1 @ V2))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.nth @ V0) @ V4)) @ V3)) @ V2)) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V4) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ V1) @ (((cList.list_update @ V0) @ V4) @ V3))))))))))))))))
(TList.listrelp_listrel_eq,(call @ (^[V0]: ((cHOL.eq @ (cList.listrelp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cList.listrel @ V0))))))))
(TList.lists_length_Suc_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ V0)) @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.Suc @ V1)))))) @ ((cSet.image @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cList.list.Cons @ V3) @ V2))))) @ ((cProduct_Type.Sigma @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ V0)) @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ V1))))) @ (^[V2]: V0)))))))))
(TList.map_replicate_const,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ (^[V2]: V0)) @ V1)) @ ((cList.replicate @ (cNat.size_class.size @ V1)) @ V0)))))))
(TList.map_tailrec_rev_def,((c== @ cList.map_tailrec_rev) @ (^[V0]: (^[V1]: (^[V2]: (cList.map_tailrec_rev_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TList.not_distinct_decomp,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cList.distinct @ V0))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.eq @ V0) @ ((cList.append @ V1) @ ((cList.append @ ((cList.list.Cons @ V4) @ cList.list.Nil)) @ ((cList.append @ V2) @ ((cList.append @ ((cList.list.Cons @ V4) @ cList.list.Nil)) @ V3)))))))))))))))))
(TList.nth_eq_iff_index_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.distinct @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V0))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.nth @ V0) @ V1)) @ ((cList.nth @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))))
(TList.nth_list_update_neq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ ((cList.nth @ (((cList.list_update @ V2) @ V0) @ V3)) @ V1)) @ ((cList.nth @ V2) @ V1))))))))))))
(TList.product_lists.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.product_lists @ ((cList.list.Cons @ V0) @ V1))) @ (cList.concat @ ((cList.map @ (^[V2]: ((cList.map @ (cList.list.Cons @ V2)) @ (cList.product_lists @ V1)))) @ V0))))))))
(TList.product_lists.simps_1,((cHOL.eq @ (cList.product_lists @ cList.list.Nil)) @ ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil)))
(TList.remdups_adj.pinduct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ V0)) @ ((c==> @ ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ cList.list.Nil)) @ (V1 @ cList.list.Nil))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ ((cList.list.Cons @ V2) @ cList.list.Nil))) @ (V1 @ ((cList.list.Cons @ V2) @ cList.list.Nil)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cList.remdups_adj_rel) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ (V1 @ ((cList.list.Cons @ V2) @ V4)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ (V1 @ ((cList.list.Cons @ V3) @ V4)))) @ (V1 @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4))))))))))))) @ (V1 @ V0))))))))))
(TList.remdups_adj_Nil_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.remdups_adj @ V0)) @ cList.list.Nil)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.remdups_adj_rel_def,((c== @ cList.remdups_adj_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((cHOL.eq @ V3) @ V4)))))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4)))))))))))))))))
(TList.remdups_map_remdups,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.remdups @ ((cList.map @ V0) @ (cList.remdups @ V1)))) @ (cList.remdups @ ((cList.map @ V0) @ V1))))))))
(TList.rotate1_is_Nil_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.rotate1 @ V0)) @ cList.list.Nil)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.rotate1_rotate_swap,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.rotate1 @ ((cList.rotate @ V0) @ V1))) @ ((cList.rotate @ V0) @ (cList.rotate1 @ V1))))))))
(TList.snoc_eq_iff_butlast,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ V2)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V2) @ cList.list.Nil))) @ ((cHOL.conj @ ((cHOL.eq @ (cList.butlast @ V2)) @ V0)) @ ((cHOL.eq @ (cList.last @ V2)) @ V1)))))))))))
(TList.splice_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.splice_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cProduct_Type.Pair @ cList.list.Nil) @ V4)) @ V4)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ cList.list.Nil)) @ ((cList.list.Cons @ V4) @ V5))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cList.splice_graph @ ((cProduct_Type.Pair @ V5) @ V7)) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ V5) @ V7)) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))) @ ((V2 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V6) @ V7))) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V6) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))))
(TList.splice_graph.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cList.splice_graph @ ((cProduct_Type.Pair @ V0) @ V1)) @ (V2 @ ((cProduct_Type.Pair @ V0) @ V1)))) @ ((cList.splice_graph @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V0)) @ ((cList.list.Cons @ V4) @ V1))) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ (V2 @ ((cProduct_Type.Pair @ V0) @ V1)))))))))))))))))
(TList.splice_graph.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((cList.splice_graph @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V1)) @ cList.list.Nil)) @ ((cList.list.Cons @ V0) @ V1)))))))
(TList.splice_graph.intros_1,(call @ (^[V0]: ((cList.splice_graph @ ((cProduct_Type.Pair @ cList.list.Nil) @ V0)) @ V0))))
(TList.sublist_shift_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ cProduct_Type.fst) @ ((cList.filter @ (^[V3]: ((cSet.member @ (cProduct_Type.snd @ V3)) @ V0))) @ ((cList.zip @ V1) @ ((cList.upt @ V2) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ (cNat.size_class.size @ V1))))))) @ ((cList.map @ cProduct_Type.fst) @ ((cList.filter @ (^[V3]: ((cSet.member @ ((cNat.plus_nat_inst.plus_nat @ (cProduct_Type.snd @ V3)) @ V2)) @ V0))) @ ((cList.zip @ V1) @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V1)))))))))))))
(TList.sublist_upt_eq_take,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.sublist @ V0) @ (cSet_Interval.ord_class.lessThan @ V1))) @ ((cList.take @ V1) @ V0)))))))
(TList.takeWhile_eq_filter,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cList.set @ ((cList.dropWhile @ V0) @ V1)))) @ (cHOL.Not @ (V0 @ V2)))))) @ ((cHOL.eq @ ((cList.takeWhile @ V0) @ V1)) @ ((cList.filter @ V0) @ V1))))))))
(TList.transpose_graph_def,((c== @ cList.transpose_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((cHOL.eq @ V2) @ cList.list.Nil))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ cList.list.Nil) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (V3 @ V4))) @ ((V0 @ V4) @ (V3 @ V4))))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ V5)) @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6))))))) @ ((V0 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))))))))))))))))))))))
(TList.transpose_rectangle,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ (cNat.size_class.size @ ((cList.nth @ V0) @ V2))) @ V1))))) @ ((cHOL.eq @ (cList.transpose @ V0)) @ ((cList.map @ (^[V2]: ((cList.map @ (^[V3]: ((cList.nth @ ((cList.nth @ V0) @ V3)) @ V2))) @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V0))))) @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ V1))))))))))
(TList.transpose_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.transpose_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ cList.list.Nil) @ V3))) @ V2))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))) @ V2))))))))) @ V2))))))))))
(TList.transpose_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.transpose_rel @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ cList.list.Nil) @ V2)))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V5]: (^[V6]: ((cList.list.Cons @ V6) @ cList.list.Nil))))) @ V4))))) @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ ((cList.list.Cons @ V2) @ V3)) @ V4))))))))))))))))
(TList.transpose_transpose,(call @ (^[V0]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ ((cList.map @ cNat.size_class.size) @ V0)))) @ ((cHOL.eq @ (cList.transpose @ (cList.transpose @ V0))) @ ((cList.takeWhile @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V1) @ cList.list.Nil)))) @ V0))))))
(TMain.typerep_sumbool_def,(call @ (^[V0]: ((cHOL.eq @ (cMain.typerep_sumbool_inst.typerep_sumbool @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil)))))
(TMap.finite_map_freshness,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ (cMap.dom @ V0))) @ ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ cOrderings.top_class.top))) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ (V0 @ V1)) @ cOption.option.None))))))))
(TMap.fun_upds_append_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (((cMap.map_upds @ V2) @ ((cList.append @ V0) @ V3)) @ V1)) @ (((cMap.map_upds @ V2) @ V0) @ V1))))))))))))
(TMap.map_add_map_of_foldr,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMap.map_add @ V0) @ (cMap.map_of @ V1))) @ (((cList.foldr @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (^[V4]: (((cFun.fun_upd @ V4) @ V2) @ (cOption.option.Some @ V3))))))) @ V1) @ V0)))))))
(TMap.map_upd_upds_conv_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cMap.map_upds @ (((cFun.fun_upd @ V0) @ V1) @ (cOption.option.Some @ V2))) @ V3) @ V4)) @ (((cHOL.If @ ((cSet.member @ V1) @ (cList.set @ ((cList.take @ (cNat.size_class.size @ V4)) @ V3)))) @ (((cMap.map_upds @ V0) @ V3) @ V4)) @ (((cFun.fun_upd @ (((cMap.map_upds @ V0) @ V3) @ V4)) @ V1) @ (cOption.option.Some @ V2)))))))))))))))
(TMap.option_map_o_map_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cFun.comp @ (cOption.map @ V0)) @ (((cFun.fun_upd @ V1) @ V2) @ (cOption.option.Some @ V3)))) @ (((cFun.fun_upd @ ((cFun.comp @ (cOption.map @ V0)) @ V1)) @ V2) @ (cOption.option.Some @ (V0 @ V3)))))))))))))
(TMetis.atomize_not_select,(call @ (^[V0]: ((c== @ ((c==> @ V0) @ (cMetis.select @ cHOL.False))) @ (cHOL.Not @ V0)))))
(TMetis.not_atomize_select,(call @ (^[V0]: ((c== @ ((c==> @ (cHOL.Not @ V0)) @ (cMetis.select @ cHOL.False))) @ V0))))
(TNat.Suc_Rep_not_Zero_Rep,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNat.Suc_Rep @ V0)) @ cNat.Zero_Rep)))))
(TNat.bot_nat_inst.bot_nat,((c== @ cNat.bot_nat_inst.bot_nat) @ cNat.bot_nat_inst.bot_nat))
(TNat.dvd.dual_order.trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V2) @ V0)) @ ((cRings.dvd_class.dvd @ V2) @ V1))))))))))
(TNat.dvd.less_imp_not_eq2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ ((cHOL.eq @ V1) @ V0)) @ cHOL.False)))))))
(TNat.dvd.lift_Suc_mono_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cRings.dvd_class.dvd @ (V0 @ V3)) @ (V0 @ (cNat.Suc @ V3)))))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cRings.dvd_class.dvd @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat.dvd.strict_mono_mono,(call @ (^[V0]: ((c==> @ ((cOrderings.order.strict_mono @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))))) @ V0)) @ ((cOrderings.order.mono @ cRings.dvd_class.dvd) @ V0)))))
(TNat.inf_nat_inst.inf_nat,((c== @ cNat.inf_nat_inst.inf_nat) @ cNat.inf_nat_inst.inf_nat))
(TNat.le_add_diff_inverse2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V0)) @ V1)))))))
(TNat.nat_add_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))))))))))
(TNat.nat_add_right_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))) @ ((cHOL.eq @ V0) @ V2)))))))))
(TNat.not_less_less_Suc_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1))) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.one_nat_inst.one_nat,((c== @ cNat.one_nat_inst.one_nat) @ cNat.one_nat_inst.one_nat))
(TNat.semiring_1.Nats_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))) @ ((c==> @ ((cSet.member @ V5) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))) @ ((cSet.member @ ((V1 @ V4) @ V5)) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))))))))))))))))))
(TNat.sup_nat_inst.sup_nat,((c== @ cNat.sup_nat_inst.sup_nat) @ cNat.sup_nat_inst.sup_nat))
(TNat_Transfer.int_if_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cHOL.If @ V0) @ (cNat.semiring_1_class.of_nat @ V1)) @ (cNat.semiring_1_class.of_nat @ V2))) @ (cNat.semiring_1_class.of_nat @ (((cHOL.If @ V0) @ V1) @ V2))))))))))
(TNat_Transfer.nat_if_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cHOL.If @ V0) @ (cInt.nat @ V1)) @ (cInt.nat @ V2))) @ (cInt.nat @ (((cHOL.If @ V0) @ V1) @ V2))))))))))
(TNat_Transfer.nat_set_def,(call @ (^[V0]: ((cHOL.eq @ (cNat_Transfer.nat_set @ V0)) @ ((cSet.Ball @ V0) @ (^[V1]: ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)))))))
(TNitpick.arity_equal_word,(cHOL.equal_class @ cTYPE))
(TNitpick.fun_box.eq.simps,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cNitpick.fun_box.FunBox @ V0)) @ (cNitpick.fun_box.FunBox @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.fun_box.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cNitpick.fun_box.FunBox @ V1)))))))
(TNitpick.inverse_frac_def,(call @ (^[V0]: ((c== @ (cNitpick.inverse_frac @ V0)) @ ((cNitpick.frac @ (cNitpick.denom @ V0)) @ (cNitpick.num @ V0))))))
(TNitpick.less_eq_frac_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.less_eq_frac @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ (cNitpick.num @ ((cNitpick.plus_frac @ V0) @ (cNitpick.uminus_frac @ V1)))) @ cInt.zero_int_inst.zero_int)))))))
(TNitpick.nat_gcd_sumC_def,((c== @ cNitpick.nat_gcd_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cNitpick.nat_gcd_graph @ V0) @ V1))))))
(TNitpick.norm_frac.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((V0 @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TNitpick.norm_frac.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cNitpick.norm_frac @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cNitpick.norm_frac_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V4) @ V5)) @ (^[V6]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V4) @ V6)) @ ((cDivides.div_int_inst.div_int @ V5) @ V6)))))))) @ ((c==> @ ((cWellfounded.accp @ cNitpick.norm_frac_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TNitpick.norm_frac.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cNitpick.norm_frac_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cNitpick.norm_frac @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V0) @ V1)) @ (^[V2]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V0) @ V2)) @ ((cDivides.div_int_inst.div_int @ V1) @ V2)))))))))))))
(TNitpick.pair_box.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TNitpick.pair_box.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cNitpick.pair_box.PairBox @ V2) @ V3))) @ V1)))))) @ V1))))))
(TNitpick.pair_box.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cNitpick.pair_box.PairBox @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TNitpick.typerep_word_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TNitpick.unit_case_unfold,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cProduct_Type.unit.unit_case @ V0) @ V1)) @ V0))))))
(TNum.add_neg_numeral_left_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))) @ V2)))))))))
(TNum.add_neg_numeral_left_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ ((cNum.neg_numeral_class.sub @ V1) @ V0)) @ V2)))))))))
(TNum.add_neg_numeral_left_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ ((cNum.neg_numeral_class.sub @ V0) @ V1)) @ V2)))))))))
(TNum.class.numeral.axioms,(call @ (^[V0]: ((c==> @ (cNum.class.numeral @ V0)) @ (cGroups.class.semigroup_add @ V0)))))
(TNum.mult_numeral_1_right,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ cNum.num.One))) @ V0))))
(TNum.numeral.numeral_code_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit1 @ V2))) @ ((cHOL.Let @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (^[V3]: ((V0 @ ((V0 @ V3) @ V3)) @ V1))))))))))))
(TNum.numeral.numeral_code_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit0 @ V2))) @ ((cHOL.Let @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (^[V3]: ((V0 @ V3) @ V3))))))))))))
(TNum.numeral.numeral_code_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ cNum.num.One)) @ V1)))))))
(TOption.arity_type_option,(cHOL.type_class @ cTYPE))
(TOption.option.Rep_option,(call @ (^[V0]: ((cSet.member @ (cOption.Rep_option @ V0)) @ (cSet.Collect @ cOption.option.option_rep_set)))))
(TOption.these_insert_None,(call @ (^[V0]: ((cHOL.eq @ (cOption.these @ ((cSet.insert @ cOption.option.None) @ V0))) @ (cOption.these @ V0)))))
(TOption.these_insert_Some,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cOption.these @ ((cSet.insert @ (cOption.option.Some @ V0)) @ V1))) @ ((cSet.insert @ V0) @ (cOption.these @ V1))))))))
(TOrderings.order.mono_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.order.mono @ V0) @ V2)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V3)) @ (V2 @ V4))))))))))))))))
(TOrderings.ordering.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((V0 @ V2) @ V3)) @ ((cHOL.conj @ ((V1 @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))))))))) @ ((c==> @ (call @ (^[V2]: ((V1 @ V2) @ V2)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))) @ ((cOrderings.ordering @ V1) @ V0))))))))))
(TOrderings.ordering.trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V2) @ V4)))))))))))))))
(TPartial_Function.if_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.monotone @ V0) @ V1) @ V2)) @ ((c==> @ (((cComplete_Partial_Order.monotone @ V0) @ V1) @ V3)) @ (((cComplete_Partial_Order.monotone @ V0) @ V1) @ (^[V5]: (((cHOL.If @ V4) @ (V2 @ V5)) @ (V3 @ V5)))))))))))))))))
(TPower.idom.power2_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V1) @ V0) @ V7) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V7)) @ ((cHOL.eq @ V6) @ (V5 @ V7))))))))))))))))))))))
(TPower.ring_1.power_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ (V5 @ V6)) @ V7)) @ ((V1 @ ((((cPower.power.power @ V0) @ V1) @ (V5 @ V0)) @ V7)) @ ((((cPower.power.power @ V0) @ V1) @ V6) @ V7)))))))))))))))))))))
(TPower.zero_compare_simps_13,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.zero_class.zero)))))
(TPower.zero_compare_simps_12,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TPower.zero_compare_simps_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)))))))))
(TPower.zero_compare_simps_10,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)))))))))
(TPower.zero_compare_simps_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)))))))))
(TPower.zero_compare_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)))))))))
(TPower.zero_compare_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)))))))))
(TPower.zero_compare_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)))))))))
(TPower.zero_compare_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)))))))))
(TPower.zero_compare_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)))))))))
(TPower.zero_compare_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))))
(TPower.zero_compare_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))))
(TPower.zero_compare_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))))
(TPredicate.arity_type_seq,(cHOL.type_class @ cTYPE))
(TPredicate.equal_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.eval.eval_pred,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.eval @ (cPredicate.pred.Pred @ V0))) @ V0))))
(TPredicate.is_empty_holds,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.is_empty @ V0)) @ (cHOL.Not @ (cPredicate.holds @ V0))))))
(TPredicate.minus_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (cPredicate.pred.Pred @ ((cGroups.minus_class.minus @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1)))))))))
(TPredicate.pred.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cPredicate.pred.Pred @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cPredicate.pred.pred_case @ V2) @ V0)) @ ((cPredicate.pred.pred_case @ V3) @ V1)))))))))))))
(TPredicate.pred.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cPredicate.pred.pred_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cPredicate.pred.Pred @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TPredicate.seq.Insert_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPredicate.seq.Insert @ V0) @ V1)) @ (cPredicate.Abs_seq @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1))))))))))))
(TPredicate.set_of_seq_def,((cHOL.eq @ cPredicate.set_of_seq) @ ((cFun.comp @ cPredicate.set_of_pred) @ cPredicate.pred_of_seq)))
(TPredicate.single_not_bot,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cPredicate.single @ V0)) @ cOrderings.bot_class.bot)))))
(TPredicate.singleton_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.singleton @ V0) @ (cPredicate.Seq @ V1))) @ ((((cPredicate.seq.seq_case @ (V0 @ cProduct_Type.Unity)) @ (^[V2]: (^[V3]: (((cHOL.If @ (cPredicate.is_empty @ V3)) @ V2) @ ((cHOL.Let @ ((cPredicate.singleton @ V0) @ V3)) @ (^[V4]: (((cHOL.If @ ((cHOL.eq @ V2) @ V4)) @ V2) @ (V0 @ cProduct_Type.Unity)))))))) @ (^[V2]: (^[V3]: (((cHOL.If @ (cPredicate.is_empty @ V2)) @ ((cPredicate.the_only @ V0) @ V3)) @ (((cHOL.If @ (cPredicate.null @ V3)) @ ((cPredicate.singleton @ V0) @ V2)) @ ((cHOL.Let @ ((cPredicate.singleton @ V0) @ V2)) @ (^[V4]: ((cHOL.Let @ ((cPredicate.the_only @ V0) @ V3)) @ (^[V5]: (((cHOL.If @ ((cHOL.eq @ V4) @ V5)) @ V4) @ (V0 @ cProduct_Type.Unity))))))))))) @ (V1 @ cProduct_Type.Unity))))))))
(TPredicate.the_only.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.the_only @ V0) @ ((cPredicate.seq.Join @ V1) @ V2))) @ (((cHOL.If @ (cPredicate.is_empty @ V1)) @ ((cPredicate.the_only @ V0) @ V2)) @ (((cHOL.If @ (cPredicate.null @ V2)) @ ((cPredicate.singleton @ V0) @ V1)) @ ((cHOL.Let @ ((cPredicate.singleton @ V0) @ V1)) @ (^[V3]: ((cHOL.Let @ ((cPredicate.the_only @ V0) @ V2)) @ (^[V4]: (((cHOL.If @ ((cHOL.eq @ V3) @ V4)) @ V3) @ (V0 @ cProduct_Type.Unity))))))))))))))))
(TPredicate.the_only.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.the_only @ V0) @ ((cPredicate.seq.Insert @ V1) @ V2))) @ (((cHOL.If @ (cPredicate.is_empty @ V2)) @ V1) @ ((cHOL.Let @ ((cPredicate.singleton @ V0) @ V2)) @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V1) @ V3)) @ V1) @ (V0 @ cProduct_Type.Unity)))))))))))))
(TPredicate.the_only.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.the_only @ V0) @ cPredicate.seq.Empty)) @ (V0 @ cProduct_Type.Unity)))))
(TPresburger.minusinfinity,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ (V1 @ V3)) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V3) @ ((cInt.times_int_inst.times_int @ V4) @ V0))))))))) @ ((c==> @ (cHOL.Ex @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V4) @ V3)) @ ((cHOL.eq @ (V2 @ V4)) @ (V1 @ V4)))))))) @ ((cHOL.implies @ (cHOL.Ex @ (^[V3]: (V1 @ V3)))) @ (cHOL.Ex @ (^[V3]: (V2 @ V3))))))))))))))
(TProduct_Type.Pair_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ V4))) @ V4)))))))))))))
(TProduct_Type.Sigma_Union,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.Sigma @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cProduct_Type.Sigma @ V2) @ V1)))))))))
(TProduct_Type.Times_empty,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1))) @ cOrderings.bot_class.bot)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))))))
(TProduct_Type.apfst_apsnd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.apfst @ V0) @ ((cProduct_Type.apsnd @ V1) @ V2))) @ ((cProduct_Type.Pair @ (V0 @ (cProduct_Type.fst @ V2))) @ (V1 @ (cProduct_Type.snd @ V2)))))))))))
(TProduct_Type.apsnd_apfst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.apsnd @ V0) @ ((cProduct_Type.apfst @ V1) @ V2))) @ ((cProduct_Type.Pair @ (V1 @ (cProduct_Type.fst @ V2))) @ (V0 @ (cProduct_Type.snd @ V2)))))))))))
(TProduct_Type.bool.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cHOL.True)) @ ((c==> @ (V0 @ cHOL.False)) @ (V0 @ V1))))))))
(TProduct_Type.bool.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cProduct_Type.bool.bool_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cHOL.True)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cHOL.False)) @ (cHOL.Not @ (V0 @ V2)))))))))))))))
(TProduct_Type.bool.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cProduct_Type.bool.bool_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cHOL.True)) @ (V0 @ V1))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cHOL.False)) @ (V0 @ V2)))))))))))))
(TProduct_Type.curry_split,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.curry @ (cProduct_Type.prod.prod_case @ V0))) @ V0))))
(TProduct_Type.fcomp_scomp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.scomp @ ((cFun.fcomp @ V0) @ V1)) @ V2)) @ ((cFun.fcomp @ V0) @ ((cProduct_Type.scomp @ V1) @ V2))))))))))
(TProduct_Type.map_pair.id,((cHOL.eq @ ((cProduct_Type.map_pair @ cFun.id) @ cFun.id)) @ cFun.id))
(TProduct_Type.mem_splitI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cSet.member @ V1) @ ((V2 @ V3) @ V4)))))))) @ ((cSet.member @ V1) @ ((cProduct_Type.prod.prod_case @ V2) @ V0))))))))))
(TProduct_Type.pair_imageI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((V3 @ V0) @ V1)) @ ((cSet.image @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((V3 @ V4) @ V5))))) @ V2))))))))))))
(TProduct_Type.prod.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cProduct_Type.Pair @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TProduct_Type.prod.inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TProduct_Type.prod.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TProduct_Type.prod.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TProduct_Type.prod_caseE',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cProduct_Type.prod.prod_case @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ (((V0 @ V4) @ V5) @ V2)) @ V3))))))) @ V3)))))))))))
(TProduct_Type.prod_caseI2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((V1 @ V2) @ V3))))))) @ ((cProduct_Type.prod.prod_case @ V1) @ V0)))))))
(TProduct_Type.prod_cases3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TProduct_Type.prod_cases4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))) @ V1)))))))))) @ V1))))))
(TProduct_Type.prod_cases5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))))) @ V1)))))))))))) @ V1))))))
(TProduct_Type.prod_cases6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7))))))) @ V1)))))))))))))) @ V1))))))
(TProduct_Type.prod_cases7,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ ((cProduct_Type.Pair @ V7) @ V8)))))))) @ V1)))))))))))))))) @ V1))))))
(TProduct_Type.prod_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ (cProduct_Type.fst @ V0)) @ (cProduct_Type.fst @ V1))) @ ((cHOL.eq @ (cProduct_Type.snd @ V0)) @ (cProduct_Type.snd @ V1)))))))))
(TProduct_Type.product_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.product @ V0) @ V1)) @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1))))))))
(TProduct_Type.scomp_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cProduct_Type.scomp @ V0) @ V1) @ V2)) @ ((cProduct_Type.prod.prod_case @ V1) @ (V0 @ V2))))))))))
(TProduct_Type.scomp_fcomp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.fcomp @ ((cProduct_Type.scomp @ V0) @ V1)) @ V2)) @ ((cProduct_Type.scomp @ V0) @ (^[V3]: ((cFun.fcomp @ (V1 @ V3)) @ V2)))))))))))
(TProduct_Type.scomp_scomp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.scomp @ ((cProduct_Type.scomp @ V0) @ V1)) @ V2)) @ ((cProduct_Type.scomp @ V0) @ (^[V3]: ((cProduct_Type.scomp @ (V1 @ V3)) @ V2)))))))))))
(TProduct_Type.split_beta',(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2))))) @ (^[V1]: ((V0 @ (cProduct_Type.fst @ V1)) @ (cProduct_Type.snd @ V1)))))))
(TProduct_Type.split_curry,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.prod.prod_case @ (cProduct_Type.curry @ V0))) @ V0))))
(TProduct_Type.split_split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TProduct_Type.split_twice,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V0) @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cProduct_Type.prod.prod_case @ V0) @ ((V1 @ V3) @ V4))))) @ V2)))))))))
(TProduct_Type.swap_inj_on,(call @ (^[V0]: ((cFun.inj_on @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cProduct_Type.Pair @ V2) @ V1))))) @ V0))))
(TProduct_Type.unit.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cProduct_Type.Unity)) @ (V0 @ V1)))))))
(TProduct_Type.unit.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.unit.unit_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cProduct_Type.Unity)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TProduct_Type.unit.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.unit.unit_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cProduct_Type.Unity)) @ (V0 @ V1))))))))))
(TPure.sort_constraint_def,((c== @ (cPure.sort_constraint @ cTYPE)) @ (cPure.term @ cTYPE)))
(TQuotient.Quotient3_refl1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V3))))))))))))))
(TQuotient.Quotient3_refl2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V4))))))))))))))
(TQuotient.quot_type.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cEquiv_Relations.part_equivp @ V0)) @ ((c==> @ (call @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V1 @ V3)) @ (cSet.Collect @ (V0 @ V4))))))))) @ ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V2 @ (V1 @ V3))) @ V3)))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ V3) @ (cSet.Collect @ (V0 @ V4))))))) @ ((cHOL.eq @ (V1 @ (V2 @ V3))) @ V3))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V4))) @ ((cHOL.eq @ V3) @ V4))))))) @ (((cQuotient.quot_type @ V0) @ V2) @ V1)))))))))))))
(TRandom.iterate_graph_def,((c== @ cRandom.iterate_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V6)) @ ((cProduct_Type.scomp @ (V5 @ V6)) @ (^[V7]: (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))) @ (cHOL.induct_forall @ (^[V7]: ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))))))))))))))))))
(TRandom.iterate_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.iterate_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ V2)))))))))))) @ V2)))))))))
(TRandom.iterate_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom.iterate_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V3) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ (cHOL.Not @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))))))
(TRandom.log_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.log_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)))) @ ((cRandom.log_graph @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.disj @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ cCode_Numeral.one_natural_inst.one_natural) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ cCode_Numeral.one_natural_inst.one_natural) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.div_natural_inst.div_natural @ V5) @ V4))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom.select_weight_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom.select_weight @ V0)) @ ((cProduct_Type.scomp @ (cRandom.range @ (cList.monoid_add_class.listsum @ ((cList.map @ cProduct_Type.fst) @ V0)))) @ (^[V1]: (cProduct_Type.Pair @ ((cRandom.pick @ V0) @ V1))))))))
(TRandom_Pred.iter'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V9) @ ((cQuickcheck_Random.random_class.random @ V7) @ V8))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V9)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V12) @ V13)) @ V10)) @ ((((V0 @ V5) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7) @ V14)))))))))))))))))))) @ ((((V0 @ V5) @ V6) @ V7) @ V8))))))))))) @ ((((V0 @ V1) @ V2) @ V3) @ V4)))))))))))))
(TRandom_Pred.iter'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ ((((cRandom_Pred.iter' @ V0) @ V1) @ V2) @ V3)) @ V4)) @ ((c==> @ ((cWellfounded.accp @ cRandom_Pred.iter'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V0) @ V6)) @ ((c==> @ ((cHOL.eq @ V1) @ V7)) @ ((c==> @ ((cHOL.eq @ V2) @ V8)) @ ((c==> @ ((cHOL.eq @ V3) @ V9)) @ ((c==> @ ((cHOL.eq @ V4) @ (((cHOL.If @ ((cHOL.eq @ V7) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V8) @ V9)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V10]: (^[V11]: (^[V12]: (cPredicate.Seq @ (^[V13]: ((cPredicate.seq.Insert @ V10) @ ((((cRandom_Pred.iter' @ V6) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V7) @ cCode_Numeral.one_natural_inst.one_natural)) @ V8) @ V12))))))))))))) @ ((c==> @ ((cWellfounded.accp @ cRandom_Pred.iter'_rel) @ ((cProduct_Type.Pair @ V6) @ ((cProduct_Type.Pair @ V7) @ ((cProduct_Type.Pair @ V8) @ V9))))) @ V5))))))))))))))) @ V5))))))))))))))))
(TRandom_Pred.iter'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cRandom_Pred.iter'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))))) @ ((cHOL.eq @ ((((cRandom_Pred.iter' @ V0) @ V1) @ V2) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V2) @ V3)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (^[V6]: (cPredicate.Seq @ (^[V7]: ((cPredicate.seq.Insert @ V4) @ ((((cRandom_Pred.iter' @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2) @ V6))))))))))))))))))))))
(TRandom_Sequence.bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.Let @ (((V0 @ V2) @ V3) @ V4)) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cHOL.Let @ (cRandom.split_seed @ V6)) @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: ((cProduct_Type.Pair @ ((cLimited_Sequence.bind @ V5) @ (^[V9]: (cProduct_Type.fst @ ((((V1 @ V9) @ V2) @ V3) @ V7))))) @ V8))))))))))))))))))
(TRandom_Sequence.iter_def,((c== @ cRandom_Sequence.iter) @ (^[V0]: (^[V1]: (^[V2]: (cRandom_Sequence.iter_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TRecord.iso_tuple_fst_def,(call @ (^[V0]: ((cHOL.eq @ (cRecord.iso_tuple_fst @ V0)) @ ((cFun.comp @ cProduct_Type.fst) @ (cRecord.repr @ V0))))))
(TRecord.iso_tuple_snd_def,(call @ (^[V0]: ((cHOL.eq @ (cRecord.iso_tuple_snd @ V0)) @ ((cFun.comp @ cProduct_Type.snd) @ (cRecord.repr @ V0))))))
(TRelation.Domain_converse,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ (cRelation.converse @ V0))) @ (cRelation.Range @ V0)))))
(TRelation.Domainp.DomainI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((cRelation.Domainp @ V0) @ V1)))))))))
(TRelation.Domainp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRelation.Domainp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ (V2 @ V3))))))) @ (V2 @ V1))))))))))
(TRelation.Image_singleton,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Image @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ (cSet.Collect @ (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)))))))))
(TRelation.Image_subset_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ (cGroups.uminus_class.uminus @ ((cRelation.Image @ (cRelation.converse @ V0)) @ (cGroups.uminus_class.uminus @ V2))))))))))))
(TRelation.Range_empty_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cRelation.Range @ V0)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TRelation.Rangep_Range_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Rangep @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: ((cSet.member @ V1) @ (cRelation.Range @ V0)))))))
(TRelation.converse.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((V3 @ V5) @ V4))))))) @ ((V3 @ V0) @ V1))))))))))))
(TRelation.converse.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ (cRelation.converse @ V2))))))))))
(TRelation.converse_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cRelation.converse @ V0)) @ (cRelation.converse @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TRelation.converse_unfold,(call @ (^[V0]: ((cHOL.eq @ (cRelation.converse @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0)))))))))
(TRelation.conversep.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cRelation.conversep @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ V4)) @ ((c==> @ ((V0 @ V4) @ V5)) @ V3)))))))) @ V3)))))))))))
(TRelation.conversep.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRelation.conversep @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V3)) @ ((V0 @ V3) @ V4)))))))))))))))
(TRelation.conversep_noteq,((cHOL.eq @ (cRelation.conversep @ (^[V0]: (^[V1]: (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))) @ (^[V0]: (^[V1]: (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))
(TRelation.finite_converse,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ (cRelation.converse @ V0))) @ (cFinite_Set.finite @ V0)))))
(TRelation.irrefl_distinct,(call @ (^[V0]: ((cHOL.eq @ (cRelation.irrefl @ V0)) @ ((cSet.Ball @ V0) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (cHOL.Not @ ((cHOL.eq @ V1) @ V2))))))))))
(TRelation.pair_in_Id_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ cRelation.Id)) @ ((cHOL.eq @ V0) @ V1)))))))
(TRelation.pred_equals_eq2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))) @ ((cHOL.eq @ V0) @ V1)))))))
(TRelation.pred_subset_eq2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TRelation.relcomp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cRelation.relcomp @ V2) @ V3))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ V3)) @ ((V4 @ V5) @ V7)))))))))) @ ((V4 @ V0) @ V1))))))))))))))
(TRelation.relcomp_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcomp @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cRelation.relcomp @ V0) @ V1)) @ ((cRelation.relcomp @ V0) @ V2))))))))))
(TRelation.relcompp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRelation.relcompp @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((V0 @ V5) @ V6)) @ ((c==> @ ((V1 @ V6) @ V7)) @ ((V4 @ V5) @ V7)))))))))) @ ((V4 @ V2) @ V3))))))))))))))
(TRelation.relcompp.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V3 @ V2) @ V4)) @ ((((cRelation.relcompp @ V0) @ V3) @ V1) @ V4))))))))))))))
(TRelation.sym_Un_converse,(call @ (^[V0]: (cRelation.sym @ ((cLattices.sup_class.sup @ V0) @ (cRelation.converse @ V0))))))
(TRelation.trans_inv_image,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.trans @ V0)) @ (cRelation.trans @ ((cRelation.inv_image @ V0) @ V1))))))))
(TRelation.transp_trans_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.transp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (cRelation.trans @ V0)))))
(TRings.class.ring_1.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((c==> @ (((((cRings.class.ring @ V2) @ V3) @ V4) @ V5) @ V1)) @ ((c==> @ ((cRings.class.zero_neq_one @ V0) @ V3)) @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))))
(TRings.class.semiring_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.class.semiring @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.conj @ (cGroups.class.semigroup_mult @ V1)) @ ((cRings.class.semiring_axioms @ V0) @ V1)))))))))
(TRings.idom.square_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V6) @ V6)) @ ((V0 @ V7) @ V7))) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V7)) @ ((cHOL.eq @ V6) @ (V5 @ V7))))))))))))))))))))))
(TRings.mult_compare_simps_18,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.one_class.one))))))))
(TRings.mult_compare_simps_17,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.one_class.one))))))))
(TRings.mult_compare_simps_16,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.one_class.one))))))))
(TRings.mult_compare_simps_15,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.one_class.one))))))))
(TRings.mult_compare_simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TRings.mult_compare_simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ V2))))))))))
(TRings.mult_compare_simps_12,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V1)))))))))
(TRings.mult_compare_simps_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.one_class.one)))))))))
(TRings.mult_compare_simps_10,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)))))))))
(TRings.mult_compare_simps_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.one_class.one)))))))))
(TRings.mult_compare_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V1)))))))))))
(TRings.mult_compare_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V0)))))))))))
(TRings.mult_compare_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V1)))))))))
(TRings.mult_compare_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one)))))))))
(TRings.mult_compare_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V0)))))))))
(TRings.mult_compare_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one)))))))))
(TRings.mult_compare_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))))
(TRings.mult_compare_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V2) @ V0)))))))))))
(TRings.ring.ring_distribs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ V5) @ ((V2 @ V6) @ V7))) @ ((V2 @ ((V4 @ V5) @ V6)) @ ((V4 @ V5) @ V7)))))))))))))))))))))
(TRings.ring.ring_distribs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ ((V2 @ V5) @ V6)) @ V7)) @ ((V2 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V7)))))))))))))))))))))
(TRings.ring.ring_distribs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ ((V0 @ V5) @ V6)) @ V7)) @ ((V0 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V7)))))))))))))))))))))
(TRings.ring.ring_distribs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ V5) @ ((V0 @ V6) @ V7))) @ ((V0 @ ((V4 @ V5) @ V6)) @ ((V4 @ V5) @ V7)))))))))))))))))))))
(TRings.ring_1_class.intro,((c==> @ (cGroups.monoid_mult_class @ cTYPE)) @ ((c==> @ (cRings.ring_class @ cTYPE)) @ ((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cRings.ring_1_class @ cTYPE)))))
(TRings.ring_1_class.super_3,((c==> @ (cRings.ring_1_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))
(TRings.ring_1_class.super_2,((c==> @ (cRings.ring_1_class @ cTYPE)) @ (cRings.ring_class @ cTYPE)))
(TRings.ring_1_class.super_1,((c==> @ (cRings.ring_1_class @ cTYPE)) @ (cGroups.monoid_mult_class @ cTYPE)))
(TRings.semiring_class_def,((c== @ (cRings.semiring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.semigroup_mult_class @ cTYPE)) @ ((cRings.class.semiring_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times)))))
(TSMT.arity_random_pattern,(cQuickcheck_Random.random_class @ cTYPE))
(TSMT.term_of_pattern_triv,(call @ (^[V0]: ((cHOL.eq @ (cSMT.term_of_pattern_inst.term_of_pattern @ V0)) @ cHOL.undefined))))
(TSet.Int_insert_right_if0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ ((cSet.insert @ V0) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TSet.Int_insert_right_if1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ ((cSet.insert @ V0) @ V2))) @ ((cSet.insert @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2)))))))))))
(TSet.bot_set_inst.bot_set,((c== @ cSet.bot_set_inst.bot_set) @ cSet.bot_set_inst.bot_set))
(TSet.inf_set_inst.inf_set,((c== @ cSet.inf_set_inst.inf_set) @ cSet.inf_set_inst.inf_set))
(TSet.psubset_subset_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.subset_Compl_self_eq,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TSet.subset_not_subset_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))))
(TSet.subset_psubset_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet.sup_set_inst.sup_set,((c== @ cSet.sup_set_inst.sup_set) @ cSet.sup_set_inst.sup_set))
(TSet.top_set_inst.top_set,((c== @ cSet.top_set_inst.top_set) @ cSet.top_set_inst.top_set))
(TSet_Interval.atLeast_Suc,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ (cNat.Suc @ V0))) @ ((cGroups.minus_class.minus @ (cSet_Interval.ord_class.atLeast @ V0)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))
(TSet_Interval.card_atMost,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ (cSet_Interval.ord_class.atMost @ V0))) @ (cNat.Suc @ V0)))))
(TSet_Interval.ivl_disj_un_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_18,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_14,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ (cSet_Interval.ord_class.atLeast @ V0))))))))
(TSet_Interval.ivl_disj_un_13,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ (cSet_Interval.ord_class.atLeast @ V0))))))))
(TSet_Interval.ivl_disj_un_12,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ (cSet_Interval.ord_class.greaterThan @ V0))))))))
(TSet_Interval.ivl_disj_un_11,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ (cSet_Interval.ord_class.greaterThan @ V0))))))))
(TSet_Interval.ivl_disj_un_10,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.ivl_disj_un_9,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.ivl_disj_un_8,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ (cSet_Interval.ord_class.lessThan @ V1))))))))
(TSet_Interval.ivl_disj_un_7,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ (cSet_Interval.ord_class.lessThan @ V1))))))))
(TSet_Interval.ivl_disj_un_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_2,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ (cSet_Interval.ord_class.atMost @ V0)))))
(TSet_Interval.ivl_disj_un_1,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ (cSet_Interval.ord_class.greaterThan @ V0))) @ (cSet_Interval.ord_class.atLeast @ V0)))))
(TSet_Interval.setsum_head,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V2 @ V3))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (V2 @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V2 @ V3))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))))))))))))
(TString.arity_enum_nibble,(cEnum.enum_class @ cTYPE))
(TString.arity_type_nibble,(cHOL.type_class @ cTYPE))
(TString.char.char_rec_def,((c== @ cString.char.char_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cString.char.char_rec_set @ V0) @ V1) @ V2)))))))
(TString.enum_all_char_def,(call @ (^[V0]: ((cHOL.eq @ (cString.enum_char_inst.enum_all_char @ V0)) @ ((cList.list_all @ V0) @ cString.enum_char_inst.enum_char)))))
(TString.equal_literal_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ (cString.explode @ V0)) @ (cString.explode @ V1))))))))
(TString.inj_nat_of_nibble,((cFun.inj_on @ cString.nat_of_nibble) @ cOrderings.top_class.top))
(TString.literal.STR_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cString.STR @ V2))) @ ((c==> @ ((cSet.member @ V2) @ cOrderings.top_class.top)) @ V1))))) @ V1))))))
(TString.nat_of_char_simps_256,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_255,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_254,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_253,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_252,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_251,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_250,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_249,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_248,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_247,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_246,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_245,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_244,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_243,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_242,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_241,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleF) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_240,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_239,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_238,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_237,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_236,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_235,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_234,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_233,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_232,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_231,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_230,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_229,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_228,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_227,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_226,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_225,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleE) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_224,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_223,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_222,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_221,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_220,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_219,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_218,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_217,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_216,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_215,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_214,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_213,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_212,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_211,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_210,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_209,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleD) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_208,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_207,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_206,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_205,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_204,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_203,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_202,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_201,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_200,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_199,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_198,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_197,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_196,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_195,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_194,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_193,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleC) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_192,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_191,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_190,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_189,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_188,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_187,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_186,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_185,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_184,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_183,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_182,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_181,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_180,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_179,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_178,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_177,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleB) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_176,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_175,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_174,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_173,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_172,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_171,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_170,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_169,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_168,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_167,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_166,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_165,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_164,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_163,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_162,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_161,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.NibbleA) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_160,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_159,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_158,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_157,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_156,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_155,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_154,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_153,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_152,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_151,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_150,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_149,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_148,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_147,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_146,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_145,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble9) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_144,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_143,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_142,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_141,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_140,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_139,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_138,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_137,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_136,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_135,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_134,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_133,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_132,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_131,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_130,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_129,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble8) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nat_of_char_simps_128,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_127,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_126,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_125,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_124,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_123,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_122,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_121,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_120,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_119,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_118,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_117,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_116,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_115,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_114,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_113,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_112,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_111,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_110,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_109,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_108,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_107,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_106,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_105,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_104,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_103,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_102,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_101,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_100,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_99,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_98,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_97,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_96,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_95,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_94,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_93,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_92,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_91,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_90,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_89,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_88,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_87,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_86,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_85,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_84,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_83,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_82,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_81,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_80,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_79,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_78,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_77,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_76,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_75,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_74,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_73,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_72,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_71,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_70,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_69,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_68,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_67,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_66,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_65,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nat_of_char_simps_64,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_63,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_62,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_61,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_60,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_59,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_58,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_57,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_56,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_55,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_54,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_53,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_52,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_51,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_50,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_49,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))))
(TString.nat_of_char_simps_48,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_47,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_46,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_45,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_44,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_43,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_42,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_41,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_40,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_39,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_38,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_37,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_36,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_35,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_34,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_33,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TString.nat_of_char_simps_32,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_31,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_30,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_29,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_28,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_27,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_26,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_25,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))
(TString.nat_of_char_simps_24,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_23,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_22,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_21,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_20,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_19,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_18,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble1))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_17,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble1) @ cString.nibble.Nibble0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TString.nat_of_char_simps_16,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleF))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_char_simps_15,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleE))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_char_simps_14,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleD))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_char_simps_13,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleC))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_char_simps_12,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleB))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_char_simps_11,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.NibbleA))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_char_simps_10,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble9))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_char_simps_9,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble8))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_char_simps_8,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble7))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))
(TString.nat_of_char_simps_7,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble6))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))
(TString.nat_of_char_simps_6,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble5))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))
(TString.nat_of_char_simps_5,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble4))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))
(TString.nat_of_char_simps_4,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble3))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))))
(TString.nat_of_char_simps_3,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble2))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TString.nat_of_char_simps_2,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble1))) @ cNat.one_nat_inst.one_nat))
(TString.nat_of_char_simps_1,((cHOL.eq @ (cString.nat_of_char @ ((cString.char.Char @ cString.nibble.Nibble0) @ cString.nibble.Nibble0))) @ cNat.zero_nat_inst.zero_nat))
(TString.nat_of_nibble_def,((c== @ cString.nat_of_nibble) @ (^[V0]: (((((((((((((((((cString.nibble.nibble_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.one_nat_inst.one_nat) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))) @ V0))))
(TString.nibble.Rep_nibble,(call @ (^[V0]: ((cSet.member @ (cString.Rep_nibble @ V0)) @ (cSet.Collect @ cString.nibble.nibble_rep_set)))))
(TString.nibble_of_nat_def,(call @ (^[V0]: ((cHOL.eq @ (cString.nibble_of_nat @ V0)) @ ((cList.nth @ cString.enum_nibble_inst.enum_nibble) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))
(TSum_Type.Projl.Projl_Inl,(call @ (^[V0]: ((cHOL.eq @ (cSum_Type.Projl @ (cSum_Type.Inl @ V0))) @ V0))))
(TSum_Type.Projr.Projr_Inr,(call @ (^[V0]: ((cHOL.eq @ (cSum_Type.Projr @ (cSum_Type.Inr @ V0))) @ V0))))
(TSum_Type.arity_equal_sum,(cHOL.equal_class @ cTYPE))
(TSum_Type.sum.sum_rec_def,((c== @ cSum_Type.sum.sum_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cSum_Type.sum.sum_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TSum_Type.sum_case_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cSum_Type.sum.sum_case @ V0) @ V1)) @ ((cSum_Type.sum.sum_case @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ V4))) @ V4)))))))))))))
(TTransfer.eq_imp_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.implies)) @ cHOL.eq) @ cHOL.eq)))))
(TTransfer.funpow_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V0)) @ ((cTransfer.fun_rel @ V0) @ V0))) @ cNat.compow) @ cNat.compow))))
(TTransfer.is_equality_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.is_equality @ V0)) @ ((cHOL.eq @ V0) @ cHOL.eq)))))
(TTransfer.rev_implies_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cTransfer.rev_implies @ V0) @ V1)) @ ((cHOL.implies @ V1) @ V0)))))))
(TTransfer.right_total_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.right_total @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TTransfer.right_total_fun,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((c==> @ (cTransfer.right_total @ V1)) @ (cTransfer.right_total @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TTransfer.right_unique_OO,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((c==> @ (cTransfer.right_unique @ V1)) @ (cTransfer.right_unique @ ((cRelation.relcompp @ V0) @ V1)))))))))
(TTransfer.right_unique_eq,(cTransfer.right_unique @ cHOL.eq))
(TTransfer.transfer_start',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ (((cTransfer.Rel @ cHOL.implies) @ V0) @ V1)) @ V1)))))))
(TTyperep.typerep.eq.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cTyperep.typerep.Typerep @ V0) @ V1)) @ ((cTyperep.typerep.Typerep @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TTyperep.typerep.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cTyperep.typerep.Typerep @ V1) @ V2)))))))))
(TTyperep.typerep_bool_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_bool_inst.typerep_bool @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_char_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_char_inst.typerep_char @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_list_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TTyperep.typerep_node_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TTyperep.typerep_prod_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TTyperep.typerep_unit_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_unit_inst.typerep_unit @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ cList.list.Nil)))))
(TWellfounded.acc_downward,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ V1)) @ ((cSet.member @ V2) @ (cWellfounded.acc @ V1)))))))))))
(TWellfounded.accp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ ((cWellfounded.accp @ V0) @ V4))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V1))))))))))
(TWellfounded.less_nat_rel,((cHOL.eq @ cNat.ord_nat_inst.less_nat) @ (cTransitive_Closure.tranclp @ (^[V0]: (^[V1]: ((cHOL.eq @ V1) @ (cNat.Suc @ V0)))))))
(TWellfounded.lex_prod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cWellfounded.lex_prod @ V0) @ V1)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V4)) @ V0)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V5)) @ V1)))))))))))))))))
(TWellfounded.max_extp_def,((c== @ cWellfounded.max_extp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V5)) @ ((cHOL.conj @ (cFinite_Set.finite @ V4)) @ ((cHOL.conj @ (cFinite_Set.finite @ V5)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V5) @ (cSet.Collect @ (^[V6]: (cOrderings.bot_class.bot @ V6)))))) @ (cHOL.induct_forall @ (^[V6]: ((cHOL.induct_implies @ ((cSet.member @ V6) @ V4)) @ ((cSet.Bex @ V5) @ (^[V7]: ((V0 @ V6) @ V7))))))))))))))))))))))
(TWellfounded.not_acc_down,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1)))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V0)) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V3) @ (cWellfounded.acc @ V1)))) @ V2))))) @ V2)))))))))
(TWellfounded.pred_nat_def,((cHOL.eq @ cWellfounded.pred_nat) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cHOL.eq @ V1) @ (cNat.Suc @ V0))))))))
(TWellfounded.wellorder.wf,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ (cWellfounded.wf @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((V1 @ V2) @ V3))))))))))))
(TWellfounded.wfP_accp_iff,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wfP @ V0)) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ V0) @ V1)))))))
(TWellfounded.wfP_acyclicP,(call @ (^[V0]: ((c==> @ (cWellfounded.wfP @ V0)) @ (cTransitive_Closure.acyclic @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2))))))))))
(TWellfounded.wf_comp_self,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ ((cRelation.relcomp @ V0) @ V0))))))
(TWellfounded.wf_inv_image,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ (cWellfounded.wf @ ((cRelation.inv_image @ V0) @ V1))))))))
(TWellfounded.wf_less_than,(cWellfounded.wf @ cWellfounded.less_than))
(TBig_Operators.Inf_fin_Min,((cHOL.eq @ cBig_Operators.semilattice_inf_class.Inf_fin) @ cBig_Operators.linorder_class.Min))
(TBig_Operators.Sup_fin_Max,((cHOL.eq @ cBig_Operators.semilattice_sup_class.Sup_fin) @ cBig_Operators.linorder_class.Max))
(TBig_Operators.abs_setprod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (cGroups.abs_class.abs @ (V0 @ V2)))) @ V1)))))))
(TBig_Operators.card_SigmaI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ (V1 @ V2))))) @ ((cHOL.eq @ (cFinite_Set.card @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cFinite_Set.card @ (V1 @ V2)))) @ V0)))))))))
(TBig_Operators.dvd_setprod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cRings.dvd_class.dvd @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)))))))))))
(TBig_Operators.setprod_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (V1 @ V2)))))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0))))))))
(TBig_Operators.setsum_SucD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ (cNat.Suc @ V2))) @ ((cSet.Bex @ V1) @ (^[V3]: ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (V0 @ V3))))))))))))
(TBig_Operators.setsum_addf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cGroups.plus_class.plus @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V2))))))))))
(TBig_Operators.setsum_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1)))))))))))))
(TBig_Operators.setsum_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cGroups.minus_class.minus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1))))))))))))
(TBig_Operators.setsum_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cOrderings.ord_class.less_eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V1 @ V3))) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V2 @ V3))) @ V0))))))))))
(TBig_Operators.setsum_negf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cGroups.uminus_class.uminus @ (V0 @ V2)))) @ V1)) @ (cGroups.uminus_class.uminus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1))))))))
(TCode_Evaluation.Const_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Evaluation.Const @ V0) @ V1)) @ cCode_Evaluation.term.dummy_term))))))
(TCode_Evaluation.term.recs,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Evaluation.term.term_rec @ V0) @ cCode_Evaluation.term.dummy_term)) @ V0))))
(TCode_Evaluation.term.size_2,((cHOL.eq @ (cCode_Evaluation.term.size_term_inst.size_term @ cCode_Evaluation.term.dummy_term)) @ cNat.zero_nat_inst.zero_nat))
(TCode_Evaluation.term.size_1,((cHOL.eq @ (cCode_Evaluation.term.term_size @ cCode_Evaluation.term.dummy_term)) @ cNat.zero_nat_inst.zero_nat))
(TCode_Numeral.Nat.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_natural) @ cInt.nat) @ cCode_Numeral.Nat))
(TCode_Numeral.Suc.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cCode_Numeral.pcr_natural) @ cNat.Suc) @ cCode_Numeral.Suc))
(TCode_Numeral.dup.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer) @ (^[V0]: ((cInt.plus_int_inst.plus_int @ V0) @ V0))) @ cCode_Numeral.dup))
(TCode_Numeral.natural.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_rec @ V0) @ V1) @ (cCode_Numeral.Suc @ V2))) @ ((V1 @ V2) @ (((cCode_Numeral.natural.natural_rec @ V0) @ V1) @ V2))))))))))
(TCode_Numeral.natural.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_rec @ V0) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ V0))))))
(TCode_Numeral.natural.size_4,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.natural.size_natural_inst.size_natural @ (cCode_Numeral.Suc @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cCode_Numeral.natural.size_natural_inst.size_natural @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TCode_Numeral.natural.size_3,((cHOL.eq @ (cCode_Numeral.natural.size_natural_inst.size_natural @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cNat.zero_nat_inst.zero_nat))
(TCode_Numeral.natural.size_2,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.natural.natural_size @ (cCode_Numeral.Suc @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ (cCode_Numeral.natural.natural_size @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TCode_Numeral.natural.size_1,((cHOL.eq @ (cCode_Numeral.natural.natural_size @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cNat.zero_nat_inst.zero_nat))
(TCode_Numeral.natural_case,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V2))) @ V1)))) @ V1))))))
(TCode_Numeral.natural_decr,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.minus_nat_inst.minus_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ (cCode_Numeral.nat_of_natural @ V0))))))
(TCode_Numeral.sub.transfer,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cCode_Numeral.pcr_integer)) @ (^[V0]: (^[V1]: ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))) @ cCode_Numeral.sub))
(TComplete_Lattices.INT_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cSet.Ball @ V1) @ (^[V3]: ((cSet.member @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.UN_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.UN_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.ball_UN,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))))))))))
(TDatatype.Push_Node_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cDatatype.Push_Node @ V0) @ V1)) @ ((cDatatype.Push_Node @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V2)) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ V4))) @ V4)))))))))))))
(TDatatype.ndepth_Push_Node,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cDatatype.ndepth @ ((cDatatype.Push_Node @ (cSum_Type.Inr @ (cNat.Suc @ V0))) @ V1))) @ (cNat.Suc @ (cDatatype.ndepth @ V1))))))))
(TDivides.div_less_dividend,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.one_nat_inst.one_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ ((cDivides.div_nat_inst.div_nat @ V1) @ V0)) @ V1))))))))
(TDivides.div_mod_equality',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ V1)) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))))))))
(TDivides.div_neg_pos_less0,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_int @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.divmod_int_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cDivides.divmod_int_rel @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cDivides.divmod_int @ V0) @ V1)) @ V2)))))))))
(TDivides.divmod_nat_rel_ex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ V2)))))) @ V2))))))))
(TDivides.divmod_nat_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cDivides.divmod_nat @ V0) @ V1)) @ V2)))))))))
(TDivides.int_div_less_self,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.one_int_inst.one_int) @ V1)) @ ((cInt.ord_int_inst.less_int @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ V0))))))))
(TDivides.mod_div_equality',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ V1))))))))
(TDivides.negDivAlg.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cDivides.negDivAlg_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cDivides.negDivAlg_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.negDivAlg_correct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cDivides.negDivAlg @ V0) @ V1)))))))))
(TDivides.negDivAlg_div_mod,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.negDivAlg @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))))))))))
(TDivides.negDivAlg_rel_def,((c== @ cDivides.negDivAlg_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))))))))))))))
(TDivides.posDivAlg.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cDivides.posDivAlg_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cDivides.posDivAlg_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.posDivAlg_0_right,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.posDivAlg @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V0)))))
(TDivides.posDivAlg_correct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cDivides.posDivAlg @ V0) @ V1)))))))))
(TDivides.posDivAlg_div_mod,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.posDivAlg @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))))))))))
(TDivides.posDivAlg_rel_def,((c== @ cDivides.posDivAlg_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))))))))))))))
(TDivides.zdiv_numeral_Bit0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ ((cDivides.div_int_inst.div_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TDivides.zdiv_numeral_Bit1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ ((cDivides.div_int_inst.div_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TDivides.zmod_numeral_Bit0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cDivides.div_int_inst.mod_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TDivides.zmod_numeral_Bit1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cDivides.div_int_inst.mod_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))) @ cInt.one_int_inst.one_int)))))))
(TDivides.zmult2_lemma_aux1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V2) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ ((cInt.times_int_inst.times_int @ V1) @ V0)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ ((cDivides.div_int_inst.mod_int @ V3) @ V0))) @ V2))))))))))))))
(TDivides.zmult2_lemma_aux2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V2) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ ((cDivides.div_int_inst.mod_int @ V3) @ V0))) @ V2)) @ cInt.zero_int_inst.zero_int)))))))))))))
(TDivides.zmult2_lemma_aux3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V2) @ ((cDivides.div_int_inst.mod_int @ V3) @ V0))) @ V1))))))))))))))
(TDivides.zmult2_lemma_aux4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ ((cInt.ord_int_inst.less_int @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V2) @ ((cDivides.div_int_inst.mod_int @ V3) @ V0))) @ V1)) @ ((cInt.times_int_inst.times_int @ V2) @ V0))))))))))))))
(TEnum.arity_equal_finite_1,(cHOL.equal_class @ cTYPE))
(TEnum.arity_equal_finite_2,(cHOL.equal_class @ cTYPE))
(TEnum.arity_equal_finite_3,(cHOL.equal_class @ cTYPE))
(TEnum.arity_equal_finite_4,(cHOL.equal_class @ cTYPE))
(TEnum.arity_equal_finite_5,(cHOL.equal_class @ cTYPE))
(TEnum.classrel_enum_finite,(cFinite_Set.finite_class @ cTYPE))
(TEnum.enum_class.UNIV_enum,((cHOL.eq @ cOrderings.top_class.top) @ (cList.set @ cEnum.enum_class.enum)))
(TEnum.enum_class.enum_UNIV,((cHOL.eq @ (cList.set @ cEnum.enum_class.enum)) @ cOrderings.top_class.top))
(TEnum.enum_class.enum_eq_I,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((cSet.member @ V1) @ (cList.set @ V0))))) @ ((cHOL.eq @ (cList.set @ cEnum.enum_class.enum)) @ (cList.set @ V0))))))
(TEnum.enum_ex_finite_1_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_1_inst.enum_ex_finite_1 @ V0)) @ (V0 @ cEnum.finite_1.a\<__caret__sub>1)))))
(TEnum.enum_ex_finite_2_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_2_inst.enum_ex_finite_2 @ V0)) @ ((cHOL.disj @ (V0 @ cEnum.finite_2.a\<__caret__sub>1)) @ (V0 @ cEnum.finite_2.a\<__caret__sub>2))))))
(TEnum.enum_ex_finite_3_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_3_inst.enum_ex_finite_3 @ V0)) @ ((cHOL.disj @ (V0 @ cEnum.finite_3.a\<__caret__sub>1)) @ ((cHOL.disj @ (V0 @ cEnum.finite_3.a\<__caret__sub>2)) @ (V0 @ cEnum.finite_3.a\<__caret__sub>3)))))))
(TEnum.enum_ex_finite_4_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_4_inst.enum_ex_finite_4 @ V0)) @ ((cHOL.disj @ (V0 @ cEnum.finite_4.a\<__caret__sub>1)) @ ((cHOL.disj @ (V0 @ cEnum.finite_4.a\<__caret__sub>2)) @ ((cHOL.disj @ (V0 @ cEnum.finite_4.a\<__caret__sub>3)) @ (V0 @ cEnum.finite_4.a\<__caret__sub>4))))))))
(TEnum.enum_ex_finite_5_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_5_inst.enum_ex_finite_5 @ V0)) @ ((cHOL.disj @ (V0 @ cEnum.finite_5.a\<__caret__sub>1)) @ ((cHOL.disj @ (V0 @ cEnum.finite_5.a\<__caret__sub>2)) @ ((cHOL.disj @ (V0 @ cEnum.finite_5.a\<__caret__sub>3)) @ ((cHOL.disj @ (V0 @ cEnum.finite_5.a\<__caret__sub>4)) @ (V0 @ cEnum.finite_5.a\<__caret__sub>5)))))))))
(TEnum.less_eq_finite_1_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.ord_finite_1_inst.less_eq_finite_1 @ V0) @ V1)) @ cHOL.True))))))
(TEnum.less_eq_finite_2_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.ord_finite_2_inst.less_eq_finite_2 @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cEnum.ord_finite_2_inst.less_finite_2 @ V0) @ V1))))))))
(TEnum.less_eq_finite_3_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEnum.ord_finite_3_inst.less_eq_finite_3 @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cEnum.ord_finite_3_inst.less_finite_3 @ V0) @ V1))))))))
(TEquiv_Relations.equiv_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((cHOL.conj @ ((cRelation.refl_on @ V0) @ V1)) @ ((cHOL.conj @ (cRelation.sym @ V1)) @ (cRelation.trans @ V1)))))))))
(TEquiv_Relations.quotientE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ ((cEquiv_Relations.quotient @ V1) @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cRelation.Image @ V2) @ ((cSet.insert @ V4) @ cOrderings.bot_class.bot)))) @ ((c==> @ ((cSet.member @ V4) @ V1)) @ V3))))) @ V3)))))))))))
(TEquiv_Relations.quotientI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ ((cRelation.Image @ V2) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ ((cEquiv_Relations.quotient @ V1) @ V2))))))))))
(TExtraction.conjI_realizer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (V2 @ V3)) @ ((cHOL.conj @ (V0 @ (cProduct_Type.fst @ ((cProduct_Type.Pair @ V1) @ V3)))) @ (V2 @ (cProduct_Type.snd @ ((cProduct_Type.Pair @ V1) @ V3)))))))))))))))
(TExtraction.disjE_realizer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cSum_Type.sum.sum_case @ (^[V6]: (V0 @ V6))) @ (^[V6]: (V1 @ V6))) @ V2)) @ ((c==> @ (call @ (^[V6]: ((c==> @ (V0 @ V6)) @ (V3 @ (V4 @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ (V1 @ V6)) @ (V3 @ (V5 @ V6)))))) @ (V3 @ (((cSum_Type.sum.sum_case @ (^[V6]: (V4 @ V6))) @ (^[V6]: (V5 @ V6))) @ V2))))))))))))))))))
(TExtraction.sumbool.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cExtraction.sumbool.Left)) @ ((c==> @ (V0 @ cExtraction.sumbool.Right)) @ (V0 @ V1))))))))
(TExtraction.sumbool.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cExtraction.sumbool.sumbool_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Left)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Right)) @ (cHOL.Not @ (V0 @ V2)))))))))))))))
(TExtraction.sumbool.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cExtraction.sumbool.sumbool_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Left)) @ (V0 @ V1))) @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Right)) @ (V0 @ V2)))))))))))))
(TFields.class.field.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cFields.class.field_axioms @ V0) @ V1) @ V2) @ V3) @ V5)))))))))))))))))))
(TFields.class.field.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cRings.class.comm_ring_1 @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TFields.field.diff_frac_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V6 @ ((V1 @ V10) @ V8)) @ ((V1 @ V11) @ V9))) @ ((V1 @ ((V6 @ ((V2 @ V10) @ V9)) @ ((V2 @ V11) @ V8))) @ ((V2 @ V8) @ V9)))))))))))))))))))))))))))))))
(TFields.field_class.axioms,(((((cFields.class.field_axioms @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.zero_class.zero))
(TFinite_Set.card_Suc_Diff1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cNat.Suc @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))) @ (cFinite_Set.card @ V0)))))))))
(TFinite_Set.card_UNIV_bool,((cHOL.eq @ (cFinite_Set.card @ cOrderings.top_class.top)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TFinite_Set.card_UNIV_unit,((cHOL.eq @ (cFinite_Set.card @ cOrderings.top_class.top)) @ cNat.one_nat_inst.one_nat))
(TFinite_Set.card_inj_on_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V2))))))))))))
(TFinite_Set.card_insert_if,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.insert @ V1) @ V0))) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (cFinite_Set.card @ V0)) @ (cNat.Suc @ (cFinite_Set.card @ V0))))))))))
(TFinite_Set.card_insert_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ ((cSet.insert @ V1) @ V0)))))))))
(TFinite_Set.card_partition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ V2)) @ V1))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))))) @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V1) @ (cFinite_Set.card @ V0))) @ (cFinite_Set.card @ (cComplete_Lattices.Sup_class.Sup @ V0))))))))))))
(TFinite_Set.finite.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (V1 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ ((cSet.insert @ V3) @ V2))))))))) @ (V1 @ V0)))))))))
(TFinite_Set.finite.insertI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ ((cSet.insert @ V1) @ V0))))))))
(TFinite_Set.finite_Pow_iff,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ (cSet.Pow @ V0))) @ (cFinite_Set.finite @ V0)))))
(TFinite_Set.finite_SigmaI2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ (cHOL.Not @ ((cHOL.eq @ (V1 @ V2)) @ cOrderings.bot_class.bot))))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (cFinite_Set.finite @ (V1 @ V2)))))) @ (cFinite_Set.finite @ ((cProduct_Type.Sigma @ V0) @ V1)))))))))
(TFinite_Set.finite_vimageD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cSet.vimage @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.finite_vimageI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cFun.inj_on @ V1) @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ ((cSet.vimage @ V1) @ V0)))))))))
(TFinite_Set.fold_graph_def,((c== @ cFinite_Set.fold_graph) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V4) @ V1))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cSet.insert @ V5) @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((V0 @ V5) @ V7))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V5) @ V6))) @ ((V2 @ V6) @ V7)))))))))))))))))))
(TFinite_Set.folding.insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V1))) @ ((cHOL.eq @ (((cFinite_Set.folding.F @ V0) @ V3) @ ((cSet.insert @ V2) @ V1))) @ ((V0 @ V2) @ (((cFinite_Set.folding.F @ V0) @ V3) @ V1)))))))))))))))
(TFinite_Set.folding.remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ (((cFinite_Set.folding.F @ V0) @ V3) @ V1)) @ ((V0 @ V2) @ (((cFinite_Set.folding.F @ V0) @ V3) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))))))))
(TFun.bij_betw_the_inv_into,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ (((cFun.bij_betw @ ((cFun.the_inv_into @ V1) @ V0)) @ V2) @ V1)))))))))
(TFun.inj_on_image_set_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V1)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cGroups.minus_class.minus @ V2) @ V3))) @ ((cGroups.minus_class.minus @ ((cSet.image @ V0) @ V2)) @ ((cSet.image @ V0) @ V3)))))))))))))))
(TFunDef.is_measure.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFunDef.is_measure @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ V2)))) @ (V1 @ V0))))))))
(TFunDef.reduction_pair_def,(call @ (^[V0]: ((cHOL.eq @ (cFunDef.reduction_pair @ V0)) @ ((cHOL.conj @ (cWellfounded.wf @ (cProduct_Type.fst @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ (cProduct_Type.fst @ V0)) @ (cProduct_Type.snd @ V0))) @ (cProduct_Type.fst @ V0)))))))
(TGroebner_Basis.bool_simps_34,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.disj @ V0) @ V1)))))))
(TGroebner_Basis.bool_simps_33,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V0)) @ V0))))
(TGroebner_Basis.bool_simps_32,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ cHOL.False) @ V0)) @ V0))))
(TGroebner_Basis.bool_simps_31,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ cHOL.False)) @ V0))))
(TGroebner_Basis.bool_simps_30,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ cHOL.True) @ V0)) @ cHOL.True))))
(TGroebner_Basis.bool_simps_29,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ cHOL.True)) @ cHOL.True))))
(TGroebner_Basis.bool_simps_28,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ (cHOL.Not @ V0)) @ V0)) @ cHOL.False))))
(TGroebner_Basis.bool_simps_27,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ (cHOL.Not @ V0))) @ cHOL.False))))
(TGroebner_Basis.bool_simps_26,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.conj @ V0) @ V1)))))))
(TGroebner_Basis.bool_simps_25,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V0)) @ V0))))
(TGroebner_Basis.bool_simps_24,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ cHOL.False) @ V0)) @ cHOL.False))))
(TGroebner_Basis.bool_simps_23,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ cHOL.False)) @ cHOL.False))))
(TGroebner_Basis.bool_simps_22,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ cHOL.True) @ V0)) @ V0))))
(TGroebner_Basis.bool_simps_21,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ cHOL.True)) @ V0))))
(TGroebner_Basis.bool_simps_20,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ (cHOL.Not @ V0))) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.bool_simps_19,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.bool_simps_18,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ V0)) @ cHOL.True))))
(TGroebner_Basis.bool_simps_17,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ cHOL.True)) @ cHOL.True))))
(TGroebner_Basis.bool_simps_16,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ cHOL.False) @ V0)) @ cHOL.True))))
(TGroebner_Basis.bool_simps_15,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ cHOL.True) @ V0)) @ V0))))
(TGroebner_Basis.bool_simps_14,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.bool_simps_13,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cHOL.False) @ V0)) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.bool_simps_12,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.True)) @ V0))))
(TGroebner_Basis.bool_simps_11,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cHOL.True) @ V0)) @ V0))))
(TGroebner_Basis.bool_simps_10,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ V0) @ (cHOL.Not @ V0))))))
(TGroebner_Basis.bool_simps_9,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cHOL.Not @ V0)) @ V0)))))
(TGroebner_Basis.bool_simps_8,((cHOL.eq @ (cHOL.Not @ cHOL.False)) @ cHOL.True))
(TGroebner_Basis.bool_simps_7,((cHOL.eq @ (cHOL.Not @ cHOL.True)) @ cHOL.False))
(TGroebner_Basis.bool_simps_6,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V0)) @ cHOL.True))))
(TGroebner_Basis.bool_simps_5,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V0)) @ cHOL.True))))
(TGroebner_Basis.bool_simps_4,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ (cHOL.Not @ V0))) @ cHOL.True))))
(TGroebner_Basis.bool_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ V0) @ (cHOL.Not @ V1))))))))
(TGroebner_Basis.bool_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TGroebner_Basis.bool_simps_1,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(TGroups.abel_semigroup_def,(call @ (^[V0]: ((c== @ (cGroups.abel_semigroup @ V0)) @ ((cHOL.conj @ (cGroups.semigroup @ V0)) @ (cGroups.abel_semigroup_axioms @ V0))))))
(TGroups.abs_if_class.intro,((c==> @ (cGroups.abs_class @ cTYPE)) @ ((c==> @ (cGroups.minus_class @ cTYPE)) @ ((c==> @ (cGroups.uminus_class @ cTYPE)) @ ((c==> @ (cGroups.zero_class @ cTYPE)) @ ((c==> @ (cOrderings.ord_class @ cTYPE)) @ ((c==> @ ((((cGroups.class.abs_if @ cGroups.abs_class.abs) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less)) @ (cGroups.abs_if_class @ cTYPE))))))))
(TGroups.abs_if_class.super_5,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ (cOrderings.ord_class @ cTYPE)))
(TGroups.abs_if_class.super_4,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TGroups.abs_if_class.super_3,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE)))
(TGroups.abs_if_class.super_2,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TGroups.abs_if_class.super_1,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ (cGroups.abs_class @ cTYPE)))
(TGroups.class.abs_if.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((cHOL.eq @ (V0 @ V4)) @ (((cHOL.If @ ((V1 @ V4) @ V2)) @ (V3 @ V4)) @ V4))))) @ ((((cGroups.class.abs_if @ V0) @ V3) @ V2) @ V1)))))))))))
(TGroups.class.sgn_if.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: ((cHOL.eq @ (V0 @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ V1)) @ V1) @ (((cHOL.If @ ((V2 @ V1) @ V5)) @ V3) @ (V4 @ V3))))))) @ (((((cGroups.class.sgn_if @ V3) @ V0) @ V4) @ V1) @ V2)))))))))))))
(TGroups.comm_monoid.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.comm_monoid @ V0) @ V1)) @ ((cGroups.comm_monoid_axioms @ V0) @ V1)))))))
(TGroups.comm_monoid.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.comm_monoid @ V0) @ V1)) @ (cGroups.abel_semigroup @ V0)))))))
(TGroups.sgn_if_class.intro,((c==> @ (cGroups.minus_class @ cTYPE)) @ ((c==> @ (cGroups.one_class @ cTYPE)) @ ((c==> @ (cGroups.sgn_class @ cTYPE)) @ ((c==> @ (cGroups.uminus_class @ cTYPE)) @ ((c==> @ (cGroups.zero_class @ cTYPE)) @ ((c==> @ (cOrderings.ord_class @ cTYPE)) @ ((c==> @ (((((cGroups.class.sgn_if @ cGroups.one_class.one) @ cGroups.sgn_class.sgn) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less)) @ (cGroups.sgn_if_class @ cTYPE)))))))))
(TGroups.sgn_if_class.super_6,((c==> @ (cGroups.sgn_if_class @ cTYPE)) @ (cOrderings.ord_class @ cTYPE)))
(TGroups.sgn_if_class.super_5,((c==> @ (cGroups.sgn_if_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TGroups.sgn_if_class.super_4,((c==> @ (cGroups.sgn_if_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE)))
(TGroups.sgn_if_class.super_3,((c==> @ (cGroups.sgn_if_class @ cTYPE)) @ (cGroups.sgn_class @ cTYPE)))
(TGroups.sgn_if_class.super_2,((c==> @ (cGroups.sgn_if_class @ cTYPE)) @ (cGroups.one_class @ cTYPE)))
(TGroups.sgn_if_class.super_1,((c==> @ (cGroups.sgn_if_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TGroups.uminus_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE)))
(TGroups.uminus_class.super,((c==> @ (cGroups.uminus_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(THilbert_Choice.LeastM_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHilbert_Choice.LeastM @ V0) @ V1)) @ (cHilbert_Choice.Eps @ (^[V2]: ((cHOL.conj @ (V1 @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ (V0 @ V3))))))))))))))
(THilbert_Choice.bacc.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHilbert_Choice.bacc @ V0) @ (cNat.Suc @ V1))) @ ((cLattices.sup_class.sup @ ((cHilbert_Choice.bacc @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V2)) @ V0)) @ ((cSet.member @ V3) @ ((cHilbert_Choice.bacc @ V0) @ V1))))))))))))))
(THilbert_Choice.bacc.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cHilbert_Choice.bacc @ V0) @ cNat.zero_nat_inst.zero_nat)) @ (cSet.Collect @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V1)) @ V0))))))))))
(THilbert_Choice.choice_iff,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((V0 @ V2) @ (V1 @ V2))))))))))
(THilbert_Choice.inv_inv_eq,(call @ (^[V0]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0))) @ V0)))))
(THilbert_Choice.some_eq_ex,(call @ (^[V0]: ((cHOL.eq @ (V0 @ (cHilbert_Choice.Eps @ (^[V1]: (V0 @ V1))))) @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))))))
(TInductive.coinduct3_lemma,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ (cInductive.complete_lattice_class.lfp @ (^[V2]: ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ (V1 @ V2)) @ V0)) @ (cInductive.complete_lattice_class.gfp @ V1))))))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.lfp @ (^[V2]: ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ (V1 @ V2)) @ V0)) @ (cInductive.complete_lattice_class.gfp @ V1))))) @ (V1 @ (cInductive.complete_lattice_class.lfp @ (^[V2]: ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ (V1 @ V2)) @ V0)) @ (cInductive.complete_lattice_class.gfp @ V1)))))))))))))
(TInt.arity_comm_ring_1_int,(cRings.comm_ring_1_class @ cTYPE))
(TInt.distrib_right_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ V2))) @ ((cGroups.times_class.times @ V1) @ (cNum.numeral_class.numeral @ V2)))))))))))
(TInt.divide_eq_eq_numeral1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V2)) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V2) @ (cNum.neg_numeral_class.neg_numeral @ V1)))) @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))))))))))
(TInt.divide_eq_eq_numeral1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ (cNum.numeral_class.numeral @ V1))) @ V2)) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V1)) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V2) @ (cNum.numeral_class.numeral @ V1)))) @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))))))))))
(TInt.divide_le_eq_numeral1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V2) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V0)))))))))
(TInt.divide_le_eq_numeral1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ (cNum.numeral_class.numeral @ V1))) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ V2) @ (cNum.numeral_class.numeral @ V1)))))))))))
(TInt.eq_divide_eq_numeral1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cFields.inverse_class.divide @ V1) @ (cNum.neg_numeral_class.neg_numeral @ V2)))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cNum.neg_numeral_class.neg_numeral @ V2))) @ V1)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))))))))))
(TInt.eq_divide_eq_numeral1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cFields.inverse_class.divide @ V1) @ (cNum.numeral_class.numeral @ V2)))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V2)) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ V2))) @ V1)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))))))))))
(TInt.int_ge_less_than2_def,(call @ (^[V0]: ((cHOL.eq @ (cInt.int_ge_less_than2 @ V0)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V2)) @ ((cInt.ord_int_inst.less_int @ V1) @ V2))))))))))
(TInt.le_divide_eq_numeral1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cFields.inverse_class.divide @ V1) @ (cNum.neg_numeral_class.neg_numeral @ V2)))) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ V0) @ (cNum.neg_numeral_class.neg_numeral @ V2)))))))))))
(TInt.le_divide_eq_numeral1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cFields.inverse_class.divide @ V1) @ (cNum.numeral_class.numeral @ V2)))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ V2))) @ V1)))))))))
(TInt.nat0_intermed_int_val,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ (cInt.abs_int_inst.abs_int @ ((cInt.minus_int_inst.minus_int @ (V1 @ ((cNat.plus_nat_inst.plus_nat @ V3) @ cNat.one_nat_inst.one_nat))) @ (V1 @ V3)))) @ cInt.one_int_inst.one_int))))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ (V1 @ cNat.zero_nat_inst.zero_nat)) @ V2)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V2) @ (V1 @ V0))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ V3)) @ V2))))))))))))))
(TInt.ord_int_inst.less_int,((c== @ cInt.ord_int_inst.less_int) @ cInt.ord_int_inst.less_int))
(TInt.ring_1.of_int_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ (cNum.numeral_class.numeral @ V6))) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6))))))))))))))))))
(TInt.ring_1_class.Ints_add,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((c==> @ ((cSet.member @ V1) @ cInt.ring_1_class.Ints)) @ ((cSet.member @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cInt.ring_1_class.Ints))))))))
(TInt.ring_1_class.Ints_def,((cHOL.eq @ cInt.ring_1_class.Ints) @ ((cSet.image @ cInt.ring_1_class.of_int) @ cOrderings.top_class.top)))
(TInt.ring_1_class.of_int_0,((cHOL.eq @ (cInt.ring_1_class.of_int @ cInt.zero_int_inst.zero_int)) @ cGroups.zero_class.zero))
(TInt.ring_1_class.of_int_1,((cHOL.eq @ (cInt.ring_1_class.of_int @ cInt.one_int_inst.one_int)) @ cGroups.one_class.one))
(TLattices.arity_uminus_fun,(cGroups.uminus_class @ cTYPE))
(TLattices.semilattice.idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLattices.semilattice @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V1)) @ V1)))))))
(TLazy_Sequence.append_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.append @ V0) @ V1)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V2]: (((cOption.option.option_case @ (cLazy_Sequence.yield @ V1)) @ (^[V3]: ((cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (cOption.option.Some @ ((cProduct_Type.Pair @ V4) @ ((cLazy_Sequence.append @ V5) @ V1)))))) @ V3))) @ (cLazy_Sequence.yield @ V0))))))))))
(TLazy_Sequence.hb_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.hb_bind @ V0) @ V1)) @ (cLazy_Sequence.hb_flat @ ((cLazy_Sequence.hb_map @ V1) @ V0))))))))
(TLazy_Sequence.hb_flat_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.hb_flat @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ (cList.concat @ ((cList.map @ ((cFun.comp @ (^[V1]: (((cOption.option.option_case @ ((cList.list.Cons @ cOption.option.None) @ cList.list.Nil)) @ (^[V2]: V2)) @ V1))) @ (cOption.map @ cLazy_Sequence.list_of_lazy_sequence))) @ (cLazy_Sequence.list_of_lazy_sequence @ V0))))))))
(TLazy_Sequence.hb_map_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.hb_map @ V0) @ V1)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V2]: ((cOption.map @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cProduct_Type.Pair @ ((cOption.map @ V0) @ V3)) @ ((cLazy_Sequence.hb_map @ V0) @ V4)))))) @ (cLazy_Sequence.yield @ V1))))))))))
(TLazy_Sequence.not_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.not_seq @ V0)) @ (((cOption.option.option_case @ (cLazy_Sequence.single @ cProduct_Type.Unity)) @ (^[V1]: ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.unit.unit_case @ cLazy_Sequence.empty) @ V2)))) @ V1))) @ (cLazy_Sequence.yield @ V0))))))
(TLazy_Sequence.product_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.product @ V0) @ V1)) @ ((cLazy_Sequence.bind @ V0) @ (^[V2]: ((cLazy_Sequence.bind @ V1) @ (^[V3]: (cLazy_Sequence.single @ ((cProduct_Type.Pair @ V2) @ V3))))))))))))
(TLazy_Sequence.single_code,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.single @ V0)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V1]: (cOption.option.Some @ ((cProduct_Type.Pair @ V0) @ cLazy_Sequence.empty))))))))
(TLifting.Quotient_alt_def2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V3 @ V4) @ V5)) @ ((cHOL.eq @ (V1 @ V4)) @ V5))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((V3 @ (V2 @ V4)) @ V4)))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((cHOL.conj @ ((V3 @ V4) @ (V1 @ V5))) @ ((V3 @ V5) @ (V1 @ V4))))))))))))))))))))
(TLifting.Quotient_alt_def3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V3 @ V4) @ V5)) @ ((cHOL.eq @ (V1 @ V4)) @ V5))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((V3 @ (V2 @ V4)) @ V4)))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V0 @ V4) @ V5)) @ (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))))))))))))))
(TLifting.Quotient_alt_def4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V3 @ V4) @ V5)) @ ((cHOL.eq @ (V1 @ V4)) @ V5))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((V3 @ (V2 @ V4)) @ V4)))) @ ((cHOL.eq @ V0) @ ((cRelation.relcompp @ V3) @ (cRelation.conversep @ V3)))))))))))))))
(TLifting.Quotient_bi_total,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cRelation.reflp @ V0)) @ (cTransfer.bi_total @ V3))))))))))))
(TLifting.Quotient_rel_abs2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ (V2 @ V4)) @ V5)) @ ((cHOL.eq @ V4) @ (V1 @ V5)))))))))))))))))
(TLifting.identity_quotient,((((cLifting.Quotient @ cHOL.eq) @ cFun.id) @ cFun.id) @ cHOL.eq))
(TLifting.pcr_Domainp_total,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V1)) @ V2)) @ ((cHOL.eq @ (cRelation.Domainp @ ((cRelation.relcompp @ V1) @ V0))) @ V2))))))))))
(TLifting.rel_pred_comp_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLifting.rel_pred_comp @ V0) @ V1)) @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((V0 @ V2) @ V3)) @ (V1 @ V3)))))))))))
(TLifting.typedef_bi_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ (cTransfer.bi_unique @ V3))))))))))))
(TLifting_Set.Ball_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq)) @ cSet.Ball) @ cSet.Ball))))
(TLifting_Set.Diff_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V0))) @ cGroups.minus_class.minus) @ cGroups.minus_class.minus)))))
(TLifting_Set.UNIV_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ (((cLifting_Set.set_rel @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)))))
(TLifting_Set.bind_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ (cLifting_Set.set_rel @ V1))) @ (cLifting_Set.set_rel @ V1))) @ cSet.bind) @ cSet.bind))))))
(TLifting_Set.card_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ cHOL.eq) @ cFinite_Set.card) @ cFinite_Set.card)))))
(TLifting_Set.reflp_set_rel,(call @ (^[V0]: ((c==> @ (cRelation.reflp @ V0)) @ (cRelation.reflp @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Sum.reflp_sum_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ (cRelation.reflp @ V1)) @ (cRelation.reflp @ ((cLifting_Sum.sum_rel @ V0) @ V1)))))))))
(TLifting_Sum.sum_rel_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting_Sum.sum_rel @ V0) @ V1) @ (cSum_Type.Inr @ V2)) @ (cSum_Type.Inr @ V3))) @ ((V1 @ V2) @ V3)))))))))))
(TLifting_Sum.sum_rel_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting_Sum.sum_rel @ V0) @ V1) @ (cSum_Type.Inr @ V2)) @ (cSum_Type.Inl @ V3))) @ cHOL.False))))))))))
(TLifting_Sum.sum_rel_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting_Sum.sum_rel @ V0) @ V1) @ (cSum_Type.Inl @ V2)) @ (cSum_Type.Inr @ V3))) @ cHOL.False))))))))))
(TLifting_Sum.sum_rel_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLifting_Sum.sum_rel @ V0) @ V1) @ (cSum_Type.Inl @ V2)) @ (cSum_Type.Inl @ V3))) @ ((V0 @ V2) @ V3)))))))))))
(TLimited_Sequence.bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (((cHOL.If @ V3) @ (cOption.option.Some @ cLazy_Sequence.empty)) @ cOption.option.None)) @ (((cOption.option.option_case @ cOption.option.None) @ (^[V4]: ((((cLimited_Sequence.map_seq @ V1) @ V4) @ V2) @ V3))) @ ((V0 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ V3)))))))))))
(TLimited_Sequence.eval_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLimited_Sequence.eval @ V0) @ V1) @ V2)) @ ((V0 @ V1) @ V2)))))))))
(TList.all_interval_int_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.all_interval_int @ V0) @ V1) @ V2)) @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2)) @ (^[V3]: (V0 @ V3)))))))))))
(TList.all_interval_nat_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.all_interval_nat @ V0) @ V1) @ V2)) @ ((cSet.Ball @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2)) @ (^[V3]: (V0 @ V3)))))))))))
(TList.all_set_conv_all_nth,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ (V1 @ ((cList.nth @ V0) @ V2)))))))))))
(TList.append_in_lists_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cList.append @ V0) @ V1)) @ (cList.lists @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ (cList.lists @ V2))) @ ((cSet.member @ V1) @ (cList.lists @ V2)))))))))))
(TList.atLeastLessThan_upto,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ (cList.set @ ((cList.upto @ V0) @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int)))))))))
(TList.card_lists_length_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ V0)) @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ V1)))))) @ ((cPower.power_class.power @ (cFinite_Set.card @ V0)) @ V1))))))))
(TList.card_lists_length_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V2)) @ V1)))))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: ((cPower.power_class.power @ (cFinite_Set.card @ V0)) @ V2))) @ (cSet_Interval.ord_class.atMost @ V1)))))))))
(TList.concat_eq_concat_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ ((cList.zip @ V0) @ V1))) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.size_class.size @ V3))))))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ (cList.concat @ V0)) @ (cList.concat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TList.concat_map_singleton,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.concat @ ((cList.map @ (^[V2]: ((cList.list.Cons @ (V0 @ V2)) @ cList.list.Nil))) @ V1))) @ ((cList.map @ V0) @ V1)))))))
(TList.distinct_list_update,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.distinct @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ ((cGroups.minus_class.minus @ (cList.set @ V0)) @ ((cSet.insert @ ((cList.nth @ V0) @ V2)) @ cOrderings.bot_class.bot))))) @ (cList.distinct @ (((cList.list_update @ V0) @ V2) @ V1)))))))))))
(TList.finite_distinct_list,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cHOL.eq @ (cList.set @ V1)) @ V0)) @ (cList.distinct @ V1))))))))
(TList.in_listrel1_converse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel1 @ (cRelation.converse @ V2)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ (cList.listrel1 @ V2)))))))))))
(TList.left_total_list_all2,(call @ (^[V0]: ((c==> @ (cLifting.left_total @ V0)) @ (cLifting.left_total @ (cList.list_all2 @ V0))))))
(TList.length_pos_if_in_set,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V1))))))))
(TList.lexord_append_rightI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ V4))))))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ ((cList.append @ V1) @ V0))) @ (cList.lexord @ V2))))))))))
(TList.lexord_partial_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ V4) @ (cList.set @ V0))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V6)) @ V1))))))))))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ (cList.lexord @ V1))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ (cList.lexord @ V1))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cList.lexord @ V1))))))))))))))
(TList.linorder.filter_sort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.filter @ V2) @ (((cList.linorder.sort_key @ V0) @ V3) @ V4))) @ (((cList.linorder.sort_key @ V0) @ V3) @ ((cList.filter @ V2) @ V4)))))))))))))))
(TList.linorder.length_sort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cNat.size_class.size @ (((cList.linorder.sort_key @ V0) @ V2) @ V3))) @ (cNat.size_class.size @ V3))))))))))))
(TList.linorder.sorted.Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: ((V0 @ V3) @ V4)))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V3) @ V2))))))))))))))
(TList.linorder.sorted_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ ((cList.linorder.sorted @ V0) @ V3)) @ ((cSet.Ball @ (cList.set @ V3)) @ (^[V4]: ((V0 @ V2) @ V4)))))))))))))))
(TList.linorder.sorted_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((cList.drop @ V3) @ V2)))))))))))))
(TList.linorder.sorted_many,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V3) @ V4))) @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4)))))))))))))))))
(TList.linorder.sorted_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cList.linorder.sorted @ V0) @ ((cList.filter @ (^[V4]: ((cHOL.eq @ V4) @ (V2 @ V3)))) @ V3))))))))))))
(TList.linorder.sorted_sort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cList.linorder.sorted @ V0) @ (((cList.linorder.sort_key @ V0) @ (^[V3]: V3)) @ V2))))))))))
(TList.linorder.sorted_take,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((cList.take @ V3) @ V2)))))))))))))
(TList.list.Abs_list_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cList.list.list_rep_set))) @ (V0 @ (cList.Abs_list @ V2)))))) @ (V0 @ V1)))))))
(TList.list.Abs_list_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cList.list.list_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cList.list.list_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cList.Abs_list @ V0)) @ (cList.Abs_list @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TList.list.Rep_list_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cList.list.list_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cList.Rep_list @ V2))))) @ (V1 @ V0))))))))
(TList.list.Rep_list_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cList.Rep_list @ V0)) @ (cList.Rep_list @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TList.list.arity_size_list,(cNat.size_class @ cTYPE))
(TList.list_nonempty_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((c==> @ (call @ (^[V2]: (V1 @ ((cList.list.Cons @ V2) @ cList.list.Nil))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cList.list.Nil))) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cList.list.Cons @ V2) @ V3))))))))) @ (V1 @ V0)))))))))
(TList.list_size_estimation,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ (V3 @ V0))) @ ((cNat.ord_nat_inst.less_nat @ V2) @ ((cList.list.list_size @ V3) @ V1)))))))))))))
(TList.list_update_nonempty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (((cList.list_update @ V0) @ V1) @ V2)) @ cList.list.Nil)) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))))))
(TList.list_update_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ ((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ V0) @ (cList.list_all2 @ V0)))) @ cList.list_update) @ cList.list_update))))
(TList.listrel_rtrancl_refl,(call @ (^[V0]: (call @ (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V0)) @ (cList.listrel @ (cTransitive_Closure.rtrancl @ V1))))))))
(TList.map.compositionality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.map @ V1) @ V2))) @ ((cList.map @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TList.map_eq_imp_length_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cList.map @ V0) @ V1)) @ ((cList.map @ V2) @ V3))) @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V3))))))))))))
(TList.map_removeAll_inj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ ((cSet.insert @ V1) @ (cList.set @ V2)))) @ ((cHOL.eq @ ((cList.map @ V0) @ ((cList.removeAll @ V1) @ V2))) @ ((cList.removeAll @ (V0 @ V1)) @ ((cList.map @ V0) @ V2)))))))))))
(TList.monoid_add.listsum_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ (^[V3]: V1)) @ V2))) @ V1)))))))))
(TList.nth_length_takeWhile,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ (cNat.size_class.size @ ((cList.takeWhile @ V0) @ V1))) @ (cNat.size_class.size @ V1))) @ (cHOL.Not @ (V0 @ ((cList.nth @ V1) @ (cNat.size_class.size @ ((cList.takeWhile @ V0) @ V1)))))))))))
(TList.remdups_adj_Cons_alt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list.Cons @ V0) @ (cList.tl @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ V1))))) @ (cList.remdups_adj @ ((cList.list.Cons @ V0) @ V1))))))))
(TList.remdups_adj_distinct,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ (cList.remdups_adj @ V0)) @ V0)))))
(TList.remdups_adj_sumC_def,((c== @ cList.remdups_adj_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cList.remdups_adj_graph @ V0) @ V1))))))
(TList.remdups_adj_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cList.list_all2 @ V0)) @ (cList.list_all2 @ V0)) @ cList.remdups_adj) @ cList.remdups_adj)))))
(TList.removeAll_filter_not,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ (V0 @ V1))) @ ((cHOL.eq @ ((cList.removeAll @ V1) @ ((cList.filter @ V0) @ V2))) @ ((cList.filter @ V0) @ V2))))))))))
(TList.set_minus_filter_out,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cList.set @ V0)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ (cList.set @ ((cList.filter @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ V2) @ V1)))) @ V0))))))))
(TList.splice_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.splice_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cProduct_Type.Pair @ cList.list.Nil) @ V4)) @ V4)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ cList.list.Nil)) @ ((cList.list.Cons @ V4) @ V5))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cList.splice_graph @ ((cProduct_Type.Pair @ V5) @ V7)) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ V5) @ V7)) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))) @ ((V2 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V6) @ V7))) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V6) @ (V3 @ ((cProduct_Type.Pair @ V5) @ V7)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))))
(TList.split_list_last_prop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ ((cHOL.conj @ (V1 @ V3)) @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V5]: (cHOL.Not @ (V1 @ V5))))))))))))))))))
(TList.transpose_max_length,(call @ (^[V0]: ((cHOL.eq @ (((cList.foldr @ (^[V1]: (cOrderings.ord_class.max @ (cNat.size_class.size @ V1)))) @ (cList.transpose @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ (cNat.size_class.size @ ((cList.filter @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V1) @ cList.list.Nil)))) @ V0))))))
(TList.transpose_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.transpose_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ V3) @ ((cList.list.Cons @ cList.list.Nil) @ V3))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5)))) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.transpose_rel.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cList.transpose_rel @ ((cList.list.Cons @ V0) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V3]: (^[V4]: ((cList.list.Cons @ V4) @ cList.list.Nil))))) @ V1)))) @ ((cList.list.Cons @ ((cList.list.Cons @ V2) @ V0)) @ V1)))))))))
(TList.transpose_rel.intros_1,(call @ (^[V0]: ((cList.transpose_rel @ V0) @ ((cList.list.Cons @ cList.list.Nil) @ V0)))))
(TList.type_definition_list,(((cTypedef.type_definition @ cList.Rep_list) @ cList.Abs_list) @ (cSet.Collect @ cList.list.list_rep_set)))
(TMain.arity_random_sumbool,(cQuickcheck_Random.random_class @ cTYPE))
(TMain.term_of_sumbool_triv,(call @ (^[V0]: ((cHOL.eq @ (cMain.term_of_sumbool_inst.term_of_sumbool @ V0)) @ cHOL.undefined))))
(TMap.dom_eq_singleton_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cMap.dom @ V0)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ (((cFun.fun_upd @ (^[V3]: cOption.option.None)) @ V1) @ (cOption.option.Some @ V2)))))))))))
(TMap.fun_upd_None_restrict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cFun.fun_upd @ ((cMap.restrict_map @ V0) @ V1)) @ V2) @ cOption.option.None)) @ (((cHOL.If @ ((cSet.member @ V2) @ V1)) @ ((cMap.restrict_map @ V0) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ ((cMap.restrict_map @ V0) @ V1))))))))))
(TMap.fun_upd_restrict_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ (((cFun.fun_upd @ ((cMap.restrict_map @ V2) @ V1)) @ V0) @ V3)) @ (((cFun.fun_upd @ ((cMap.restrict_map @ V2) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))) @ V0) @ V3))))))))))))
(TMap.fun_upds_append2_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (((cMap.map_upds @ V2) @ V0) @ ((cList.append @ V1) @ V3))) @ (((cMap.map_upds @ V2) @ V0) @ V1))))))))))))
(TMap.map_add_dom_app_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cMap.dom @ V1)))) @ ((cHOL.eq @ (((cMap.map_add @ V2) @ V1) @ V0)) @ (V2 @ V0))))))))))
(TMap.map_add_dom_app_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cMap.dom @ V1)))) @ ((cHOL.eq @ (((cMap.map_add @ V1) @ V2) @ V0)) @ (V2 @ V0))))))))))
(TMap.map_add_dom_app_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cMap.dom @ V1))) @ ((cHOL.eq @ (((cMap.map_add @ V2) @ V1) @ V0)) @ (V1 @ V0))))))))))
(TMap.map_le_implies_dom_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cMap.map_le @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cMap.dom @ V0)) @ (cMap.dom @ V1))))))))
(TMap.map_upds_apply_nontin,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((cHOL.eq @ ((((cMap.map_upds @ V2) @ V1) @ V3) @ V0)) @ (V2 @ V0))))))))))))
(TMap.map_upds_fold_map_upd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cMap.map_upds @ V0) @ V1) @ V2)) @ (((cList.foldl @ (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (((cFun.fun_upd @ V3) @ V4) @ (cOption.option.Some @ V5))))))) @ V0) @ ((cList.zip @ V1) @ V2))))))))))
(TMap.restrict_map_to_empty,(call @ (^[V0]: ((cHOL.eq @ ((cMap.restrict_map @ V0) @ cOrderings.bot_class.bot)) @ (^[V1]: cOption.option.None)))))
(TNat.Suc_diff_eq_diff_pred,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V1)) @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)))))))))
(TNat.Suc_mult_less_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cNat.times_nat_inst.times_nat @ (cNat.Suc @ V0)) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)))))))))
(TNat.diff_Suc_eq_diff_pred,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.Suc @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ V1)))))))
(TNat.dvd.dual_order.irrefl,(call @ (^[V0]: (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V0)))))))
(TNat.dvd.le_imp_less_or_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.dvd.less_imp_not_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))))) @ cHOL.True)))))))
(TNat.dvd.ord_eq_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.dvd.ord_less_eq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.less_imp_add_positive,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ V1))))))))))
(TNat.less_mono_imp_le_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V4)) @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V3)) @ (V0 @ V4)))))))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat.nat.nat_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.nat.nat_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V2) @ (cNat.Suc @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ ((V1 @ V5) @ V6))) @ ((c==> @ ((((cNat.nat.nat_rec_set @ V0) @ V1) @ V5) @ V6)) @ V4)))))))) @ V4))))))))))))))
(TNat.nat.nat_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNat.nat.nat_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V3) @ V0))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cNat.Suc @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((V1 @ V4) @ V5))) @ ((((cNat.nat.nat_rec_set @ V0) @ V1) @ V4) @ V5))))))))))))))))))
(TNat.ord_nat_inst.less_nat,((c== @ cNat.ord_nat_inst.less_nat) @ cNat.ord_nat_inst.less_nat))
(TNat.semiring_1.Nats_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V4) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6))) @ V5)))) @ V5))))))))))))))))
(TNat.semiring_1.of_nat_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ (cNat.Suc @ V4))) @ ((V2 @ V0) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)))))))))))))))
(TNat.semiring_1.of_nat_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V5))) @ ((V2 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V5)))))))))))))))))
(TNat.semiring_1.of_nat_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ (((cNat.compow @ V4) @ (V2 @ V0)) @ V3))))))))))))))
(TNitpick.arity_random_word,(cQuickcheck_Random.random_class @ cTYPE))
(TNitpick.equal_fun_box_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.fold_graph'.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNitpick.fold_graph' @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)) @ ((c==> @ ((cHOL.eq @ V3) @ V6)) @ V4))))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V0) @ V7)) @ ((c==> @ ((cHOL.eq @ V1) @ V8)) @ ((c==> @ ((cHOL.eq @ V2) @ V6)) @ ((c==> @ ((cHOL.eq @ V3) @ ((V7 @ V5) @ V9))) @ ((c==> @ ((cSet.member @ V5) @ V6)) @ ((c==> @ ((((cNitpick.fold_graph' @ V7) @ V8) @ ((cGroups.minus_class.minus @ V6) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ V9)) @ V4))))))))))))))))) @ V4))))))))))))))
(TNitpick.fold_graph'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNitpick.fold_graph' @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V3) @ V5))))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V6)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V7)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((V6 @ V4) @ V8))) @ ((cHOL.conj @ ((cSet.member @ V4) @ V5)) @ ((((cNitpick.fold_graph' @ V6) @ V7) @ ((cGroups.minus_class.minus @ V5) @ ((cSet.insert @ V4) @ cOrderings.bot_class.bot))) @ V8)))))))))))))))))))))))))))
(TNitpick.fun_box.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cNitpick.fun_box.FunBox @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cNitpick.fun_box.fun_box_case @ V2) @ V0)) @ ((cNitpick.fun_box.fun_box_case @ V3) @ V1)))))))))))))
(TNitpick.fun_box.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.fun_box.fun_box_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cNitpick.fun_box.FunBox @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TNitpick.nat_gcd_graph_def,((c== @ cNitpick.nat_gcd_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat)) @ V4) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat))) @ ((V0 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))))))))))))))))
(TNitpick.nat_gcd_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.nat_gcd_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))) @ V2)))))))) @ V2)))))))))
(TNitpick.nat_gcd_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.nat_gcd_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cDivides.div_nat_inst.mod_nat @ V2) @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.eq @ V3) @ cNat.zero_nat_inst.zero_nat))))))))))))))
(TNitpick.norm_frac.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cNitpick.norm_frac_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cNitpick.norm_frac_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((V2 @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.norm_frac_rel_def,((c== @ cNitpick.norm_frac_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)))))))))))))
(TNitpick.pair_box.eq.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cNitpick.pair_box.PairBox @ V0) @ V1)) @ ((cNitpick.pair_box.PairBox @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TNitpick.pair_box.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cNitpick.pair_box.PairBox @ V1) @ V2)))))))))
(TNitpick.term_of_word_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TNitpick.word.word_rec_def,((c== @ cNitpick.word.word_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cNitpick.word.word_rec_set @ V0) @ V1) @ V2)))))))
(TNum.Suc_nat_number_of_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ V0)) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))) @ V1)))))))
(TNum.class.neg_numeral_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ (cNum.class.numeral @ V1))))))))))))
(TNum.class.ring_char_0_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TNum.neg_numeral.dbl_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cNum.neg_numeral.dbl @ V1) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))) @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.num.Bit0 @ V5)))))))))))))))))
(TNum.neg_numeral.dbl_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cNum.neg_numeral.dbl @ V1) @ V4)) @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))
(TNum.neg_numeral.dbl_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cNum.neg_numeral.dbl @ V1) @ V2)) @ V2)))))))))))
(TNum.neg_numeral.dbl_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cNum.neg_numeral.dbl @ V1) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ (cNum.num.Bit0 @ V5)))))))))))))))))
(TNum.neg_numeral.minus_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ V4)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ cNum.num.One))))))))))))))
(TNum.neg_numeral_class_def,((c== @ (cNum.neg_numeral_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.group_add_class @ cTYPE)) @ (cNum.numeral_class @ cTYPE))))
(TNum.num.num_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cNum.num.One)) @ ((c==> @ ((cHOL.eq @ V4) @ V0)) @ V5))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V3) @ (cNum.num.Bit0 @ V6))) @ ((c==> @ ((cHOL.eq @ V4) @ ((V1 @ V6) @ V7))) @ ((c==> @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V6) @ V7)) @ V5)))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V3) @ (cNum.num.Bit1 @ V6))) @ ((c==> @ ((cHOL.eq @ V4) @ ((V2 @ V6) @ V7))) @ ((c==> @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V6) @ V7)) @ V5)))))))) @ V5)))))))))))))))))
(TNum.num.num_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cNum.num.One)) @ ((cHOL.eq @ V4) @ V0))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cNum.num.Bit0 @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((V1 @ V5) @ V6))) @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V5) @ V6)))))))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cNum.num.Bit1 @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((V2 @ V5) @ V6))) @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V5) @ V6)))))))))))))))))))))
(TNum.numeral.numeral.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit1 @ V2))) @ ((V0 @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (((cNum.numeral.numeral @ V1) @ V0) @ V2))) @ V1))))))))))
(TNum.numeral.numeral.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit0 @ V2))) @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)))))))))))
(TNum.numeral.numeral.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ cNum.num.One)) @ V1)))))))
(TNum.ord_num_inst.less_num,((c== @ cNum.ord_num_inst.less_num) @ cNum.ord_num_inst.less_num))
(TNum.ring_1_class.iszero_0,(cNum.ring_1_class.iszero @ cGroups.zero_class.zero))
(TNum.ring_char_0_class_def,((c== @ (cNum.ring_char_0_class @ cTYPE)) @ ((cPure.conjunction @ (cNat.semiring_char_0_class @ cTYPE)) @ (cRings.ring_1_class @ cTYPE))))
(TOption.arity_equal_option,(cHOL.equal_class @ cTYPE))
(TOption.option_map_eq_Some,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cOption.map @ V0) @ V1)) @ (cOption.option.Some @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cOption.option.Some @ V3))) @ ((cHOL.eq @ (V0 @ V3)) @ V2))))))))))))
(TOption.option_map_is_None,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cOption.map @ V0) @ V1)) @ cOption.option.None)) @ ((cHOL.eq @ V1) @ cOption.option.None)))))))
(TOption.these_not_empty_eq,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ (cOption.these @ V0)) @ cOrderings.bot_class.bot))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ (cHOL.Not @ ((cHOL.eq @ V0) @ ((cSet.insert @ cOption.option.None) @ cOrderings.bot_class.bot))))))))
(TOrderings.arity_order_fun,(cOrderings.order_class @ cTYPE))
(TOrderings.bot_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cOrderings.bot_class @ cTYPE)))
(TOrderings.bot_class.super,((c==> @ (cOrderings.bot_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TOrderings.class.order_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.preorder @ V0) @ V1)) @ (cOrderings.class.order_axioms @ V0))))))))
(TOrderings.linorder.linear,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.disj @ ((V0 @ V2) @ V3)) @ ((V0 @ V3) @ V2))))))))))))
(TOrderings.linorder.not_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((V0 @ V2) @ V3))) @ ((V1 @ V3) @ V2))))))))))))
(TOrderings.linorder_linear,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TOrderings.linorder_not_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TOrderings.ord_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cOrderings.ord_class @ cTYPE)))
(TOrderings.ord_class.super,((c==> @ (cOrderings.ord_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TOrderings.ord_eq_le_subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.ord_le_eq_subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_class_def,((c== @ (cOrderings.order_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.preorder_class @ cTYPE)) @ (cOrderings.class.order_axioms @ cOrderings.ord_class.less_eq))))
(TOrderings.order_less_asym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V2)) @ ((cOrderings.ord_class.less @ V1) @ V0))) @ V2)))))))))
(TOrderings.ordering.irrefl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ (cHOL.Not @ ((V1 @ V2) @ V2))))))))))
(TOrderings.rev_predicate1D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ (V2 @ V1))))))))))
(TOrderings.rev_predicate2D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V3)) @ ((V3 @ V1) @ V2))))))))))))
(TOrderings.top_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cOrderings.top_class @ cTYPE)))
(TOrderings.top_class.super,((c==> @ (cOrderings.top_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TPartial_Function.let_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (((cComplete_Partial_Order.monotone @ V0) @ V1) @ (^[V5]: ((V2 @ V5) @ V4)))))) @ (((cComplete_Partial_Order.monotone @ V0) @ V1) @ (^[V4]: ((cHOL.Let @ V3) @ (V2 @ V4))))))))))))))
(TPower.power.power.power_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ cNat.zero_nat_inst.zero_nat)) @ V0))))))))
(TPower.power2_nat_le_eq_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TPower.ring_1.power2_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ (V5 @ V6)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V0) @ V1) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))))))))
(TPredicate.arity_equal_seq,(cHOL.equal_class @ cTYPE))
(TPredicate.arity_type_pred,(cHOL.type_class @ cTYPE))
(TPredicate.contained.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.contained @ ((cPredicate.seq.Join @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cPredicate.contained @ V1) @ V2))))))))))
(TPredicate.contained.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.contained @ ((cPredicate.seq.Insert @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cPredicate.eval @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TPredicate.contained.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cPredicate.contained @ cPredicate.seq.Empty) @ V0)) @ cHOL.True))))
(TPredicate.eval_singletonI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: ((cPredicate.eval @ V0) @ V2)))) @ ((cPredicate.eval @ V0) @ ((cPredicate.singleton @ V1) @ V0))))))))
(TPredicate.pred_of_seq_def,((c== @ cPredicate.pred_of_seq) @ (^[V0]: ((((cPredicate.seq.seq_rec @ cOrderings.bot_class.bot) @ (^[V1]: (^[V2]: ((cLattices.sup_class.sup @ (cPredicate.single @ V1)) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: ((cLattices.sup_class.sup @ V1) @ V3))))) @ V0))))
(TPredicate.pred_of_set_def,((cHOL.eq @ cPredicate.pred_of_set) @ ((cFun.comp @ cPredicate.pred.Pred) @ (^[V0]: (^[V1]: ((cSet.member @ V1) @ V0))))))
(TPredicate.seq.seq_rec_def,((c== @ cPredicate.seq.seq_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cHOL.The @ (^[V4]: (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)))))))))
(TPredicate.set_of_pred_def,((cHOL.eq @ cPredicate.set_of_pred) @ ((cFun.comp @ cSet.Collect) @ cPredicate.eval)))
(TPredicate.uminus_pred_def,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cPredicate.pred.Pred @ (cGroups.uminus_class.uminus @ (cPredicate.eval @ V0)))))))
(TPredicate.unit_pred_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cOrderings.bot_class.bot)) @ ((c==> @ (V0 @ (cPredicate.single @ cProduct_Type.Unity))) @ (V0 @ V1))))))))
(TPresburger.unity_coeff_ex,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (cHOL.Ex @ (^[V2]: (V0 @ ((cGroups.times_class.times @ V1) @ V2))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ ((cGroups.plus_class.plus @ V2) @ cGroups.zero_class.zero))) @ (V0 @ V2))))))))))
(TProduct_Type.If_case_cert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c== @ V0) @ (^[V3]: (((cHOL.If @ V3) @ V1) @ V2)))) @ ((cPure.conjunction @ ((c== @ (V0 @ cHOL.True)) @ V1)) @ ((c== @ (V0 @ cHOL.False)) @ V2))))))))))
(TProduct_Type.Pair_Rep_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.Pair_Rep @ V0) @ V1)) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V0)) @ ((cHOL.eq @ V3) @ V1))))))))))
(TProduct_Type.Sigma_empty1,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.Sigma @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TProduct_Type.Sigma_empty2,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V1]: cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot))))
(TProduct_Type.The_split_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.The @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))) @ ((cProduct_Type.Pair @ V0) @ V1)))))))
(TProduct_Type.bool.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TProduct_Type.bool.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cHOL.True)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cHOL.False)) @ V1)) @ V1)))))))
(TProduct_Type.bool.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cHOL.True)) @ ((c==> @ (V0 @ cHOL.False)) @ (V0 @ V1))))))))
(TProduct_Type.fst_map_pair,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cProduct_Type.fst @ (((cProduct_Type.map_pair @ V0) @ V1) @ V2))) @ (V0 @ (cProduct_Type.fst @ V2))))))))))
(TProduct_Type.map_pair_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.map_pair @ V0) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ (V0 @ V2)) @ (V1 @ V3)))))))))))
(TProduct_Type.prod.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TProduct_Type.prod.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TProduct_Type.prod.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cProduct_Type.Pair @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TProduct_Type.prod_caseI2',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)) @ (((V1 @ V3) @ V4) @ V2))))))) @ (((cProduct_Type.prod.prod_case @ V1) @ V0) @ V2)))))))))
(TProduct_Type.prod_induct3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (V0 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))))))))) @ (V0 @ V1)))))))
(TProduct_Type.prod_induct4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (V0 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))))) @ (V0 @ V1)))))))
(TProduct_Type.prod_induct5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (V0 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))))))))))))))) @ (V0 @ V1)))))))
(TProduct_Type.prod_induct6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (V0 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7))))))))))))))))))) @ (V0 @ V1)))))))
(TProduct_Type.prod_induct7,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (V0 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ ((cProduct_Type.Pair @ V7) @ V8)))))))))))))))))))))) @ (V0 @ V1)))))))
(TProduct_Type.scomp_unfold,((cHOL.eq @ cProduct_Type.scomp) @ (^[V0]: (^[V1]: (^[V2]: ((V1 @ (cProduct_Type.fst @ (V0 @ V2))) @ (cProduct_Type.snd @ (V0 @ V2))))))))
(TProduct_Type.snd_prod_fun,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cProduct_Type.snd @ (((cProduct_Type.map_pair @ V0) @ V1) @ V2))) @ (V1 @ (cProduct_Type.snd @ V2))))))))))
(TProduct_Type.swap_product,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ V3) @ V2))))) @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1)))) @ ((cProduct_Type.Sigma @ V1) @ (^[V2]: V0))))))))
(TProduct_Type.times_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V4]: V1))) @ ((cProduct_Type.Sigma @ V2) @ (^[V4]: V3)))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.conj @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))))))))))))))
(TProduct_Type.unit.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TProduct_Type.unit.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cProduct_Type.Unity)) @ V1)) @ V1))))))
(TProduct_Type.unit.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cProduct_Type.Unity)) @ (V0 @ V1)))))))
(TProduct_Type.unit_all_eq1,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (V0 @ cProduct_Type.Unity)))))
(TProduct_Type.unit_all_eq2,(call @ (^[V0]: ((c== @ (call @ (^[V1]: V0))) @ V0))))
(TProduct_Type.vimage_Times,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: V2)))) @ ((cLattices.inf_class.inf @ ((cSet.vimage @ ((cFun.comp @ cProduct_Type.fst) @ V0)) @ V1)) @ ((cSet.vimage @ ((cFun.comp @ cProduct_Type.snd) @ V0)) @ V2))))))))))
(TPure.triv_forall_equality,(call @ (^[V0]: ((c== @ (call @ (^[V1]: V0))) @ V0))))
(TQuotient.OOO_eq_quotient3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ (((cQuotient.Quotient3 @ cHOL.eq) @ V3) @ V4)) @ (((cQuotient.Quotient3 @ ((cRelation.relcompp @ V0) @ ((cRelation.relcompp @ cHOL.eq) @ V0))) @ ((cFun.comp @ V3) @ V1)) @ ((cFun.comp @ V2) @ V4)))))))))))))))
(TQuotient.Quotient3_transp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ (cRelation.transp @ V0)))))))))
(TQuotient.quot_type.equivp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ (cEquiv_Relations.part_equivp @ V0)))))))))
(TQuotient.rep_abs_rsp_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ (V2 @ (V1 @ V3))) @ V4))))))))))))))
(TRandom.iterate_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.iterate_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V6))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom.iterate_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom.iterate_rel @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V3)))))))))))))
(TRandom_Pred.iter'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cRandom_Pred.iter'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cWellfounded.accp @ cRandom_Pred.iter'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ ((cProduct_Type.Pair @ V7) @ V8))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V9) @ ((cQuickcheck_Random.random_class.random @ V7) @ V8))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V9)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V12) @ V13)) @ V10)) @ ((((V4 @ V5) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7) @ V14)))))))))))))))))))) @ ((((V4 @ V5) @ V6) @ V7) @ V8)))))))))))) @ ((((V4 @ V0) @ V1) @ V2) @ V3))))))))))))))
(TRandom_Pred.iter'_rel_def,((c== @ cRandom_Pred.iter'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: (cHOL.Ex @ (^[V12]: (cHOL.Ex @ (^[V13]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V12))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.conj @ ((cHOL.eq @ V7) @ ((cQuickcheck_Random.random_class.random @ V5) @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8))))))))))))))))))))))))))))))))))
(TRandom_Sequence.empty_def,((cHOL.eq @ cRandom_Sequence.empty) @ (^[V0]: (^[V1]: (cProduct_Type.Pair @ cLimited_Sequence.empty)))))
(TRandom_Sequence.union_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.union @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.Let @ (((V0 @ V2) @ V3) @ V4)) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cHOL.Let @ (((V1 @ V2) @ V3) @ V6)) @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: ((cProduct_Type.Pair @ ((cLimited_Sequence.union @ V5) @ V7)) @ V8))))))))))))))))))
(TRecord.iso_tuple_cons_def,(call @ (^[V0]: ((cHOL.eq @ (cRecord.iso_tuple_cons @ V0)) @ (cProduct_Type.curry @ (cRecord.abst @ V0))))))
(TRelation.Domain_empty_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cRelation.Domain @ V0)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TRelation.Image_INT_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cRelation.Image @ V0) @ (V2 @ V3))))))))))))
(TRelation.Image_Int_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cRelation.Image @ V0) @ V1)) @ ((cRelation.Image @ V0) @ V2))))))))))
(TRelation.Range_Int_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cRelation.Range @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cRelation.Range @ V0)) @ (cRelation.Range @ V1))))))))
(TRelation.antisym_converse,(call @ (^[V0]: ((cHOL.eq @ (cRelation.antisym @ (cRelation.converse @ V0))) @ (cRelation.antisym @ V0)))))
(TRelation.converse.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((V3 @ V5) @ V4))))))) @ ((V3 @ V0) @ V1))))))))))))
(TRelation.converse_relcomp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.converse @ ((cRelation.relcomp @ V0) @ V1))) @ ((cRelation.relcomp @ (cRelation.converse @ V1)) @ (cRelation.converse @ V0))))))))
(TRelation.conversep.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cRelation.conversep @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V3 @ V5) @ V4))))))) @ ((V3 @ V1) @ V2))))))))))))
(TRelation.conversep.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cRelation.conversep @ V0) @ V2) @ V1)))))))))
(TRelation.conversep_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cRelation.conversep @ V0)) @ (cRelation.conversep @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TRelation.refl_on_converse,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.refl_on @ V0) @ (cRelation.converse @ V1))) @ ((cRelation.refl_on @ V0) @ V1)))))))
(TRelation.relcomp.relcompI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V4)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ ((cRelation.relcomp @ V2) @ V4)))))))))))))))
(TRelation.relcomp_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcomp @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cRelation.relcomp @ V0) @ V2)) @ ((cRelation.relcomp @ V1) @ V2))))))))))
(TRelation.relcompp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRelation.relcompp @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((V0 @ V5) @ V6)) @ ((c==> @ ((V1 @ V6) @ V7)) @ ((V4 @ V5) @ V7)))))))))) @ ((V4 @ V2) @ V3))))))))))))))
(TRelation.relcompp_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcompp @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cRelation.relcompp @ V0) @ V1)) @ ((cRelation.relcompp @ V0) @ V2))))))))))
(TRelation.single_valued_Id,(cRelation.single_valued @ cRelation.Id))
(TRelation.sym_Int_converse,(call @ (^[V0]: (cRelation.sym @ ((cLattices.inf_class.inf @ V0) @ (cRelation.converse @ V0))))))
(TRelation.total_on_diff_Id,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.total_on @ V0) @ ((cGroups.minus_class.minus @ V1) @ cRelation.Id))) @ ((cRelation.total_on @ V0) @ V1)))))))
(TRings.class.comm_ring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.comm_semiring @ V0) @ V4))))))))))))))
(TRings.class.mult_zero_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.class.mult_zero @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V1)))) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V1))))))))))
(TRings.class.ring_1.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cRings.class.zero_neq_one @ V0) @ V3)))))))))))))))
(TRings.class.ring_1.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cRings.class.ring @ V2) @ V3) @ V4) @ V5) @ V1)))))))))))))))
(TRings.class.ring_1.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cGroups.class.monoid_mult @ V0) @ V1)))))))))))))))
(TRings.comm_ring_class_def,((c== @ (cRings.comm_ring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_group_add_class @ cTYPE)) @ (cRings.comm_semiring_class @ cTYPE))))
(TRings.mult_zero_class_def,((c== @ (cRings.mult_zero_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.times_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.zero_class @ cTYPE)) @ ((cRings.class.mult_zero @ cGroups.times_class.times) @ cGroups.zero_class.zero)))))
(TSMT.arity_term_of_pattern,(cCode_Evaluation.term_of_class @ cTYPE))
(TSMT.arity_typerep_pattern,(cTyperep.typerep_class @ cTYPE))
(TSet.ord_set_inst.less_set,((c== @ cSet.ord_set_inst.less_set) @ cSet.ord_set_inst.less_set))
(TSet.subset_iff_psubset_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TSet_Interval.Compl_atMost,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cSet_Interval.ord_class.atMost @ V0))) @ (cSet_Interval.ord_class.greaterThan @ V0)))))
(TSet_Interval.Sup_lessThan,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ (cSet_Interval.ord_class.lessThan @ V0))) @ V0))))
(TSet_Interval.UN_le_eq_Un0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet_Interval.ord_class.atMost @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastAtMost @ cNat.one_nat_inst.one_nat) @ V0)) @ (^[V2]: (V1 @ V2)))) @ (V1 @ cNat.zero_nat_inst.zero_nat))))))))
(TSet_Interval.ivl_disj_int_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.lessThan_Suc,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.lessThan @ (cNat.Suc @ V0))) @ ((cSet.insert @ V0) @ (cSet_Interval.ord_class.lessThan @ V0))))))
(TString.arity_equal_nibble,(cHOL.equal_class @ cTYPE))
(TString.arity_size_literal,(cNat.size_class @ cTYPE))
(TString.arity_type_literal,(cHOL.type_class @ cTYPE))
(TString.char.char_case_def,((c== @ cString.char.char_case) @ (^[V0]: (cString.char.char_rec @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2)))))))
(TString.char.char_size_def,((c== @ cString.char.char_size) @ (cString.char.char_rec @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat)))))
(TString.enum_ex_nibble_def,(call @ (^[V0]: ((cHOL.eq @ (cString.enum_nibble_inst.enum_ex_nibble @ V0)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble0)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble1)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble2)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble3)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble4)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble5)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble6)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble7)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble8)) @ ((cHOL.disj @ (V0 @ cString.nibble.Nibble9)) @ ((cHOL.disj @ (V0 @ cString.nibble.NibbleA)) @ ((cHOL.disj @ (V0 @ cString.nibble.NibbleB)) @ ((cHOL.disj @ (V0 @ cString.nibble.NibbleC)) @ ((cHOL.disj @ (V0 @ cString.nibble.NibbleD)) @ ((cHOL.disj @ (V0 @ cString.nibble.NibbleE)) @ (V0 @ cString.nibble.NibbleF))))))))))))))))))))
(TString.literal.STR_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ cOrderings.top_class.top)) @ (V0 @ (cString.STR @ V2)))))) @ (V0 @ V1)))))))
(TString.literal.STR_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cSet.member @ V1) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHOL.eq @ (cString.STR @ V0)) @ (cString.STR @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TString.nat_of_char_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cString.nat_of_char @ V0)) @ (cString.nat_of_char @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.nat_of_char_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cString.nat_of_char @ (cString.char_of_nat @ V0))) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))
(TString.nibble.Nibble0_def,((c== @ cString.nibble.Nibble0) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.Nibble1_def,((c== @ cString.nibble.Nibble1) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TString.nibble.Nibble2_def,((c== @ cString.nibble.Nibble2) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.Nibble3_def,((c== @ cString.nibble.Nibble3) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TString.nibble.Nibble4_def,((c== @ cString.nibble.Nibble4) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.Nibble5_def,((c== @ cString.nibble.Nibble5) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TString.nibble.Nibble6_def,((c== @ cString.nibble.Nibble6) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.Nibble7_def,((c== @ cString.nibble.Nibble7) @ (cString.Abs_nibble @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TString.nibble.Nibble8_def,((c== @ cString.nibble.Nibble8) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.Nibble9_def,((c== @ cString.nibble.Nibble9) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TString.nibble.NibbleA_def,((c== @ cString.nibble.NibbleA) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.NibbleB_def,((c== @ cString.nibble.NibbleB) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TString.nibble.NibbleC_def,((c== @ cString.nibble.NibbleC) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.NibbleD_def,((c== @ cString.nibble.NibbleD) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TString.nibble.NibbleE_def,((c== @ cString.nibble.NibbleE) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))))
(TString.nibble.NibbleF_def,((c== @ cString.nibble.NibbleF) @ (cString.Abs_nibble @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))))
(TSum_Type.sum.sum_case_def,((c== @ cSum_Type.sum.sum_case) @ (^[V0]: (^[V1]: ((cSum_Type.sum.sum_rec @ (^[V2]: (V0 @ V2))) @ (^[V2]: (V1 @ V2)))))))
(TSum_Type.sum.sum_size_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSum_Type.sum.sum_size @ V0) @ V1)) @ ((cSum_Type.sum.sum_rec @ (^[V2]: ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))) @ (^[V2]: ((cNat.plus_nat_inst.plus_nat @ (V1 @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TSum_Type.sum_map.identity,((cHOL.eq @ ((cSum_Type.sum_map @ (^[V0]: V0)) @ (^[V0]: V0))) @ cFun.id))
(TTransfer.Domainp_transfer,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq)) @ cRelation.Domainp) @ cRelation.Domainp)))))))
(TTransfer.bi_total_alt_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ cHOL.All) @ cHOL.All)))))
(TTransfer.fun_upd_transfer,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V0) @ V1)))) @ cFun.fun_upd) @ cFun.fun_upd)))))))
(TTransfer.nat_rec_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ V0) @ V0))) @ ((cTransfer.fun_rel @ cHOL.eq) @ V0))) @ cNat.nat.nat_rec) @ cNat.nat.nat_rec))))
(TTransfer.right_unique_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.right_unique @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V1) @ V2)) @ ((cHOL.implies @ ((V0 @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TTransfer.right_unique_fun,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_total @ V0)) @ ((c==> @ (cTransfer.right_unique @ V1)) @ (cTransfer.right_unique @ ((cTransfer.fun_rel @ V0) @ V1)))))))))
(TTransfer.untransfer_start,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ (((cTransfer.Rel @ cHOL.eq) @ V1) @ V0)) @ V1)))))))
(TTyperep.arity_typerep_fun,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_int,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_nat,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_num,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_set,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_sum,(cTyperep.typerep_class @ cTYPE))
(TTyperep.equal_typerep_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TTyperep.typerep.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cTyperep.typerep.Typerep @ V4) @ V5))) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))) @ ((cHOL.eq @ ((cTyperep.typerep.typerep_case @ V2) @ V0)) @ ((cTyperep.typerep.typerep_case @ V3) @ V1)))))))))))))
(TTyperep.typerep.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cTyperep.typerep.typerep_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cTyperep.typerep.Typerep @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TTyperep.typerep_class_def,((c== @ (cTyperep.typerep_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TWellfounded.acc_downwards,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ (cTransitive_Closure.rtrancl @ V1))) @ ((cSet.member @ V2) @ (cWellfounded.acc @ V1)))))))))))
(TWellfounded.accp_downward,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V1)) @ ((cWellfounded.accp @ V0) @ V2))))))))))
(TWellfounded.less_than_def,((cHOL.eq @ cWellfounded.less_than) @ (cTransitive_Closure.trancl @ cWellfounded.pred_nat)))
(TWellfounded.less_than_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ cWellfounded.less_than)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TWellfounded.max_ext.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.max_ext @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V4)) @ ((cSet.Bex @ V5) @ (^[V7]: ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ V2))))))) @ V3))))))))))) @ V3)))))))))))
(TWellfounded.max_ext.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.max_ext @ V2))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.conj @ (cFinite_Set.finite @ V3)) @ ((cHOL.conj @ (cFinite_Set.finite @ V4)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V4) @ cOrderings.bot_class.bot))) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cSet.member @ V5) @ V3)) @ ((cSet.Bex @ V4) @ (^[V6]: ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)))))))))))))))))))))))
(TWellfounded.mlex_prod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cWellfounded.mlex_prod @ V0) @ V1)) @ ((cRelation.inv_image @ ((cWellfounded.lex_prod @ cWellfounded.less_than) @ V1)) @ (^[V2]: ((cProduct_Type.Pair @ (V0 @ V2)) @ V2)))))))))
(TWellfounded.not_accp_down,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cWellfounded.accp @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((V0 @ V3) @ V1)) @ ((c==> @ (cHOL.Not @ ((cWellfounded.accp @ V0) @ V3))) @ V2))))) @ V2)))))))))
(TWellfounded.wf_eq_minimal,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wf @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ V2) @ V1)) @ ((cSet.Bex @ V1) @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)) @ (cHOL.Not @ ((cSet.member @ V4) @ V1))))))))))))))))
(TWellfounded.wf_if_measure,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cNat.ord_nat_inst.less_nat @ (V1 @ (V2 @ V3))) @ (V1 @ V3)))))) @ (cWellfounded.wf @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cHOL.conj @ (V0 @ V4)) @ ((cHOL.eq @ V3) @ (V2 @ V4))))))))))))))))
(TWellfounded.wf_wellorderI,((c==> @ (cWellfounded.wf @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V0) @ V1))))))) @ ((c==> @ (cOrderings.linorder_class @ cTYPE)) @ (cOrderings.wellorder_class @ cTYPE))))
(TBig_Operators.setprod_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)))))))))))))
(TBig_Operators.setprod_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V1 @ V3))) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cOrderings.ord_class.less_eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))
(TBig_Operators.setprod_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Bex @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ cGroups.zero_class.zero))))))))
(TBig_Operators.setsum_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: ((V2 @ V3) @ V4))) @ (V1 @ V3)))) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V2 @ V3) @ V4))))) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3))))))))))))))
(TBig_Operators.setsum_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (((cHOL.If @ (V1 @ V4)) @ (V2 @ V4)) @ (V3 @ V4)))) @ V0)) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.inf_class.inf @ V0) @ (cSet.Collect @ (^[V4]: (V1 @ V4)))))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cLattices.inf_class.inf @ V0) @ (cGroups.uminus_class.uminus @ (cSet.Collect @ (^[V4]: (V1 @ V4))))))))))))))))))
(TBig_Operators.setsum_delta,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ V1)) @ (V2 @ V3)) @ cGroups.zero_class.zero))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.zero_class.zero))))))))))
(TBig_Operators.setsum_diff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ (((cHOL.If @ ((cSet.member @ V2) @ V0)) @ ((cGroups.minus_class.minus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ (V1 @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)))))))))))
(TBig_Operators.setsum_empty,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ cOrderings.bot_class.bot)) @ cGroups.zero_class.zero))))
(TBig_Operators.setsum_mono2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V2 @ V3)))))) @ ((cOrderings.ord_class.less_eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.setsum_mono3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V2 @ V3))))) @ ((cOrderings.ord_class.less_eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TCode_Evaluation.term.cases,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Evaluation.term.term_case @ V0) @ cCode_Evaluation.term.dummy_term)) @ V0))))
(TCode_Evaluation.term.simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Evaluation.term.term_rec @ V0) @ cCode_Evaluation.term.dummy_term)) @ V0))))
(TCode_Evaluation.term.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Evaluation.term.term_case @ V0) @ cCode_Evaluation.term.dummy_term)) @ V0))))
(TCode_Evaluation.term.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cCode_Evaluation.term.term_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cCode_Evaluation.term.dummy_term)) @ (V0 @ V1))))))))))
(TCode_Evaluation.valapp_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Evaluation.valapp @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cProduct_Type.fst @ V0) @ (cProduct_Type.fst @ V1))) @ (^[V2]: ((cCode_Evaluation.App @ ((cProduct_Type.snd @ V0) @ cProduct_Type.Unity)) @ ((cProduct_Type.snd @ V1) @ cProduct_Type.Unity))))))))))
(TCode_Numeral.natural.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_case @ V0) @ V1) @ (cCode_Numeral.Suc @ V2))) @ (V1 @ V2)))))))))
(TCode_Numeral.natural.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_case @ V0) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ V0))))))
(TCode_Numeral.natural.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_rec @ V0) @ V1) @ (cCode_Numeral.Suc @ V2))) @ ((V1 @ V2) @ (((cCode_Numeral.natural.natural_rec @ V0) @ V1) @ V2))))))))))
(TCode_Numeral.natural.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_rec @ V0) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ V0))))))
(TCode_Numeral.natural.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_case @ V0) @ V1) @ (cCode_Numeral.Suc @ V2))) @ (V1 @ V2)))))))))
(TCode_Numeral.natural.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cCode_Numeral.natural.natural_case @ V0) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ V0))))))
(TCode_Numeral.natural.simps_3,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cCode_Numeral.Suc @ V0)) @ cCode_Numeral.zero_natural_inst.zero_natural)))))
(TCode_Numeral.natural.simps_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cCode_Numeral.zero_natural_inst.zero_natural) @ (cCode_Numeral.Suc @ V0))))))
(TCode_Numeral.natural.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cCode_Numeral.Suc @ V0)) @ (cCode_Numeral.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TCode_Numeral.natural.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cCode_Numeral.natural.natural_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cCode_Numeral.Suc @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TComplete_Lattices.Compl_UN,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (cGroups.uminus_class.uminus @ (V1 @ V2))))))))))
(TComplete_Lattices.INF1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3))) @ V2)) @ ((cSet.Ball @ V0) @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TComplete_Lattices.INF2_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V1 @ V4))) @ V2) @ V3)) @ ((cSet.Ball @ V0) @ (^[V4]: (((V1 @ V4) @ V2) @ V3)))))))))))))
(TComplete_Lattices.INTER_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2)))) @ (cSet.Collect @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cSet.member @ V2) @ (V1 @ V3))))))))))))
(TComplete_Lattices.INT_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.Inter_eq,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cSet.Collect @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cSet.member @ V1) @ V2)))))))))
(TComplete_Lattices.SUP1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3))) @ V2)) @ ((cSet.Bex @ V0) @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TComplete_Lattices.SUP2_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V1 @ V4))) @ V2) @ V3)) @ ((cSet.Bex @ V0) @ (^[V4]: (((V1 @ V4) @ V2) @ V3)))))))))))))
(TComplete_Lattices.UNION_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2)))) @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V0) @ (^[V3]: ((cSet.member @ V2) @ (V1 @ V3))))))))))))
(TComplete_Lattices.UN_empty,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.bot_class.bot) @ (^[V1]: (V0 @ V1)))) @ cOrderings.bot_class.bot))))
(TComplete_Lattices.UN_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V2))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TComplete_Lattices.UN_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet.image @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ (V0 @ V3))))))))))))
(TComplete_Lattices.UN_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.SUPR @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))))))))))
(TComplete_Lattices.UN_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V2) @ (^[V3]: (V1 @ V3)))))))))))
(TComplete_Lattices.UN_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cGroups.minus_class.minus @ V1) @ (V2 @ V3))))) @ ((cGroups.minus_class.minus @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.UN_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cGroups.minus_class.minus @ (V1 @ V3)) @ V2)))) @ ((cGroups.minus_class.minus @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TComplete_Lattices.UN_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ V1) @ (V2 @ V3))))) @ ((cLattices.inf_class.inf @ V1) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.UN_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ V2)))) @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TComplete_Lattices.UN_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ V1) @ (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ ((cLattices.sup_class.sup @ V1) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3)))))))))))))
(TComplete_Lattices.UN_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2))))))))))
(TComplete_Lattices.UN_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cSet.insert @ V1) @ (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ ((cSet.insert @ V1) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3)))))))))))))
(TComplete_Lattices.UN_upper,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.Un_Inter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V2]: ((cLattices.sup_class.sup @ V0) @ V2)))))))))
(TComplete_Lattices.Un_eq_UN,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: (((cHOL.If @ V2) @ V0) @ V1)))))))))
(TComplete_Lattices.Union_eq,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cSet.Collect @ (^[V1]: ((cSet.Bex @ V0) @ (^[V2]: ((cSet.member @ V1) @ V2)))))))))
(TComplete_Lattices.image_UN,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cSet.image @ V0) @ (V2 @ V3))))))))))))
(TDatatype.dsum_subset_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V6]: V2)))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ ((cProduct_Type.Sigma @ V4) @ (^[V6]: V5)))) @ ((cOrderings.ord_class.less_eq @ ((cDatatype.dsum @ V0) @ V3)) @ ((cProduct_Type.Sigma @ ((cDatatype.usum @ V1) @ V4)) @ (^[V6]: ((cDatatype.usum @ V2) @ V5)))))))))))))))))))
(TDatatype.ntrunc_o_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ (cDatatype.ntrunc @ V2)) @ V0)) @ ((cFun.comp @ (cDatatype.ntrunc @ V2)) @ V1))))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDivides.arity_ring_div_int,(cDivides.ring_div_class @ cTYPE))
(TDivides.class.ring_div_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cRings.class.comm_ring_1 @ V0) @ V5) @ V3) @ V4) @ V6) @ V7))))))))))))))))))))
(TDivides.div_mult_self_is_m,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V0)) @ V0)) @ V1)))))))
(TDivides.div_nonneg_neg_le0,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.div_nonpos_pos_le0,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.divmod_int_correct,(call @ (^[V0]: (call @ (^[V1]: (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cDivides.divmod_int @ V0) @ V1)))))))
(TDivides.divmod_int_mod_div,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_int @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))))))))
(TDivides.divmod_int_rel_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_int_rel @ V0) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ V2)) @ V3))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V3)) @ ((cInt.ord_int_inst.less_int @ V3) @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V1) @ V3)) @ ((cInt.ord_int_inst.less_eq_int @ V3) @ cInt.zero_int_inst.zero_int))) @ ((cHOL.eq @ V2) @ cInt.zero_int_inst.zero_int)))))))))))))
(TDivides.divmod_int_rel_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cDivides.divmod_int_rel @ (cInt.uminus_int_inst.uminus_int @ V0)) @ (cInt.uminus_int_inst.uminus_int @ V1)) @ V2)) @ (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ V2))))))))))
(TDivides.divmod_nat_div_mod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_nat @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))))))))
(TDivides.divmod_nat_rel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ (cProduct_Type.fst @ V2)) @ V1)) @ (cProduct_Type.snd @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ (cProduct_Type.fst @ V2)) @ cNat.zero_nat_inst.zero_nat)) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ cNat.zero_nat_inst.zero_nat) @ (cProduct_Type.snd @ V2))) @ ((cNat.ord_nat_inst.less_nat @ (cProduct_Type.snd @ V2)) @ V1))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cProduct_Type.snd @ V2))) @ ((cNat.ord_nat_inst.less_eq_nat @ (cProduct_Type.snd @ V2)) @ cNat.zero_nat_inst.zero_nat)))))))))))))
(TDivides.int_power_div_base,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ ((cPower.power_class.power @ V1) @ V0)) @ V1)) @ ((cPower.power_class.power @ V1) @ ((cNat.minus_nat_inst.minus_nat @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))))
(TDivides.mod_Suc_eq_Suc_mod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ V0)) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))) @ V1)))))))
(TDivides.mod_Suc_le_divisor,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.Suc @ V1))) @ V1))))))
(TDivides.negDivAlg_sumC_def,((c== @ cDivides.negDivAlg_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cDivides.negDivAlg_graph @ V0) @ V1))))))
(TDivides.posDivAlg_sumC_def,((c== @ cDivides.posDivAlg_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cDivides.posDivAlg_graph @ V0) @ V1))))))
(TDivides.ring_div_class_def,((c== @ (cDivides.ring_div_class @ cTYPE)) @ ((cPure.conjunction @ (cDivides.semiring_div_class @ cTYPE)) @ (cRings.comm_ring_1_class @ cTYPE))))
(TDivides.semiring_div.div_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ V4) @ V6)) @ V4)))))))))))))))))
(TDivides.semiring_div.mod_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ V4) @ V6)) @ V4)))))))))))))))))
(TDivides.zdiv_zminus1_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ (cInt.uminus_int_inst.uminus_int @ V1)) @ V0)) @ (((cHOL.If @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)) @ cInt.zero_int_inst.zero_int)) @ (cInt.uminus_int_inst.uminus_int @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ ((cInt.minus_int_inst.minus_int @ (cInt.uminus_int_inst.uminus_int @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ cInt.one_int_inst.one_int)))))))))
(TDivides.zdiv_zminus2_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V1) @ (cInt.uminus_int_inst.uminus_int @ V0))) @ (((cHOL.If @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V1) @ V0)) @ cInt.zero_int_inst.zero_int)) @ (cInt.uminus_int_inst.uminus_int @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ ((cInt.minus_int_inst.minus_int @ (cInt.uminus_int_inst.uminus_int @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ cInt.one_int_inst.one_int)))))))))
(TDivides.zmod_zdiv_equality,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ V0) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V1) @ ((cDivides.div_int_inst.div_int @ V0) @ V1))) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))))))))
(TDivides.zmod_zminus1_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cInt.uminus_int_inst.uminus_int @ V0)) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)) @ cInt.zero_int_inst.zero_int) @ ((cInt.minus_int_inst.minus_int @ V1) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)))))))))
(TDivides.zmod_zminus2_eq_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ (cInt.uminus_int_inst.uminus_int @ V1))) @ (((cHOL.If @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)) @ cInt.zero_int_inst.zero_int) @ ((cInt.minus_int_inst.minus_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V1))))))))
(TEnum.enum_all_finite_1_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_1_inst.enum_all_finite_1 @ V0)) @ (V0 @ cEnum.finite_1.a\<__caret__sub>1)))))
(TEnum.enum_all_finite_2_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_2_inst.enum_all_finite_2 @ V0)) @ ((cHOL.conj @ (V0 @ cEnum.finite_2.a\<__caret__sub>1)) @ (V0 @ cEnum.finite_2.a\<__caret__sub>2))))))
(TEnum.enum_all_finite_3_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_3_inst.enum_all_finite_3 @ V0)) @ ((cHOL.conj @ (V0 @ cEnum.finite_3.a\<__caret__sub>1)) @ ((cHOL.conj @ (V0 @ cEnum.finite_3.a\<__caret__sub>2)) @ (V0 @ cEnum.finite_3.a\<__caret__sub>3)))))))
(TEnum.enum_all_finite_4_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_4_inst.enum_all_finite_4 @ V0)) @ ((cHOL.conj @ (V0 @ cEnum.finite_4.a\<__caret__sub>1)) @ ((cHOL.conj @ (V0 @ cEnum.finite_4.a\<__caret__sub>2)) @ ((cHOL.conj @ (V0 @ cEnum.finite_4.a\<__caret__sub>3)) @ (V0 @ cEnum.finite_4.a\<__caret__sub>4))))))))
(TEnum.enum_all_finite_5_def,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_finite_5_inst.enum_all_finite_5 @ V0)) @ ((cHOL.conj @ (V0 @ cEnum.finite_5.a\<__caret__sub>1)) @ ((cHOL.conj @ (V0 @ cEnum.finite_5.a\<__caret__sub>2)) @ ((cHOL.conj @ (V0 @ cEnum.finite_5.a\<__caret__sub>3)) @ ((cHOL.conj @ (V0 @ cEnum.finite_5.a\<__caret__sub>4)) @ (V0 @ cEnum.finite_5.a\<__caret__sub>5)))))))))
(TEnum.finite_1.Rep_finite_1,(call @ (^[V0]: ((cSet.member @ (cEnum.Rep_finite_1 @ V0)) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set)))))
(TEnum.finite_2.Rep_finite_2,(call @ (^[V0]: ((cSet.member @ (cEnum.Rep_finite_2 @ V0)) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set)))))
(TEnum.finite_3.Rep_finite_3,(call @ (^[V0]: ((cSet.member @ (cEnum.Rep_finite_3 @ V0)) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set)))))
(TEnum.finite_4.Rep_finite_4,(call @ (^[V0]: ((cSet.member @ (cEnum.Rep_finite_4 @ V0)) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set)))))
(TEnum.finite_5.Rep_finite_5,(call @ (^[V0]: ((cSet.member @ (cEnum.Rep_finite_5 @ V0)) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set)))))
(TEquiv_Relations.congruentD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.congruent @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)) @ ((cHOL.eq @ (V1 @ V2)) @ (V1 @ V3)))))))))))))
(TEquiv_Relations.congruentI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)) @ ((cHOL.eq @ (V1 @ V2)) @ (V1 @ V3)))))))) @ ((cEquiv_Relations.congruent @ V0) @ V1)))))))
(TEquiv_Relations.equiv_type,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V0)))))))))
(TEquiv_Relations.equivp_def,(call @ (^[V0]: ((cHOL.eq @ (cEquiv_Relations.equivp @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TExtraction.disjE_realizer2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cOption.option.option_case @ V0) @ (^[V6]: (V1 @ V6))) @ V2)) @ ((c==> @ ((c==> @ V0) @ (V3 @ V4))) @ ((c==> @ (call @ (^[V6]: ((c==> @ (V1 @ V6)) @ (V3 @ (V5 @ V6)))))) @ (V3 @ (((cOption.option.option_case @ V4) @ (^[V6]: (V5 @ V6))) @ V2))))))))))))))))))
(TExtraction.disjE_realizer3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cExtraction.sumbool.sumbool_case @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ V0) @ (V3 @ V4))) @ ((c==> @ ((c==> @ V1) @ (V3 @ V5))) @ (V3 @ (((cExtraction.sumbool.sumbool_case @ V4) @ V5) @ V2))))))))))))))))))
(TExtraction.sumbool.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TExtraction.sumbool.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cExtraction.sumbool.Left)) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cExtraction.sumbool.Right)) @ V1)) @ V1)))))))
(TExtraction.sumbool.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cExtraction.sumbool.Left)) @ ((c==> @ (V0 @ cExtraction.sumbool.Right)) @ (V0 @ V1))))))))
(TFields.classrel_field_idom,(cRings.idom_class @ cTYPE))
(TFields.field.field_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V2 @ (V0 @ V8)) @ V8)) @ V3))))))))))))))))))))))
(TFields.inverse_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cFields.inverse_class @ cTYPE)))
(TFields.inverse_class.super,((c==> @ (cFields.inverse_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TFinite_Set.Set_filter_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cSet.filter @ V1) @ V0)) @ (((cFinite_Set.fold @ (^[V2]: (^[V3]: (((cHOL.If @ (V1 @ V2)) @ ((cSet.insert @ V2) @ V3)) @ V3)))) @ cOrderings.bot_class.bot) @ V0))))))))
(TFinite_Set.bij_betw_finite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ V2))))))))))
(TFinite_Set.card_Diff1_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ (cFinite_Set.card @ V0)))))))))
(TFinite_Set.card_Diff2_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ (cFinite_Set.card @ V0))))))))))))
(TFinite_Set.card_le_Suc_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ V1)) @ (cFinite_Set.card @ V0))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cSet.insert @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ (cFinite_Set.card @ V3))) @ (cFinite_Set.finite @ V3)))))))))))))))
(TFinite_Set.finite_Plus_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.finite @ ((cSum_Type.Plus @ V0) @ V1))) @ ((cHOL.conj @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.finite_surj_inj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.image @ V1) @ V0))) @ ((cFun.inj_on @ V1) @ V0))))))))
(TFinite_Set.fold_union_pair,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cSet.insert @ ((cProduct_Type.Pair @ V1) @ V3)) @ cOrderings.bot_class.bot)))) @ V2)) @ (((cFinite_Set.fold @ (^[V3]: (cSet.insert @ ((cProduct_Type.Pair @ V1) @ V3)))) @ V2) @ V0))))))))))
(TFinite_Set.folding.eq_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((cHOL.eq @ (((cFinite_Set.folding.F @ V0) @ V1) @ V2)) @ (((cFinite_Set.fold @ V0) @ V1) @ V2))))))))))
(TFun.inj_image_Compl_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cSet.image @ V0) @ V1)))))))))
(TFun.inj_on_Un_image_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ ((cSet.image @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TFun.inj_on_imp_inj_on_swap,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cFun.inj_on @ (((cFun.swap @ V2) @ V3) @ V0)) @ V1)))))))))))))
(TGroups.abs_if_class.abs_if,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ (cGroups.uminus_class.uminus @ V0)) @ V0)))))
(TGroups.abs_if_class.axioms,((((cGroups.class.abs_if @ cGroups.abs_class.abs) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less))
(TGroups.class.group_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cGroups.class.monoid_add @ V1) @ V2)) @ ((((cGroups.class.group_add_axioms @ V0) @ V1) @ V2) @ V3))))))))))))
(TGroups.group_add.diff_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V4)) @ V2)))))))))))))
(TGroups.group_add.minus_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ ((V1 @ V4) @ V5))) @ ((V1 @ (V3 @ V5)) @ (V3 @ V4)))))))))))))))))
(TGroups.group_add_class_def,((c== @ (cGroups.group_add_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.minus_class @ cTYPE)) @ (cGroups.monoid_add_class @ cTYPE))) @ ((cPure.conjunction @ (cGroups.uminus_class @ cTYPE)) @ ((((cGroups.class.group_add_axioms @ cGroups.minus_class.minus) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus)))))
(TGroups.monoid.left_neutral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.monoid @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))))))))
(TGroups.monoid_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))) @ ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))) @ ((cGroups.monoid_axioms @ V0) @ V1))))))))
(TGroups.sgn_if_class.axioms,(((((cGroups.class.sgn_if @ cGroups.one_class.one) @ cGroups.sgn_class.sgn) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less))
(TGroups.sgn_if_class.sgn_if,(call @ (^[V0]: ((cHOL.eq @ (cGroups.sgn_class.sgn @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ cGroups.one_class.one) @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)))))))
(THOL.equal_class.equal_refl,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V0)) @ cHOL.True))))
(THOL.induct_rulify_fallback_6,((c== @ cHOL.False) @ cHOL.False))
(THOL.induct_rulify_fallback_5,((c== @ cHOL.True) @ cHOL.True))
(THOL.induct_rulify_fallback_4,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_conj @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V1)))))))
(THOL.induct_rulify_fallback_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(THOL.induct_rulify_fallback_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.induct_implies @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(THOL.induct_rulify_fallback_1,(call @ (^[V0]: ((c== @ (cHOL.induct_forall @ V0)) @ (cHOL.All @ (^[V1]: (V0 @ V1)))))))
(THilbert_Choice.GreatestMI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V1)))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((c==> @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (V0 @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V5)) @ (V2 @ V4)))))) @ (V3 @ V4)))))) @ (V3 @ ((cHilbert_Choice.GreatestM @ V2) @ V0))))))))))))))
(THilbert_Choice.Greatest_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V0 @ V3)) @ ((cNat.ord_nat_inst.less_nat @ V3) @ V2))))) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ (cHilbert_Choice.Greatest @ (^[V3]: (V0 @ V3)))))))))))))
(THilbert_Choice.LeastM_natI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ (V0 @ ((cHilbert_Choice.LeastM @ V2) @ V0))))))))))
(THilbert_Choice.acc_bacc_eq,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cWellfounded.acc @ V0)) @ ((cHilbert_Choice.bacc @ V0) @ (cFinite_Set.card @ cOrderings.top_class.top)))))))
(THilbert_Choice.bchoice_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V2]: (cHOL.Ex @ (^[V3]: ((V1 @ V2) @ V3)))))) @ (cHOL.Ex @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((V1 @ V3) @ (V2 @ V3))))))))))))
(THilbert_Choice.choice_iff',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (cHOL.Ex @ (^[V3]: ((V1 @ V2) @ V3))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ (V0 @ V3)) @ ((V1 @ V3) @ (V2 @ V3)))))))))))))
(TInductive.def_coinduct_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.gfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ (V1 @ ((cLattices.sup_class.sup @ V3) @ V0)))) @ ((cSet.member @ V2) @ V0))))))))))))))
(TInt.diff_int_def_symmetric,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ V0) @ (cInt.uminus_int_inst.uminus_int @ V1))) @ ((cInt.minus_int_inst.minus_int @ V0) @ V1)))))))
(TInt.divide_less_eq_numeral_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V2))))))))))))
(TInt.divide_less_eq_numeral_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V2)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V2))))))))))))
(TInt.less_divide_eq_numeral_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.less_divide_eq_numeral_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))) @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))))))))
(TInt.minus_less_iff_numeral_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V0)))))))
(TInt.minus_less_iff_numeral_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V1))) @ V0)))))))
(TInt.not_int_zless_negative,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cInt.ord_int_inst.less_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ V1)))))))))
(TInt.plus_int_inst.plus_int,((c== @ cInt.plus_int_inst.plus_int) @ cInt.plus_int_inst.plus_int))
(TInt.ring_1.of_int.transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cTransfer.fun_rel @ cInt.cr_int) @ cHOL.eq) @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: ((V4 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V7)))))) @ ((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4))))))))))))))))
(TInt.ring_1_class.Ints_diff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((c==> @ ((cSet.member @ V1) @ cInt.ring_1_class.Ints)) @ ((cSet.member @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cInt.ring_1_class.Ints))))))))
(TInt.ring_1_class.Ints_mult,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((c==> @ ((cSet.member @ V1) @ cInt.ring_1_class.Ints)) @ ((cSet.member @ ((cGroups.times_class.times @ V0) @ V1)) @ cInt.ring_1_class.Ints))))))))
(TInt.zero_int_inst.zero_int,((c== @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int))
(TInt.zless_nat_eq_int_zless,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cInt.nat @ V1))) @ ((cInt.ord_int_inst.less_int @ (cNat.semiring_1_class.of_nat @ V0)) @ V1)))))))
(TLattices.arity_lattice_fun,(cLattices.lattice_class @ cTYPE))
(TLattices.class.lattice_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ (((cLattices.class.semilattice_sup @ V3) @ V1) @ V2))))))))))))
(TLattices.lattice_class_def,((c== @ (cLattices.lattice_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.semilattice_inf_class @ cTYPE)) @ (cLattices.semilattice_sup_class @ cTYPE))))
(TLattices.semilattice.intro,(call @ (^[V0]: ((c==> @ (cGroups.abel_semigroup @ V0)) @ ((c==> @ (cLattices.semilattice_axioms @ V0)) @ (cLattices.semilattice @ V0))))))
(TLazy_Sequence.hb_flat_code,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.hb_flat @ V0)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V1]: (((cOption.option.option_case @ cOption.option.None) @ (^[V2]: ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (cLazy_Sequence.yield @ ((cLazy_Sequence.append @ (((cOption.option.option_case @ cLazy_Sequence.hit_bound) @ (^[V5]: V5)) @ V3)) @ (cLazy_Sequence.hb_flat @ V4)))))) @ V2))) @ (cLazy_Sequence.yield @ V0))))))))
(TLifting.Quotient_rep_reflp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((V0 @ (V2 @ V4)) @ (V2 @ V4))))))))))))))
(TLifting.invariant_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ cLifting.invariant) @ cLifting.invariant)))))
(TLifting_Set.Compl_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V0)) @ cGroups.uminus_class.uminus) @ cGroups.uminus_class.uminus))))))
(TLifting_Set.Inter_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ (cLifting_Set.set_rel @ V0))) @ (cLifting_Set.set_rel @ V0)) @ (^[V1]: (cComplete_Lattices.Inf_class.Inf @ V1))) @ (^[V1]: (cComplete_Lattices.Inf_class.Inf @ V1))))))))
(TLifting_Set.UNION_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ (cLifting_Set.set_rel @ V1))) @ (cLifting_Set.set_rel @ V1))) @ cComplete_Lattices.complete_lattice_class.SUPR) @ cComplete_Lattices.complete_lattice_class.SUPR))))))
(TLifting_Set.Union_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ (cLifting_Set.set_rel @ V0))) @ (cLifting_Set.set_rel @ V0)) @ (^[V1]: (cComplete_Lattices.Sup_class.Sup @ V1))) @ (^[V1]: (cComplete_Lattices.Sup_class.Sup @ V1))))))
(TLifting_Set.empty_transfer,(call @ (^[V0]: (((cLifting_Set.set_rel @ V0) @ cOrderings.bot_class.bot) @ cOrderings.bot_class.bot))))
(TLifting_Set.image_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V1))) @ cSet.image) @ cSet.image))))))
(TLifting_Set.inter_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V0))) @ cLattices.inf_class.inf) @ cLattices.inf_class.inf)))))
(TLifting_Set.union_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V0))) @ cLattices.sup_class.sup) @ cLattices.sup_class.sup))))
(TLimited_Sequence.empty_def,((cHOL.eq @ cLimited_Sequence.empty) @ (^[V0]: (^[V1]: (cOption.option.Some @ cLazy_Sequence.empty)))))
(TLimited_Sequence.union_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.union @ V0) @ V1)) @ (^[V2]: (^[V3]: ((cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (((cOption.option.option_case @ cOption.option.None) @ (^[V6]: (((cOption.option.option_case @ cOption.option.None) @ (^[V7]: (cOption.option.Some @ ((cLazy_Sequence.append @ V6) @ V7)))) @ V5))) @ V4)))) @ ((cProduct_Type.Pair @ ((V0 @ V2) @ V3)) @ ((V1 @ V2) @ V3)))))))))))
(TLimited_Sequence.yield_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLimited_Sequence.yield @ V0) @ V1) @ V2)) @ (((cOption.option.option_case @ cOption.option.None) @ (^[V3]: ((((cFun.comp @ cOption.map) @ cProduct_Type.apsnd) @ (^[V4]: (^[V5]: (^[V6]: (cOption.option.Some @ V4))))) @ (cLazy_Sequence.yield @ V3)))) @ (((cLimited_Sequence.eval @ V0) @ V1) @ V2))))))))))
(TList.append_eq_append_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.disj @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ (cNat.size_class.size @ V3)))) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V2)) @ ((cList.append @ V1) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TList.append_in_listsp_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.listsp @ V0) @ ((cList.append @ V1) @ V2))) @ ((cHOL.conj @ ((cList.listsp @ V0) @ V1)) @ ((cList.listsp @ V0) @ V2))))))))))
(TList.distinct_set_sublists,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ ((cList.map @ cList.set) @ (cList.sublists @ V0)))))))
(TList.dropWhile_eq_Nil_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.dropWhile @ V0) @ V1)) @ cList.list.Nil)) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: (V0 @ V2)))))))))
(TList.greaterThanAtMost_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ (cList.set @ ((cList.upt @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1)))))))))
(TList.left_unique_list_all2,(call @ (^[V0]: ((c==> @ (cLifting.left_unique @ V0)) @ (cLifting.left_unique @ (cList.list_all2 @ V0))))))
(TList.length_greater_0_conv,(call @ (^[V0]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V0))) @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))))))
(TList.length_remdups_concat,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.remdups @ (cList.concat @ V0)))) @ (cFinite_Set.card @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cList.set @ V0)) @ (^[V1]: (cList.set @ V1))))))))
(TList.linorder.sort_key_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cList.linorder.sort_key @ V0) @ V2) @ V3)) @ (((cList.foldr @ ((cList.linorder.insort_key @ V0) @ V2)) @ V3) @ cList.list.Nil))))))))))))
(TList.linorder.sorted.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V5) @ V4))) @ ((c==> @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: ((V0 @ V5) @ V6)))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V4)) @ V3)))))))) @ V3)))))))))))))
(TList.linorder.sorted.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ V3))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V3)) @ (^[V5]: ((V0 @ V4) @ V5)))) @ ((cList.linorder.sorted @ V0) @ V3)))))))))))))))))
(TList.list.Abs_list_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cList.list.list_rep_set))) @ ((cHOL.eq @ (cList.Rep_list @ (cList.Abs_list @ V0))) @ V0)))))
(TList.list.Rep_list_inverse,(call @ (^[V0]: ((cHOL.eq @ (cList.Abs_list @ (cList.Rep_list @ V0))) @ V0))))
(TList.list.list_rec_set_def,((c== @ cList.list.list_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ ((cHOL.eq @ V4) @ V0))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V7) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ (((V1 @ V7) @ V5) @ V6))) @ ((V2 @ V5) @ V6))))))))))))))))))
(TList.list.list_rep_set_def,((c== @ cList.list.list_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V3)) @ V2)))) @ (V0 @ V2))))))))))))
(TList.list_all2_update_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ (((cList.list_all2 @ V0) @ (((cList.list_update @ V1) @ V5) @ V3)) @ (((cList.list_update @ V2) @ V5) @ V4)))))))))))))))))
(TList.list_size_estimation',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ (V3 @ V0))) @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ ((cList.list.list_size @ V3) @ V1)))))))))))))
(TList.list_update_overwrite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.list_update @ (((cList.list_update @ V0) @ V1) @ V2)) @ V1) @ V3)) @ (((cList.list_update @ V0) @ V1) @ V3)))))))))))
(TList.list_update_same_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ (((cList.list_update @ V1) @ V0) @ V2)) @ V1)) @ ((cHOL.eq @ ((cList.nth @ V1) @ V0)) @ V2))))))))))
(TList.listrel_rtrancl_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ (cTransitive_Closure.rtrancl @ V2)))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cList.listrel @ (cTransitive_Closure.rtrancl @ V2)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cList.listrel @ (cTransitive_Closure.rtrancl @ V2))))))))))))))
(TList.map_filter_map_filter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ V0) @ ((cList.filter @ V1) @ V2))) @ ((cList.map_filter @ (^[V3]: (((cHOL.If @ (V1 @ V3)) @ (cOption.option.Some @ (V0 @ V3))) @ cOption.option.None))) @ V2)))))))))
(TList.map_replicate_trivial,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map @ (^[V2]: V0)) @ ((cList.upt @ cNat.zero_nat_inst.zero_nat) @ V1))) @ ((cList.replicate @ V1) @ V0)))))))
(TList.map_tailrec_rev.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V3)))) @ V1)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ V5)))) @ V1)))))))))) @ V1)))))))
(TList.map_tailrec_rev.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cList.map_tailrec_rev @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ V6)) @ ((c==> @ ((cHOL.eq @ V3) @ V6)) @ V4))))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ V2) @ V8)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cList.map_tailrec_rev @ V5) @ V7) @ ((cList.list.Cons @ (V5 @ V6)) @ V8)))) @ V4))))))))))))) @ V4))))))))))))))
(TList.map_tailrec_rev.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.map_tailrec_rev @ V0) @ ((cList.list.Cons @ V1) @ V2)) @ V3)) @ (((cList.map_tailrec_rev @ V0) @ V2) @ ((cList.list.Cons @ (V0 @ V1)) @ V3))))))))))))
(TList.map_tailrec_rev.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.map_tailrec_rev @ V0) @ cList.list.Nil) @ V1)) @ V1))))))
(TList.member_le_listsum_nat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cList.monoid_add_class.listsum @ V1))))))))
(TList.partition_filter_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.partition @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cList.filter @ V0) @ V1)) @ ((cList.filter @ ((cFun.comp @ cHOL.Not) @ V0)) @ V1))))))))
(TList.remdups_adj_graph_def,((c== @ cList.remdups_adj_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((cHOL.eq @ V2) @ cList.list.Nil))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ cList.list.Nil))) @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V4) @ cList.list.Nil)))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V4) @ V5)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))) @ ((cList.list.Cons @ V4) @ (V3 @ ((cList.list.Cons @ V5) @ V6)))))) @ ((cHOL.conj @ ((cHOL.induct_implies @ ((cHOL.eq @ V4) @ V5)) @ ((V0 @ ((cList.list.Cons @ V4) @ V6)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((V0 @ ((cList.list.Cons @ V5) @ V6)) @ (V3 @ ((cList.list.Cons @ V5) @ V6)))))))))))))))))))))))
(TList.remdups_adj_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.remdups_adj_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ ((cHOL.eq @ V3) @ V4)) @ V2)))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ V2)))))))))) @ V2))))))))))
(TList.remdups_adj_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.remdups_adj_rel @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ ((cHOL.eq @ V2) @ V3)))))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3)))))))))))))))))
(TList.remdups_adj_singleton,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cList.remdups_adj @ V0)) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ ((cHOL.eq @ V0) @ ((cList.replicate @ (cNat.size_class.size @ V0)) @ V1))))))))
(TList.replicate.replicate_0,(call @ (^[V0]: ((cHOL.eq @ ((cList.replicate @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cList.list.Nil))))
(TList.replicate_append_same,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.append @ ((cList.replicate @ V0) @ V1)) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ ((cList.list.Cons @ V1) @ ((cList.replicate @ V0) @ V1))))))))
(TList.replicate_length_same,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cHOL.eq @ V2) @ V1)))) @ ((cHOL.eq @ ((cList.replicate @ (cNat.size_class.size @ V0)) @ V1)) @ V0)))))))
(TList.right_total_list_all2,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ (cTransfer.right_total @ (cList.list_all2 @ V0))))))
(TList.set_replicate_conv_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.replicate @ V0) @ V1))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cOrderings.bot_class.bot) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))
(TList.split_list_first_prop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ ((cHOL.conj @ (V1 @ V3)) @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V5]: (cHOL.Not @ (V1 @ V5))))))))))))))))))
(TList.split_list_last_propE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V3]: (V1 @ V3)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.append @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ (V1 @ V4)) @ ((c==> @ ((cSet.Ball @ (cList.set @ V5)) @ (^[V6]: (cHOL.Not @ (V1 @ V6))))) @ V2)))))))))) @ V2)))))))))
(TList.takeWhile_eq_all_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cList.takeWhile @ V0) @ V1)) @ V1)) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: (V0 @ V2)))))))))
(TList.take_Suc_conv_app_nth,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.take @ (cNat.Suc @ V0)) @ V1)) @ ((cList.append @ ((cList.take @ V0) @ V1)) @ ((cList.list.Cons @ ((cList.nth @ V1) @ V0)) @ cList.list.Nil)))))))))
(TList.transpose.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ ((cList.list.Cons @ cList.list.Nil) @ V1))) @ V0)))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V4]: (^[V5]: ((cList.list.Cons @ V5) @ cList.list.Nil))))) @ V3)))) @ ((cList.list.Cons @ ((cList.list.Cons @ V1) @ V2)) @ V3))) @ V0)))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cList.transpose_rel) @ V1)))))))))
(TList.transpose_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.transpose_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ V2))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ cList.list.Nil) @ V4))) @ ((c==> @ ((cHOL.eq @ V1) @ (V3 @ V4))) @ ((c==> @ ((cList.transpose_graph @ V4) @ (V3 @ V4))) @ V2)))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ V5)) @ V6))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6))))))) @ ((c==> @ ((cList.transpose_graph @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))))) @ V2)))))))))))) @ V2)))))))))))
(TList.transpose_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.transpose_graph @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ cList.list.Nil) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (V2 @ V3))) @ ((cList.transpose_graph @ V3) @ (V2 @ V3))))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V6) @ cList.list.Nil))))) @ V5)))) @ (V2 @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5))))))) @ ((cList.transpose_graph @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5)))) @ (V2 @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5)))))))))))))))))))))))
(TList.transpose_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.transpose_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ V3) @ ((cList.list.Cons @ cList.list.Nil) @ V3))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V6]: (^[V7]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V5)))) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V4)) @ V5))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TMain.arity_term_of_sumbool,(cCode_Evaluation.term_of_class @ cTYPE))
(TMain.arity_typerep_sumbool,(cTyperep.typerep_class @ cTYPE))
(TNat.dvd.dual_order.antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.dvd.lift_Suc_mono_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ (V0 @ V3)) @ (V0 @ (cNat.Suc @ V3)))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ (V0 @ (cNat.Suc @ V3))) @ (V0 @ V3))))))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ (V0 @ V1)) @ (V0 @ V2))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ (V0 @ V2)) @ (V0 @ V1)))))))))))))
(TNat.dvd.order.strict_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.nat.nat_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TNat.nat.nat_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNat.nat.nat_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((((cNat.nat.nat_rec_set @ V0) @ V1) @ (cNat.Suc @ V2)) @ ((V1 @ V2) @ V3))))))))))))
(TNat.nat.nat_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cNat.nat.nat_rec_set @ V0) @ V1) @ cNat.zero_nat_inst.zero_nat) @ V0))))))
(TNat.nat_add_left_cancel_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)))))))))
(TNat.order.lift_Suc_mono_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (call @ (^[V5]: ((V0 @ (V2 @ V5)) @ (V2 @ (cNat.Suc @ V5)))))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V4)) @ ((V0 @ (V2 @ V3)) @ (V2 @ V4))))))))))))))))
(TNat.plus_nat_inst.plus_nat,((c== @ cNat.plus_nat_inst.plus_nat) @ cNat.plus_nat_inst.plus_nat))
(TNat.semiring_1.Nats_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: (V5 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6))))) @ (V5 @ V4)))))))))))))))))
(TNat.semiring_1.of_nat_code,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ (((cNat.semiring_1.of_nat_aux @ (^[V5]: ((V2 @ V5) @ V0))) @ V4) @ V3))))))))))))))
(TNat.semiring_1.of_nat_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ ((cNat.times_nat_inst.times_nat @ V4) @ V5))) @ ((V1 @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V5)))))))))))))))))
(TNat.zero_nat_inst.zero_nat,((c== @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat))
(TNitpick.arity_term_of_word,(cCode_Evaluation.term_of_class @ cTYPE))
(TNitpick.arity_type_fun_box,(cHOL.type_class @ cTYPE))
(TNitpick.arity_typerep_word,(cTyperep.typerep_class @ cTYPE))
(TNitpick.equal_pair_box_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.fold_graph'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNitpick.fold_graph' @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((((V4 @ V5) @ V6) @ cOrderings.bot_class.bot) @ V6)))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cSet.member @ V5) @ V6)) @ ((c==> @ ((((cNitpick.fold_graph' @ V7) @ V8) @ ((cGroups.minus_class.minus @ V6) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ V9)) @ ((c==> @ ((((V4 @ V7) @ V8) @ ((cGroups.minus_class.minus @ V6) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ V9)) @ ((((V4 @ V7) @ V8) @ V6) @ ((V7 @ V5) @ V9)))))))))))))))) @ ((((V4 @ V0) @ V1) @ V2) @ V3)))))))))))))))
(TNitpick.fold_graph'.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((((cNitpick.fold_graph' @ V2) @ V3) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V4)) @ ((((cNitpick.fold_graph' @ V2) @ V3) @ V1) @ ((V2 @ V0) @ V4)))))))))))))))
(TNitpick.fold_graph'.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cNitpick.fold_graph' @ V0) @ V1) @ cOrderings.bot_class.bot) @ V1))))))
(TNitpick.fun_box.FunBox_def,(call @ (^[V0]: ((c== @ (cNitpick.fun_box.FunBox @ V0)) @ (cNitpick.Abs_fun_box @ (cDatatype.Leaf @ V0))))))
(TNitpick.nat_gcd_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.nat_gcd_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.nat_gcd_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cNitpick.nat_gcd_rel @ ((cProduct_Type.Pair @ V0) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0))) @ ((cProduct_Type.Pair @ V1) @ V0))))))))
(TNitpick.norm_frac_sumC_def,((c== @ cNitpick.norm_frac_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cNitpick.norm_frac_graph @ V0) @ V1))))))
(TNitpick.number_of_frac_def,(call @ (^[V0]: ((c== @ (cNitpick.number_of_frac @ V0)) @ (cNitpick.Abs_Frac @ ((cProduct_Type.Pair @ V0) @ cInt.one_int_inst.one_int))))))
(TNitpick.pair_box.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cNitpick.pair_box.PairBox @ V4) @ V5))) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))) @ ((cHOL.eq @ ((cNitpick.pair_box.pair_box_case @ V2) @ V0)) @ ((cNitpick.pair_box.pair_box_case @ V3) @ V1)))))))))))))
(TNitpick.pair_box.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cNitpick.pair_box.pair_box_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cNitpick.pair_box.PairBox @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TNitpick.random_fun_box_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cNitpick.random_aux_fun_box @ V0) @ V0)))))
(TNitpick.word.word_case_def,((c== @ cNitpick.word.word_case) @ (^[V0]: (cNitpick.word.word_rec @ (^[V1]: (V0 @ V1))))))
(TNitpick.word.word_size_def,(call @ (^[V0]: ((c== @ (cNitpick.word.word_size @ V0)) @ (cNitpick.word.word_rec @ (^[V1]: cNat.zero_nat_inst.zero_nat))))))
(TNum.neg_numeral.is_num_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c== @ (((cNum.neg_numeral.is_num @ V1) @ V3) @ V4)) @ (cInductive.complete_lattice_class.lfp @ (^[V5]: (^[V6]: ((cHOL.disj @ ((cHOL.eq @ V6) @ V4)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V6) @ (V3 @ V7))) @ (V5 @ V7))))) @ (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V6) @ ((V1 @ V7) @ V8))) @ ((cHOL.conj @ (V5 @ V7)) @ (V5 @ V8)))))))))))))))))))))))))
(TNum.num.num_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TNum.num.num_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ (cNum.num.Bit1 @ V3)) @ ((V2 @ V3) @ V4))))))))))))))
(TNum.num.num_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ (cNum.num.Bit0 @ V3)) @ ((V1 @ V3) @ V4))))))))))))))
(TNum.num.num_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cNum.num.num_rec_set @ V0) @ V1) @ V2) @ cNum.num.One) @ V0))))))))
(TNum.num.num_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.num.num_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNum.num.num_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ V2)))))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNum.num.num_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ V2)))))))) @ (V1 @ V0))))))))))
(TNum.num.num_rep_set.intros_3,(call @ (^[V0]: ((c==> @ (cNum.num.num_rep_set @ V0)) @ (cNum.num.num_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ V0)))))))
(TNum.num.num_rep_set.intros_2,(call @ (^[V0]: ((c==> @ (cNum.num.num_rep_set @ V0)) @ (cNum.num.num_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ V0)))))))
(TNum.num.num_rep_set.intros_1,(cNum.num.num_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TNum.plus_num_inst.plus_num,((c== @ cNum.plus_num_inst.plus_num) @ cNum.plus_num_inst.plus_num))
(TOption.Some_image_these_eq,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cOption.option.Some) @ (cOption.these @ V0))) @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cSet.member @ V1) @ V0)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOption.option.None)))))))))
(TOption.these_image_Some_eq,(call @ (^[V0]: ((cHOL.eq @ (cOption.these @ ((cSet.image @ cOption.option.Some) @ V0))) @ V0))))
(TOrderings.class.no_bot_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.no_bot @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.order @ V0) @ V1)) @ (cOrderings.class.no_bot_axioms @ V1))))))))
(TOrderings.class.no_top_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.no_top @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.order @ V0) @ V1)) @ (cOrderings.class.no_top_axioms @ V1))))))))
(TOrderings.linorder.neq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.disj @ ((V1 @ V2) @ V3)) @ ((V1 @ V3) @ V2)))))))))))))
(TOrderings.linorder.not_leE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((V0 @ V2) @ V3))) @ ((V1 @ V3) @ V2))))))))))))
(TOrderings.linorder_neq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.no_bot_class_def,((c== @ (cOrderings.no_bot_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ (cOrderings.class.no_bot_axioms @ cOrderings.ord_class.less))))
(TOrderings.no_top_class_def,((c== @ (cOrderings.no_top_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ (cOrderings.class.no_top_axioms @ cOrderings.ord_class.less))))
(TOrderings.order.dual_order,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cOrderings.class.order @ (^[V2]: (^[V3]: ((V0 @ V3) @ V2)))) @ (^[V2]: (^[V3]: ((V1 @ V3) @ V2))))))))))
(TOrderings.order_bot.le_bot,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V0)) @ ((cHOL.eq @ V3) @ V0))))))))))))
(TOrderings.order_less_asym',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)))))))))
(TOrderings.order_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_top.top_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V3) @ V2))))))))))))
(TOrderings.ordering.antisym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.ordering_top_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cOrderings.ordering @ V0) @ V1)) @ ((cOrderings.ordering_top_axioms @ V0) @ V2))))))))))
(TOrderings.preorder.eq_refl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((V0 @ V2) @ V3))))))))))))
(TOrderings.wellorder.LeastI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ (V2 @ ((cOrderings.ord.Least @ V0) @ (^[V4]: (V2 @ V4)))))))))))))))
(TPartial_Function.bind_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ V0)) @ ((c==> @ (call @ (^[V2]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (^[V3]: ((V1 @ V2) @ V3)))))) @ (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (^[V2]: ((cOption.bind @ (V0 @ V2)) @ (^[V3]: ((V1 @ V3) @ V2))))))))))))
(TPartial_Function.call_mono,(call @ (^[V0]: (call @ (^[V1]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ V0)) @ V0) @ (^[V2]: (V2 @ V1))))))))
(TPartial_Function.chain_fun,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cComplete_Partial_Order.chain @ (cPartial_Function.fun_ord @ V0)) @ V1)) @ ((cComplete_Partial_Order.chain @ V0) @ (cSet.Collect @ (^[V3]: ((cSet.Bex @ V1) @ (^[V4]: ((cHOL.eq @ V3) @ (V4 @ V2)))))))))))))))
(TPower.power2_nat_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TPredicate.arity_equal_pred,(cHOL.equal_class @ cTYPE))
(TPredicate.eval_pred_of_set,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.eval @ (cPredicate.pred_of_set @ V0)) @ V1)) @ ((cSet.member @ V1) @ V0)))))))
(TPredicate.iterate_upto_def,((c== @ cPredicate.iterate_upto) @ (^[V0]: (^[V1]: (^[V2]: (cPredicate.iterate_upto_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TPredicate.less_eq_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cPredicate.eval @ V0)) @ (cPredicate.eval @ V1))))))))
(TPredicate.seq.seq_case_def,((c== @ cPredicate.seq.seq_case) @ (^[V0]: (^[V1]: (^[V2]: (((cPredicate.seq.seq_rec @ V0) @ (^[V3]: (^[V4]: ((V1 @ V3) @ V4)))) @ (^[V3]: (^[V4]: (^[V5]: ((V2 @ V3) @ V4))))))))))
(TPredicate.seq.seq_size_def,(call @ (^[V0]: ((c== @ (cPredicate.seq.seq_size @ V0)) @ (((cPredicate.seq.seq_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ ((cPredicate.pred.pred_size @ V0) @ V2))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))) @ (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cPredicate.pred.pred_size @ V0) @ V1)) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TPredicate.single_singleton,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: ((cPredicate.eval @ V0) @ V2)))) @ ((cHOL.eq @ (cPredicate.single @ ((cPredicate.singleton @ V1) @ V0))) @ V0)))))))
(TPredicate.singleton_single,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.singleton @ V0) @ (cPredicate.single @ V1))) @ V1))))))
(TPresburger.decr_mult_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V3) @ V0)))))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V3) @ ((cInt.times_int_inst.times_int @ V2) @ V0))))))))))))))))
(TPresburger.incr_mult_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ (V1 @ ((cInt.plus_int_inst.plus_int @ V3) @ V0)))))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ (V1 @ ((cInt.plus_int_inst.plus_int @ V3) @ ((cInt.times_int_inst.times_int @ V2) @ V0))))))))))))))))
(TPresburger.uminus_dvd_conv_2,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ (cInt.uminus_int_inst.uminus_int @ V1))))))))
(TPresburger.uminus_dvd_conv_1,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ (cInt.uminus_int_inst.uminus_int @ V0)) @ V1)))))))
(TPresburger.zdiff_int_split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ (cNat.semiring_1_class.of_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V2)))) @ ((cHOL.conj @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V1)) @ (V0 @ ((cInt.minus_int_inst.minus_int @ (cNat.semiring_1_class.of_nat @ V1)) @ (cNat.semiring_1_class.of_nat @ V2))))) @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ (V0 @ cInt.zero_int_inst.zero_int)))))))))))
(TProduct_Type.Collect_split,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V3))))))) @ ((cProduct_Type.Sigma @ (cSet.Collect @ V0)) @ (^[V2]: (cSet.Collect @ V1)))))))))
(TProduct_Type.apfst_compose,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.apfst @ V0) @ ((cProduct_Type.apfst @ V1) @ V2))) @ ((cProduct_Type.apfst @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TProduct_Type.apfst_eq_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.apfst @ V0) @ V1)) @ ((cProduct_Type.apfst @ V2) @ V1))) @ ((cHOL.eq @ (V0 @ (cProduct_Type.fst @ V1))) @ (V2 @ (cProduct_Type.fst @ V1)))))))))))
(TProduct_Type.apsnd_compose,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.apsnd @ V0) @ ((cProduct_Type.apsnd @ V1) @ V2))) @ ((cProduct_Type.apsnd @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TProduct_Type.apsnd_eq_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.apsnd @ V0) @ V1)) @ ((cProduct_Type.apsnd @ V2) @ V1))) @ ((cHOL.eq @ (V0 @ (cProduct_Type.snd @ V1))) @ (V2 @ (cProduct_Type.snd @ V1)))))))))))
(TProduct_Type.bool.distinct_2,(cHOL.Not @ ((cHOL.eq @ cHOL.False) @ cHOL.True)))
(TProduct_Type.bool.distinct_1,(cHOL.Not @ ((cHOL.eq @ cHOL.True) @ cHOL.False)))
(TProduct_Type.bool.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cHOL.True) @ cHOL.True)) @ cHOL.True))
(TProduct_Type.bool.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cHOL.False) @ cHOL.False)) @ cHOL.True))
(TProduct_Type.bool.eq.simps_2,((c== @ ((cHOL.equal_class.equal @ cHOL.True) @ cHOL.False)) @ cHOL.False))
(TProduct_Type.bool.eq.simps_1,((c== @ ((cHOL.equal_class.equal @ cHOL.False) @ cHOL.True)) @ cHOL.False))
(TProduct_Type.bool.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cHOL.True)) @ ((cHOL.eq @ V0) @ cHOL.False)))))
(TProduct_Type.map_pair.comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cFun.comp @ ((cProduct_Type.map_pair @ V0) @ V1)) @ ((cProduct_Type.map_pair @ V2) @ V3))) @ ((cProduct_Type.map_pair @ ((cFun.comp @ V0) @ V2)) @ ((cFun.comp @ V1) @ V3))))))))))))
(TProduct_Type.map_pair_simp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cProduct_Type.map_pair @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cProduct_Type.Pair @ (V0 @ V2)) @ (V1 @ V3))))))))))))
(TProduct_Type.map_pair_surj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ ((cSet.image @ V1) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ ((cProduct_Type.map_pair @ V0) @ V1)) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))))))))
(TProduct_Type.mem_Sigma_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Sigma @ V2) @ V3))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V2)) @ ((cSet.member @ V1) @ (V3 @ V0)))))))))))))
(TProduct_Type.pair_collapse,(call @ (^[V0]: ((cHOL.eq @ ((cProduct_Type.Pair @ (cProduct_Type.fst @ V0)) @ (cProduct_Type.snd @ V0))) @ V0))))
(TProduct_Type.prod.Rep_prod,(call @ (^[V0]: ((cSet.member @ (cProduct_Type.Rep_prod @ V0)) @ cProduct_Type.prod))))
(TProduct_Type.prod.eq.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TProduct_Type.prod.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))))))))
(TProduct_Type.split_comp_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (^[V2]: ((V0 @ (V1 @ (cProduct_Type.fst @ V2))) @ (cProduct_Type.snd @ V2)))) @ (cProduct_Type.prod.prod_case @ (^[V2]: (V0 @ (V1 @ V2))))))))))
(TProduct_Type.unit.Rep_unit,(call @ (^[V0]: ((cSet.member @ (cProduct_Type.Rep_unit @ V0)) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot)))))
(TProduct_Type.unit.eq.simps,((c== @ ((cHOL.equal_class.equal @ cProduct_Type.Unity) @ cProduct_Type.Unity)) @ cHOL.True))
(TProduct_Type.unit.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.eq @ V0) @ cProduct_Type.Unity))))
(TQuotient.Quotient3_abs_rep,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (V1 @ (V2 @ V3))) @ V3)))))))))))
(TQuotient.Quotient3_rel_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V4)))))))))))))))
(TQuotient.Quotient3_rel_rep,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ (V2 @ V3)) @ (V2 @ V4))) @ ((cHOL.eq @ V3) @ V4))))))))))))))
(TQuotient.Quotient3_rep_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V3)) @ ((V0 @ (V2 @ (V1 @ V3))) @ V3))))))))))))
(TQuotient.bex_reg_eqv_range,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((cHOL.eq @ ((cSet.Bex @ (cLifting.Respects @ ((cTransfer.fun_rel @ V1) @ V0))) @ (^[V4]: (V2 @ (V4 @ V3))))) @ (cHOL.Ex @ (^[V4]: (V2 @ (V4 @ V3)))))))))))))))
(TQuotient.quot_type.abs_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cQuotient.quot_type.abs @ V0) @ V1) @ V3)) @ (V1 @ (cSet.Collect @ (V0 @ V3))))))))))))))
(TQuotient.quot_type.rep_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cQuotient.quot_type.rep @ V2) @ V3)) @ (cHilbert_Choice.Eps @ (^[V4]: ((cSet.member @ V4) @ (V2 @ V3)))))))))))))))
(TRandom.iterate.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V2) @ V4))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cRandom.iterate_rel) @ V1))))))))
(TRandom.iterate_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.iterate_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V6)) @ ((cProduct_Type.scomp @ (V5 @ V6)) @ (^[V7]: (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom.iterate_graph @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))) @ V2)))))))))))) @ V2)))))))))
(TRandom.iterate_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom.iterate_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V5)) @ ((cProduct_Type.scomp @ (V4 @ V5)) @ (^[V6]: (V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V6)))))))) @ (cHOL.All @ (^[V6]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom.iterate_graph @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V6))) @ (V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V6)))))))))))))))))))))))
(TRandom.iterate_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.iterate_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V6))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Pred.iter'_sumC_def,((c== @ cRandom_Pred.iter'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cRandom_Pred.iter'_graph @ V0) @ V1))))))
(TRandom_Sequence.Random_def,((c== @ cRandom_Sequence.Random) @ (^[V0]: (^[V1]: (cRandom_Sequence.Random_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TRandom_Sequence.iter.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TRandom_Sequence.iter.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cRandom_Sequence.iter @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cHOL.eq @ V6) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V8]: ((cHOL.Let @ (V5 @ V7)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V9]: (^[V10]: (^[V11]: (cOption.option.Some @ ((cProduct_Type.Pair @ V9) @ (((cRandom_Sequence.iter @ V5) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V11)))))))))))))) @ V4))))))))))) @ V4)))))))))))))
(TRandom_Sequence.iter.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRandom_Sequence.iter @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V3]: ((cHOL.Let @ (V0 @ V2)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (^[V6]: (cOption.option.Some @ ((cProduct_Type.Pair @ V4) @ (((cRandom_Sequence.iter @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))))))))))))))))))
(TRandom_Sequence.single_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.single @ V0)) @ (^[V1]: (^[V2]: (cProduct_Type.Pair @ (cLimited_Sequence.single @ V0))))))))
(TRecord.iso_tuple_True_simp,(call @ (^[V0]: ((c== @ ((c==> @ cHOL.True) @ V0)) @ V0))))
(TRecord.tuple_iso_tuple_def,((c== @ cRecord.tuple_iso_tuple) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ cFun.id) @ cFun.id)))
(TRelation.Domain_Int_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cRelation.Domain @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cRelation.Domain @ V0)) @ (cRelation.Domain @ V1))))))))
(TRelation.Domainp_Domain_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domainp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: ((cSet.member @ V1) @ (cRelation.Domain @ V0)))))))
(TRelation.Range_Diff_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ (cRelation.Range @ V0)) @ (cRelation.Range @ V1))) @ (cRelation.Range @ ((cGroups.minus_class.minus @ V0) @ V1))))))))
(TRelation.converse_converse,(call @ (^[V0]: ((cHOL.eq @ (cRelation.converse @ (cRelation.converse @ V0))) @ V0))))
(TRelation.converse_relcompp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.conversep @ ((cRelation.relcompp @ V0) @ V1))) @ ((cRelation.relcompp @ (cRelation.conversep @ V1)) @ (cRelation.conversep @ V0))))))))
(TRelation.conversep.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cRelation.conversep @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V3 @ V5) @ V4))))))) @ ((V3 @ V1) @ V2))))))))))))
(TRelation.conversep_le_swap,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cRelation.conversep @ V1))) @ ((cOrderings.ord_class.less_eq @ (cRelation.conversep @ V0)) @ V1)))))))
(TRelation.relcompp.relcompI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V3 @ V2) @ V4)) @ ((((cRelation.relcompp @ V0) @ V3) @ V1) @ V4))))))))))))))
(TRelation.relcompp_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcompp @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cRelation.relcompp @ V0) @ V2)) @ ((cRelation.relcompp @ V1) @ V2))))))))))
(TRelation.single_valued_def,(call @ (^[V0]: ((cHOL.eq @ (cRelation.single_valued @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V0)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TRelation.total_on_converse,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.total_on @ V0) @ (cRelation.converse @ V1))) @ ((cRelation.total_on @ V0) @ V1)))))))
(TRings.class.semiring.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((c==> @ (cGroups.class.semigroup_mult @ V1)) @ ((c==> @ ((cRings.class.semiring_axioms @ V0) @ V1)) @ ((cRings.class.semiring @ V0) @ V1)))))))))
(TRings.class.semiring_0_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.semiring_0 @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.conj @ ((cRings.class.mult_zero @ V2) @ V1)) @ ((cRings.class.semiring @ V0) @ V2)))))))))))
(TRings.class.semiring_1_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.conj @ (((cRings.class.semiring_0 @ V2) @ V3) @ V1)) @ ((cRings.class.zero_neq_one @ V0) @ V3)))))))))))))
(TRings.comm_ring_1.dvd_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)) @ (((cRings.dvd.dvd @ V0) @ V6) @ ((V4 @ V7) @ V8))))))))))))))))))))))))
(TRings.ring.minus_mult_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ (V3 @ ((V4 @ V5) @ V6))) @ ((V4 @ (V3 @ V5)) @ V6))))))))))))))))))
(TRings.ring.mult_minus_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ (V3 @ V5)) @ V6)) @ (V3 @ ((V4 @ V5) @ V6)))))))))))))))))))
(TRings.semiring_0_class_def,((c== @ (cRings.semiring_0_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.mult_zero_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))))
(TRings.semiring_1_class_def,((c== @ (cRings.semiring_1_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.monoid_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.semiring_0_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))))
(TRings.semiring_class.intro,((c==> @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.semigroup_mult_class @ cTYPE)) @ ((c==> @ ((cRings.class.semiring_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times)) @ (cRings.semiring_class @ cTYPE)))))
(TRings.semiring_class.super_2,((c==> @ (cRings.semiring_class @ cTYPE)) @ (cGroups.semigroup_mult_class @ cTYPE)))
(TRings.semiring_class.super_1,((c==> @ (cRings.semiring_class @ cTYPE)) @ (cGroups.ab_semigroup_add_class @ cTYPE)))
(TSMT.pattern.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSMT.pattern.pattern_case @ V2) @ V0)) @ ((cSMT.pattern.pattern_case @ V2) @ V1))))))))))
(TSMT.random_aux_pattern_def,((c== @ cSMT.random_aux_pattern) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cSMT.pattern.Pattern) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cSMT.pattern.Pattern) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TSet.Compl_subset_Compl_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet.disjoint_iff_not_equal,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V1) @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ V2) @ V3))))))))))))
(TSet_Interval.Compl_atLeast,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cSet_Interval.ord_class.atLeast @ V0))) @ (cSet_Interval.ord_class.lessThan @ V0)))))
(TSet_Interval.UN_finite2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V3)) @ (^[V4]: (V0 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V1))) @ (^[V4]: (V2 @ V4))))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V3]: (V0 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V3]: (V2 @ V3))))))))))))
(TSet_Interval.atMost_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ (cSet_Interval.ord_class.atMost @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet_Interval.card_lessThan,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ (cSet_Interval.ord_class.lessThan @ V0))) @ V0))))
(TSet_Interval.card_less_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ (cNat.Suc @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ (cNat.Suc @ V2)) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ V2) @ V1))))))) @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.Suc @ V1)))))))))))))
(TSet_Interval.finite_atMost,(call @ (^[V0]: (cFinite_Set.finite @ (cSet_Interval.ord_class.atMost @ V0)))))
(TSet_Interval.geometric_sum,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.one_class.one))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: ((cPower.power_class.power @ V0) @ V2))) @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V1))) @ ((cFields.inverse_class.divide @ ((cGroups.minus_class.minus @ ((cPower.power_class.power @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cGroups.minus_class.minus @ V0) @ cGroups.one_class.one)))))))))
(TSet_Interval.greaterThan_0,((cHOL.eq @ (cSet_Interval.ord_class.greaterThan @ cNat.zero_nat_inst.zero_nat)) @ ((cSet.image @ cNat.Suc) @ cOrderings.top_class.top)))
(TString.arity_equal_literal,(cHOL.equal_class @ cTYPE))
(TString.char.Abs_char_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cString.Abs_char @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cString.char.char_rep_set))) @ V1))))) @ V1))))))
(TString.char.Rep_char_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.char.char_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cString.Rep_char @ V2))) @ V1)))) @ V1)))))))
(TString.char.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cString.char.char_case @ V2) @ V0)) @ ((cString.char.char_case @ V2) @ V1))))))))))
(TString.char_of_nat_mod_256,(call @ (^[V0]: ((cHOL.eq @ (cString.char_of_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))) @ (cString.char_of_nat @ V0)))))
(TString.char_of_nat_of_char,(call @ (^[V0]: ((cHOL.eq @ (cString.char_of_nat @ (cString.nat_of_char @ V0))) @ V0))))
(TString.enum_all_nibble_def,(call @ (^[V0]: ((cHOL.eq @ (cString.enum_nibble_inst.enum_all_nibble @ V0)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble0)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble1)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble2)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble3)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble4)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble5)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble6)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble7)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble8)) @ ((cHOL.conj @ (V0 @ cString.nibble.Nibble9)) @ ((cHOL.conj @ (V0 @ cString.nibble.NibbleA)) @ ((cHOL.conj @ (V0 @ cString.nibble.NibbleB)) @ ((cHOL.conj @ (V0 @ cString.nibble.NibbleC)) @ ((cHOL.conj @ (V0 @ cString.nibble.NibbleD)) @ ((cHOL.conj @ (V0 @ cString.nibble.NibbleE)) @ (V0 @ cString.nibble.NibbleF))))))))))))))))))))
(TString.literal.STR_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (cString.explode @ (cString.STR @ V0))) @ V0)))))
(TString.nat_of_nibble.simps_16,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.NibbleF)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_15,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.NibbleE)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_14,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.NibbleD)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_13,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.NibbleC)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_12,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.NibbleB)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_11,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.NibbleA)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_10,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble9)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_9,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble8)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))
(TString.nat_of_nibble.simps_8,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble7)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))
(TString.nat_of_nibble.simps_7,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble6)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))
(TString.nat_of_nibble.simps_6,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble5)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))
(TString.nat_of_nibble.simps_5,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble4)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))
(TString.nat_of_nibble.simps_4,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble3)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))))
(TString.nat_of_nibble.simps_3,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble2)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TString.nat_of_nibble.simps_2,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble1)) @ cNat.one_nat_inst.one_nat))
(TString.nat_of_nibble.simps_1,((cHOL.eq @ (cString.nat_of_nibble @ cString.nibble.Nibble0)) @ cNat.zero_nat_inst.zero_nat))
(TString.nibble_of_nat_simps_16,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))) @ cString.nibble.NibbleF))
(TString.nibble_of_nat_simps_15,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One)))))) @ cString.nibble.NibbleE))
(TString.nibble_of_nat_simps_14,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))) @ cString.nibble.NibbleD))
(TString.nibble_of_nat_simps_13,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))) @ cString.nibble.NibbleC))
(TString.nibble_of_nat_simps_12,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))) @ cString.nibble.NibbleB))
(TString.nibble_of_nat_simps_11,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One)))))) @ cString.nibble.NibbleA))
(TString.nibble_of_nat_simps_10,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))) @ cString.nibble.Nibble9))
(TString.nibble_of_nat_simps_9,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))) @ cString.nibble.Nibble8))
(TString.nibble_of_nat_simps_8,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit1 @ cNum.num.One))))) @ cString.nibble.Nibble7))
(TString.nibble_of_nat_simps_7,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One))))) @ cString.nibble.Nibble6))
(TString.nibble_of_nat_simps_6,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ cNum.num.One))))) @ cString.nibble.Nibble5))
(TString.nibble_of_nat_simps_5,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))) @ cString.nibble.Nibble4))
(TString.nibble_of_nat_simps_4,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One)))) @ cString.nibble.Nibble3))
(TString.nibble_of_nat_simps_3,((cHOL.eq @ (cString.nibble_of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cString.nibble.Nibble2))
(TString.nibble_of_nat_simps_2,((cHOL.eq @ (cString.nibble_of_nat @ cNat.one_nat_inst.one_nat)) @ cString.nibble.Nibble1))
(TString.nibble_of_nat_simps_1,((cHOL.eq @ (cString.nibble_of_nat @ cNat.zero_nat_inst.zero_nat)) @ cString.nibble.Nibble0))
(TSum_Type.sum.Abs_sum_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Abs_sum @ V2))) @ ((c==> @ ((cSet.member @ V2) @ cSum_Type.sum)) @ V1))))) @ V1))))))
(TSum_Type.sum.Rep_sum_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cSum_Type.sum)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSum_Type.Rep_sum @ V2))) @ V1)))) @ V1)))))))
(TTransfer.bi_unique_alt_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ cHOL.eq)))))
(TTransfer.nat_case_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ cHOL.eq) @ V0)) @ ((cTransfer.fun_rel @ cHOL.eq) @ V0))) @ cNat.nat.nat_case) @ cNat.nat.nat_case))))
(TTransfer.relcompp_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V2) @ cHOL.eq))) @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V2) @ cHOL.eq)))) @ cRelation.relcompp) @ cRelation.relcompp)))))))))
(TTransitive_Closure.tranclD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V1)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.tranclE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V1)) @ V2)) @ V3))))) @ V3))))))))))))
(TTyperep.arity_type_typerep,(cHOL.type_class @ cTYPE))
(TTyperep.arity_typerep_bool,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_char,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_list,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_node,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_prod,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_unit,(cTyperep.typerep_class @ cTYPE))
(TTyperep.typerep_itself_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TTyperep.typerep_nibble_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_nibble_inst.typerep_nibble @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_option_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TWellfounded.accp_downwards,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ V0) @ V1)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V1)) @ ((cWellfounded.accp @ V0) @ V2))))))))))
(TWellfounded.max_ext.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.max_ext @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V4)) @ ((cSet.Bex @ V5) @ (^[V7]: ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ V2))))))) @ ((V3 @ V4) @ V5)))))))))) @ ((V3 @ V0) @ V1))))))))))))
(TWellfounded.max_ext.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cSet.Bex @ V1) @ (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V2))))))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.max_ext @ V2)))))))))))))
(TWellfounded.max_extp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cWellfounded.max_extp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V5)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ (cSet.Collect @ (^[V6]: (cOrderings.bot_class.bot @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V4)) @ ((cSet.Bex @ V5) @ (V0 @ V6)))))) @ V3))))))))))) @ V3)))))))))))
(TWellfounded.max_extp.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cWellfounded.max_extp @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.conj @ (cFinite_Set.finite @ V3)) @ ((cHOL.conj @ (cFinite_Set.finite @ V4)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V4) @ (cSet.Collect @ (^[V5]: (cOrderings.bot_class.bot @ V5)))))) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cSet.member @ V5) @ V3)) @ ((cSet.Bex @ V4) @ (V0 @ V5))))))))))))))))))))))
(TWellfounded.trans_lex_prod,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.trans @ V0)) @ ((c==> @ (cRelation.trans @ V1)) @ (cRelation.trans @ ((cWellfounded.lex_prod @ V0) @ V1)))))))))
(TWellfounded.wfP_eq_minimal,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wfP @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cSet.member @ V2) @ V1)) @ ((cSet.Bex @ V1) @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V4) @ V3)) @ (cHOL.Not @ ((cSet.member @ V4) @ V1))))))))))))))))
(TWellfounded.wf_bounded_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)) @ ((cHOL.conj @ (cFinite_Set.finite @ (V1 @ V3))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V3))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V1 @ V3))) @ ((cOrderings.ord_class.less @ (V2 @ V3)) @ (V2 @ V4))))))))))) @ (cWellfounded.wf @ V0)))))))))
(TWellfounded.wf_induct_rule,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))))))
(TWellfounded.wf_union_merge,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cWellfounded.wf @ ((cLattices.sup_class.sup @ V0) @ V1))) @ (cWellfounded.wf @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ ((cRelation.relcomp @ V0) @ V0)) @ ((cRelation.relcomp @ V1) @ V0))) @ V1))))))))
(TBig_Operators.setprod_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V4]: ((V2 @ V3) @ V4))) @ (V1 @ V3)))) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V2 @ V3) @ V4))))) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3))))))))))))))
(TBig_Operators.setprod_delta,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ V1)) @ (V2 @ V3)) @ cGroups.one_class.one))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.one_class.one))))))))))
(TBig_Operators.setprod_diff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ (V1 @ V2)) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ (((cHOL.If @ ((cSet.member @ V2) @ V0)) @ ((cFields.inverse_class.divide @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ (V1 @ V2))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0))))))))))))
(TBig_Operators.setprod_empty,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ cOrderings.bot_class.bot)) @ cGroups.one_class.one))))
(TBig_Operators.setsum_Un_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1)))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1))))))))))))
(TBig_Operators.setsum_Un_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))))))
(TBig_Operators.setsum_delta',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V1) @ V3)) @ (V2 @ V3)) @ cGroups.zero_class.zero))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.zero_class.zero))))))))))
(TBig_Operators.setsum_diff1',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cGroups.plus_class.plus @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))))
(TBig_Operators.setsum_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet.insert @ V1) @ V0))) @ ((cGroups.plus_class.plus @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.setsum_nonneg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V1 @ V2))))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0))))))))
(TBig_Operators.setsum_nonpos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ (V1 @ V2)) @ cGroups.zero_class.zero)))) @ ((cOrderings.ord_class.less_eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ cGroups.zero_class.zero)))))))
(TCode_Evaluation.eq_eq_TrueD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c== @ ((c== @ V0) @ V1)) @ cHOL.True)) @ ((c== @ V0) @ V1)))))))
(TCode_Evaluation.term.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cCode_Evaluation.term.dummy_term)) @ (V0 @ V1)))))))
(TCode_Evaluation.term.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cCode_Evaluation.term.term_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cCode_Evaluation.term.dummy_term)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TCode_Evaluation.term.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cCode_Evaluation.term.term_case @ V1) @ V2))) @ ((cHOL.implies @ ((cHOL.eq @ V2) @ cCode_Evaluation.term.dummy_term)) @ (V0 @ V1))))))))))
(TCode_Evaluation.termify_def,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.termify @ V0)) @ cCode_Evaluation.term.dummy_term))))
(TCode_Evaluation.tracing_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Evaluation.tracing @ V0) @ V1)) @ V1))))))
(TCode_Evaluation.valapp_code,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cProduct_Type.Pair @ (V0 @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ (V1 @ cProduct_Type.Unity)) @ (V3 @ cProduct_Type.Unity))))))))))))))
(TCode_Generator.implies_code_2,(call @ (^[V0]: ((c== @ ((c==> @ V0) @ cCode_Generator.holds)) @ cCode_Generator.holds))))
(TCode_Generator.implies_code_1,(call @ (^[V0]: ((c== @ ((c==> @ cCode_Generator.holds) @ V0)) @ V0))))
(TCode_Numeral.cr_integer_def,((c== @ cCode_Numeral.cr_integer) @ (^[V0]: (^[V1]: ((cHOL.eq @ V0) @ (cCode_Numeral.int_of_integer @ V1))))))
(TCode_Numeral.cr_natural_def,((c== @ cCode_Numeral.cr_natural) @ (^[V0]: (^[V1]: ((cHOL.eq @ V0) @ (cCode_Numeral.nat_of_natural @ V1))))))
(TCode_Numeral.divmod_abs_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.divmod_abs @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cCode_Numeral.div_integer_inst.div_integer @ (cCode_Numeral.abs_integer_inst.abs_integer @ V0)) @ (cCode_Numeral.abs_integer_inst.abs_integer @ V1))) @ ((cCode_Numeral.div_integer_inst.mod_integer @ (cCode_Numeral.abs_integer_inst.abs_integer @ V0)) @ (cCode_Numeral.abs_integer_inst.abs_integer @ V1)))))))))
(TCode_Numeral.fst_divmod_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cCode_Numeral.divmod_abs @ V0) @ V1))) @ ((cCode_Numeral.div_integer_inst.div_integer @ (cCode_Numeral.abs_integer_inst.abs_integer @ V0)) @ (cCode_Numeral.abs_integer_inst.abs_integer @ V1))))))))
(TCode_Numeral.integer.domain,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ cHOL.eq)) @ V0)) @ ((cHOL.eq @ (cRelation.Domainp @ cCode_Numeral.pcr_integer)) @ V0)))))
(TCode_Numeral.integer_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.integer_of_num_3,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_num @ (cNum.num.Bit1 @ V0))) @ ((cHOL.Let @ (cCode_Numeral.integer_of_num @ V0)) @ (^[V1]: ((cCode_Numeral.plus_integer_inst.plus_integer @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ V1)) @ cCode_Numeral.one_integer_inst.one_integer)))))))
(TCode_Numeral.integer_of_num_2,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_num @ (cNum.num.Bit0 @ V0))) @ ((cHOL.Let @ (cCode_Numeral.integer_of_num @ V0)) @ (^[V1]: ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ V1)))))))
(TCode_Numeral.integer_of_num_1,((cHOL.eq @ (cCode_Numeral.integer_of_num @ cNum.num.One)) @ cCode_Numeral.one_integer_inst.one_integer))
(TCode_Numeral.natural.domain,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ cHOL.eq)) @ V0)) @ ((cHOL.eq @ (cRelation.Domainp @ cCode_Numeral.pcr_natural)) @ V0)))))
(TCode_Numeral.natural.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cCode_Numeral.Suc @ V2)))))) @ (V0 @ V1))))))))
(TCode_Numeral.natural.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cCode_Numeral.Suc @ V0)) @ (cCode_Numeral.Suc @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TCode_Numeral.natural.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cCode_Numeral.natural.natural_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cCode_Numeral.Suc @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TCode_Numeral.natural.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cCode_Numeral.natural.natural_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cCode_Numeral.Suc @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TCode_Numeral.natural_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.snd_divmod_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cCode_Numeral.divmod_abs @ V0) @ V1))) @ ((cCode_Numeral.div_integer_inst.mod_integer @ (cCode_Numeral.abs_integer_inst.abs_integer @ V0)) @ (cCode_Numeral.abs_integer_inst.abs_integer @ V1))))))))
(TComplete_Lattices.Compl_INT,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (cGroups.uminus_class.uminus @ (V1 @ V2))))))))))
(TComplete_Lattices.INF_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3))) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TComplete_Lattices.INT_empty,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ cOrderings.bot_class.bot) @ (^[V1]: (V0 @ V1)))) @ cOrderings.top_class.top))))
(TComplete_Lattices.INT_lower,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3)))) @ (V2 @ V0))))))))))
(TComplete_Lattices.INT_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cSet.image @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ (V0 @ V3))))))))))))
(TComplete_Lattices.INT_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.INFI @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))))))))))
(TComplete_Lattices.INT_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ (^[V3]: (V1 @ V3)))))))))))
(TComplete_Lattices.INT_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ V1) @ (V2 @ V3))))) @ ((cLattices.sup_class.sup @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.INT_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ V2)))) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TComplete_Lattices.INT_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cSet.insert @ V1) @ (V2 @ V3))))) @ ((cSet.insert @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.INT_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cGroups.minus_class.minus @ V1) @ (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top) @ ((cGroups.minus_class.minus @ V1) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3)))))))))))))
(TComplete_Lattices.INT_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cGroups.minus_class.minus @ (V1 @ V3)) @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top) @ ((cGroups.minus_class.minus @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2))))))))))
(TComplete_Lattices.INT_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ V1) @ (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top) @ ((cLattices.inf_class.inf @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3)))))))))))))
(TComplete_Lattices.INT_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top) @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2))))))))))
(TComplete_Lattices.Inf_apply,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.Inf_class.Inf @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V2 @ V1)))))))))
(TComplete_Lattices.Int_Union,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: ((cLattices.inf_class.inf @ V0) @ V2)))))))))
(TComplete_Lattices.Inter_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ ((cSet.Ball @ V1) @ (^[V2]: ((cSet.member @ V0) @ V2)))))))))
(TComplete_Lattices.SUP_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3))) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TComplete_Lattices.Sup_apply,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.Sup_class.Sup @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V2 @ V1)))))))))
(TComplete_Lattices.UN_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.UN_empty2,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot))))
(TComplete_Lattices.UN_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet.insert @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.sup_class.sup @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V2))))))))))
(TComplete_Lattices.Union_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((cSet.Bex @ V1) @ (^[V2]: ((cSet.member @ V0) @ V2)))))))))
(TComplete_Lattices.mem_simps_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ ((cSet.Ball @ V1) @ (^[V2]: ((cSet.member @ V0) @ V2)))))))))
(TComplete_Lattices.mem_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cSet.Ball @ V1) @ (^[V3]: ((cSet.member @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.mem_simps_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((cSet.Bex @ V1) @ (^[V2]: ((cSet.member @ V0) @ V2)))))))))
(TComplete_Lattices.mem_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cSet.Bex @ V1) @ (^[V3]: ((cSet.member @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.mem_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cSet.Collect @ V1))) @ (V1 @ V0)))))))
(TComplete_Lattices.mem_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V1)) @ (cHOL.Not @ ((cSet.member @ V0) @ V2)))))))))))
(TComplete_Lattices.mem_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cHOL.Not @ ((cSet.member @ V0) @ V1))))))))
(TComplete_Lattices.mem_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cHOL.conj @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TComplete_Lattices.mem_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cHOL.disj @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TComplete_Lattices.mem_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cSet.member @ V0) @ cOrderings.bot_class.bot)) @ cHOL.False))))
(TComplete_Lattices.mem_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.insert @ V1) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cSet.member @ V0) @ V2))))))))))
(TComplete_Lattices.vimage_UN,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cSet.vimage @ V0) @ (V2 @ V3))))))))))))
(TDatatype.dprod_subset_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V6]: V2)))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ ((cProduct_Type.Sigma @ V4) @ (^[V6]: V5)))) @ ((cOrderings.ord_class.less_eq @ ((cDatatype.dprod @ V0) @ V3)) @ ((cProduct_Type.Sigma @ ((cDatatype.uprod @ V1) @ V4)) @ (^[V6]: ((cDatatype.uprod @ V2) @ V5)))))))))))))))))))
(TDivides.Suc_div_eq_add3_div,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ V0)))) @ V1)) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V0)) @ V1)))))))
(TDivides.Suc_mod_eq_add3_mod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ V0)))) @ V1)) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V0)) @ V1)))))))
(TDivides.Suc_n_div_2_gt_zero,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ cNat.one_nat_inst.one_nat)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))
(TDivides.div_Suc_eq_div_add3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V0) @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ V1))))) @ ((cDivides.div_nat_inst.div_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V1))))))))
(TDivides.div_eq_dividend_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1)) @ V0)) @ ((cHOL.eq @ V1) @ cNat.one_nat_inst.one_nat))))))))
(TDivides.div_mult_self1_is_m,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ V0)) @ V1)))))))
(TDivides.div_neg_neg_trivial,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.div_pos_neg_trivial,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))))))))
(TDivides.div_pos_pos_trivial,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.mod_Suc_eq_mod_add3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ V1))))) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V1))))))))
(TDivides.mod_neg_neg_trivial,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V1) @ V0)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V0))))))))
(TDivides.mod_pos_neg_trivial,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1)))))))))
(TDivides.mod_pos_pos_trivial,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V0))))))))
(TDivides.negDivAlg_graph_def,((c== @ cDivides.negDivAlg_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))))))))))))))))
(TDivides.negDivAlg_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.negDivAlg_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ V2)))))))) @ V2)))))))))
(TDivides.negDivAlg_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.negDivAlg_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V2) @ V3))) @ ((cInt.ord_int_inst.less_eq_int @ V3) @ cInt.zero_int_inst.zero_int)))))))))))))))
(TDivides.one_div_nat_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ (cNum.numeral_class.numeral @ V0))) @ (cInt.nat @ ((cDivides.div_int_inst.div_int @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0)))))))
(TDivides.one_mod_nat_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ (cNum.numeral_class.numeral @ V0))) @ (cInt.nat @ ((cDivides.div_int_inst.mod_int @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0)))))))
(TDivides.posDivAlg_graph_def,((c== @ cDivides.posDivAlg_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))))))))))))))))
(TDivides.posDivAlg_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.posDivAlg_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ V2)))))))) @ V2)))))))))
(TDivides.posDivAlg_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.posDivAlg_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V2) @ V3)) @ ((cInt.ord_int_inst.less_eq_int @ V3) @ cInt.zero_int_inst.zero_int)))))))))))))))
(TDivides.zmod_zdiv_equality',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ ((cInt.minus_int_inst.minus_int @ V0) @ ((cInt.times_int_inst.times_int @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ V1))))))))
(TEnum.enum_class.enum_axioms,(((cEnum.class.enum @ cEnum.enum_class.enum) @ cEnum.enum_class.enum_all) @ cEnum.enum_class.enum_ex))
(TEnum.enum_fun_inst.enum_fun,((c== @ cEnum.enum_fun_inst.enum_fun) @ cEnum.enum_fun_inst.enum_fun))
(TEnum.enum_set_inst.enum_set,((c== @ cEnum.enum_set_inst.enum_set) @ cEnum.enum_set_inst.enum_set))
(TEnum.enum_sum_inst.enum_sum,((c== @ cEnum.enum_sum_inst.enum_sum) @ cEnum.enum_sum_inst.enum_sum))
(TEnum.finite_1.a\<__caret__sub>1_def,((c== @ cEnum.finite_1.a\<__caret__sub>1) @ (cEnum.Abs_finite_1 @ cHOL.undefined)))
(TEnum.finite_2.a\<__caret__sub>1_def,((c== @ cEnum.finite_2.a\<__caret__sub>1) @ (cEnum.Abs_finite_2 @ (cDatatype.In0 @ cHOL.undefined))))
(TEnum.finite_2.a\<__caret__sub>2_def,((c== @ cEnum.finite_2.a\<__caret__sub>2) @ (cEnum.Abs_finite_2 @ (cDatatype.In1 @ cHOL.undefined))))
(TEnum.finite_3.a\<__caret__sub>1_def,((c== @ cEnum.finite_3.a\<__caret__sub>1) @ (cEnum.Abs_finite_3 @ (cDatatype.In0 @ cHOL.undefined))))
(TEnum.finite_3.a\<__caret__sub>2_def,((c== @ cEnum.finite_3.a\<__caret__sub>2) @ (cEnum.Abs_finite_3 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))
(TEnum.finite_3.a\<__caret__sub>3_def,((c== @ cEnum.finite_3.a\<__caret__sub>3) @ (cEnum.Abs_finite_3 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))
(TEnum.finite_4.a\<__caret__sub>1_def,((c== @ cEnum.finite_4.a\<__caret__sub>1) @ (cEnum.Abs_finite_4 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))
(TEnum.finite_4.a\<__caret__sub>2_def,((c== @ cEnum.finite_4.a\<__caret__sub>2) @ (cEnum.Abs_finite_4 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))
(TEnum.finite_4.a\<__caret__sub>3_def,((c== @ cEnum.finite_4.a\<__caret__sub>3) @ (cEnum.Abs_finite_4 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))
(TEnum.finite_4.a\<__caret__sub>4_def,((c== @ cEnum.finite_4.a\<__caret__sub>4) @ (cEnum.Abs_finite_4 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))
(TEnum.finite_5.a\<__caret__sub>1_def,((c== @ cEnum.finite_5.a\<__caret__sub>1) @ (cEnum.Abs_finite_5 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))
(TEnum.finite_5.a\<__caret__sub>2_def,((c== @ cEnum.finite_5.a\<__caret__sub>2) @ (cEnum.Abs_finite_5 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))
(TEnum.finite_5.a\<__caret__sub>3_def,((c== @ cEnum.finite_5.a\<__caret__sub>3) @ (cEnum.Abs_finite_5 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))
(TEnum.finite_5.a\<__caret__sub>4_def,((c== @ cEnum.finite_5.a\<__caret__sub>4) @ (cEnum.Abs_finite_5 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))))
(TEnum.finite_5.a\<__caret__sub>5_def,((c== @ cEnum.finite_5.a\<__caret__sub>5) @ (cEnum.Abs_finite_5 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))))
(TEnum.map_of_zip_enum_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ cEnum.enum_class.enum))) @ ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ cEnum.enum_class.enum))) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ cEnum.enum_class.enum) @ V0)))) @ ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ cEnum.enum_class.enum) @ V1))))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TEquiv_Relations.comp_equivI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cRelation.relcomp @ (cRelation.converse @ V0)) @ V0)) @ V0)) @ ((c==> @ ((cHOL.eq @ (cRelation.Domain @ V0)) @ V1)) @ ((cEquiv_Relations.equiv @ V1) @ V0))))))))
(TEquiv_Relations.congruent2D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cEquiv_Relations.congruent2 @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V1)) @ ((cHOL.eq @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V6))))))))))))))))))))
(TEquiv_Relations.congruent2I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cEquiv_Relations.equiv @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V1)) @ ((cHOL.eq @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V7))))))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V3)) @ ((cHOL.eq @ ((V4 @ V7) @ V5)) @ ((V4 @ V7) @ V6))))))))))) @ (((cEquiv_Relations.congruent2 @ V1) @ V3) @ V4))))))))))))))))
(TEquiv_Relations.equivp_symp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TExtraction.sumbool.Left_def,((c== @ cExtraction.sumbool.Left) @ (cExtraction.Abs_sumbool @ (cDatatype.In0 @ cHOL.undefined))))
(TExtraction.sumbool.distinct_2,(cHOL.Not @ ((cHOL.eq @ cExtraction.sumbool.Right) @ cExtraction.sumbool.Left)))
(TExtraction.sumbool.distinct_1,(cHOL.Not @ ((cHOL.eq @ cExtraction.sumbool.Left) @ cExtraction.sumbool.Right)))
(TExtraction.sumbool.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cExtraction.sumbool.Left) @ cExtraction.sumbool.Left)) @ cHOL.True))
(TExtraction.sumbool.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cExtraction.sumbool.Right) @ cExtraction.sumbool.Right)) @ cHOL.True))
(TExtraction.sumbool.eq.simps_2,((c== @ ((cHOL.equal_class.equal @ cExtraction.sumbool.Left) @ cExtraction.sumbool.Right)) @ cHOL.False))
(TExtraction.sumbool.eq.simps_1,((c== @ ((cHOL.equal_class.equal @ cExtraction.sumbool.Right) @ cExtraction.sumbool.Left)) @ cHOL.False))
(TExtraction.sumbool.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cExtraction.sumbool.Left)) @ ((cHOL.eq @ V0) @ cExtraction.sumbool.Right)))))
(TFinite_Set.arity_finite_fun,(cFinite_Set.finite_class @ cTYPE))
(TFinite_Set.arity_finite_set,(cFinite_Set.finite_class @ cTYPE))
(TFinite_Set.arity_finite_sum,(cFinite_Set.finite_class @ cTYPE))
(TFinite_Set.card_Diff_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V2))) @ ((cHOL.eq @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ V2)))) @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ V2))) @ cNat.one_nat_inst.one_nat))))))))))))
(TFinite_Set.card_Diff_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V0))))))))))
(TFinite_Set.card_Un_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1)))))))))))
(TFinite_Set.card_ge_0_finite,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cFinite_Set.card @ V0))) @ (cFinite_Set.finite @ V0)))))
(TFinite_Set.class.finite_def,((c== @ (cFinite_Set.class.finite @ cTYPE)) @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TFinite_Set.ex_new_if_finite,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ cOrderings.top_class.top))) @ ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: (cHOL.Not @ ((cSet.member @ V1) @ V0)))))))))
(TFinite_Set.finite_Prod_UNIV,((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ cOrderings.top_class.top))))
(TFinite_Set.finite_class_def,((c== @ (cFinite_Set.finite_class @ cTYPE)) @ ((cPure.conjunction @ (cHOL.type_class @ cTYPE)) @ (cFinite_Set.class.finite @ cTYPE))))
(TFinite_Set.finite_image_set,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (V0 @ V2))))) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (V1 @ V3))) @ (V0 @ V3)))))))))))))
(TFinite_Set.finite_ne_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: (V1 @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cSet.insert @ V2) @ V3))))))))))) @ (V1 @ V0))))))))))
(TFinite_Set.fold_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)) @ ((c==> @ ((cHOL.eq @ V3) @ V1)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V2) @ ((cSet.insert @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V3) @ ((V0 @ V5) @ V7))) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V5) @ V6))) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V6) @ V7)) @ V4))))))))))) @ V4))))))))))))))
(TFinite_Set.fold_graph.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V3) @ V1))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cSet.insert @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((V0 @ V4) @ V6))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V4) @ V5))) @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V5) @ V6)))))))))))))))))))))
(TFinite_Set.folding.infinite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V1))) @ ((cHOL.eq @ (((cFinite_Set.folding.F @ V0) @ V2) @ V1)) @ V2))))))))))
(TFinite_Set.folding_idem_def,(call @ (^[V0]: ((c== @ (cFinite_Set.folding_idem @ V0)) @ ((cHOL.conj @ (cFinite_Set.folding @ V0)) @ (cFinite_Set.folding_idem_axioms @ V0))))))
(TFinite_Set.insert_partition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((c==> @ ((cSet.Ball @ ((cSet.insert @ V0) @ V1)) @ (^[V2]: ((cSet.Ball @ ((cSet.insert @ V0) @ V1)) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ cOrderings.bot_class.bot))))))))
(TFinite_Set.inter_Set_filter,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ V0)) @ ((cSet.filter @ (^[V2]: ((cSet.member @ V2) @ V1))) @ V0))))))))
(TFun.inj_on_vimage_singleton,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ ((cSet.vimage @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ V1)) @ ((cSet.insert @ (cHOL.The @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V1)) @ ((cHOL.eq @ (V0 @ V3)) @ V2))))) @ cOrderings.bot_class.bot))))))))))
(TFun.override_on_apply_notin,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((cHOL.eq @ ((((cFun.override_on @ V2) @ V3) @ V1) @ V0)) @ (V2 @ V0))))))))))))
(TFun.surj_Compl_image_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ ((cSet.image @ V0) @ V1))) @ ((cSet.image @ V0) @ (cGroups.uminus_class.uminus @ V1)))))))))
(TFunDef.fundef_default_value,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c== @ V0) @ (^[V5]: ((cFunDef.THE_default @ (V1 @ V5)) @ (^[V6]: ((V2 @ V5) @ V6)))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((V2 @ V5) @ V6)) @ (V3 @ V5))))))) @ ((c==> @ (cHOL.Not @ (V3 @ V4))) @ ((cHOL.eq @ (V0 @ V4)) @ (V1 @ V4))))))))))))))))
(TFunDef.fundef_ex1_existence,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c== @ V0) @ (^[V4]: ((cFunDef.THE_default @ (V1 @ V4)) @ (^[V5]: ((V2 @ V4) @ V5)))))) @ ((c==> @ (cHOL.Ex1 @ (^[V4]: ((V2 @ V3) @ V4)))) @ ((V2 @ V3) @ (V0 @ V3)))))))))))))
(TFunDef.reduction_pair_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFunDef.reduction_pair @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ (cProduct_Type.fst @ V0))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (cProduct_Type.snd @ V0))) @ ((c==> @ (cWellfounded.wf @ V2)) @ (cWellfounded.wf @ ((cLattices.sup_class.sup @ V1) @ V2)))))))))))))
(TGroups.abel_semigroup.intro,(call @ (^[V0]: ((c==> @ (cGroups.semigroup @ V0)) @ ((c==> @ (cGroups.abel_semigroup_axioms @ V0)) @ (cGroups.abel_semigroup @ V0))))))
(TGroups.class.monoid_add_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.class.semigroup_add @ V0)) @ ((cGroups.class.monoid_add_axioms @ V0) @ V1))))))))
(TGroups.group_add.diff_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ V6)) @ ((cHOL.eq @ V4) @ ((V1 @ V6) @ V5)))))))))))))))))))
(TGroups.group_add.diff_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ (V3 @ V5)))))))))))))))))
(TGroups.group_add.eq_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V4) @ ((V0 @ V5) @ V6))) @ ((cHOL.eq @ ((V1 @ V4) @ V6)) @ V5))))))))))))))))))
(TGroups.group_add.left_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ (V3 @ V4)) @ V4)) @ V2)))))))))))))
(TGroups.group_add.minus_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ V2)) @ V2)))))))))))
(TGroups.monoid.right_neutral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.monoid @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))))))))
(TGroups.monoid_add_class_def,((c== @ (cGroups.monoid_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.zero_class @ cTYPE)) @ ((cGroups.class.monoid_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))))
(THilbert_Choice.Eps_split_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHilbert_Choice.Eps @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))) @ ((cProduct_Type.Pair @ V0) @ V1)))))))
(THilbert_Choice.Greatest_def,((c== @ cHilbert_Choice.Greatest) @ (cHilbert_Choice.GreatestM @ (^[V0]: V0))))
(THilbert_Choice.bchoice_iff',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ (cHOL.Ex @ (^[V4]: ((V2 @ V3) @ V4))))))) @ (cHOL.Ex @ (^[V3]: ((cSet.Ball @ V0) @ (^[V4]: ((cHOL.implies @ (V1 @ V4)) @ ((V2 @ V4) @ (V3 @ V4)))))))))))))))
(THilbert_Choice.f_inv_into_f,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cSet.image @ V1) @ V2))) @ ((cHOL.eq @ (V1 @ (((cHilbert_Choice.inv_into @ V2) @ V1) @ V0))) @ V0)))))))))
(THilbert_Choice.inj_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ ((cSet.image @ V0) @ cOrderings.top_class.top))) @ (V1 @ (((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0) @ V3)))))) @ (V1 @ V2))))))))))
(THilbert_Choice.inv_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ (V1 @ V2))) @ V2)))) @ ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V1 @ (V0 @ V2))) @ V2)))) @ ((cHOL.eq @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V1)) @ V0))))))))
(THilbert_Choice.inv_into_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHilbert_Choice.inv_into @ V0) @ V1)) @ (^[V2]: (cHilbert_Choice.Eps @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ V3)) @ V2)))))))))))
(THilbert_Choice.inv_into_f_f,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ (((cHilbert_Choice.inv_into @ V1) @ V0) @ (V0 @ V2))) @ V2))))))))))
(THilbert_Choice.inv_o_cancel,(call @ (^[V0]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cFun.comp @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ V0)) @ cFun.id)))))
(THilbert_Choice.surj_f_inv_f,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (V0 @ (((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0) @ V1))) @ V1)))))))
(THilbert_Choice.surj_iff_all,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ (cHOL.All @ (^[V1]: ((cHOL.eq @ (V0 @ (((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0) @ V1))) @ V1)))))))
(TInt.divide_le_0_iff_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)))))))))
(TInt.divide_less_eq_numeral1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V2) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V0)))))))))
(TInt.divide_less_eq_numeral1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ (cNum.numeral_class.numeral @ V1))) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ V2) @ (cNum.numeral_class.numeral @ V1)))))))))))
(TInt.less_divide_eq_numeral1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cFields.inverse_class.divide @ V1) @ (cNum.neg_numeral_class.neg_numeral @ V2)))) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ V0) @ (cNum.neg_numeral_class.neg_numeral @ V2)))))))))))
(TInt.less_divide_eq_numeral1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cFields.inverse_class.divide @ V1) @ (cNum.numeral_class.numeral @ V2)))) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ V2))) @ V1)))))))))
(TInt.ring_1.of_int_of_nat_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ (cNat.semiring_1_class.of_nat @ V6))) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V6))))))))))))))))))
(TInt.ring_1_class.Ints_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cInt.ring_1_class.of_int @ V2))) @ V1)))) @ V1)))))))
(TInt.ring_1_class.Ints_minus,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((cSet.member @ (cGroups.uminus_class.uminus @ V0)) @ cInt.ring_1_class.Ints)))))
(TInt.ring_1_class.Ints_power,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((cSet.member @ ((cPower.power_class.power @ V0) @ V1)) @ cInt.ring_1_class.Ints)))))))
(TInt.ring_1_class.of_int.rsp,((((cTransfer.fun_rel @ cInt.intrel) @ cHOL.eq) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cGroups.minus_class.minus @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1)))))) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cGroups.minus_class.minus @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1)))))))
(TInt.ring_1_class.of_int_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))))))))
(TInt.ring_1_class.of_int_def,((c== @ cInt.ring_1_class.of_int) @ (((cFun.map_fun @ cInt.Rep_Integ) @ cFun.id) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cGroups.minus_class.minus @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TInt.ring_1_class.of_nat_nat,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cInt.nat @ V0))) @ (cInt.ring_1_class.of_int @ V0))))))
(TInt.zmult_zless_mono2_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cInt.ord_int_inst.less_int @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ V2)) @ V0)) @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ V2)) @ V1)))))))))))
(TLattices.semilattice.axioms_2,(call @ (^[V0]: ((c==> @ (cLattices.semilattice @ V0)) @ (cLattices.semilattice_axioms @ V0)))))
(TLattices.semilattice.axioms_1,(call @ (^[V0]: ((c==> @ (cLattices.semilattice @ V0)) @ (cGroups.abel_semigroup @ V0)))))
(TLazy_Sequence.case_yield_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cOption.option.option_case @ V0) @ V1) @ (cLazy_Sequence.yield @ V2))) @ (((cList.list.list_case @ V0) @ (^[V3]: ((cFun.comp @ ((cProduct_Type.curry @ V1) @ V3)) @ cLazy_Sequence.lazy_sequence.lazy_sequence_of_list))) @ (cLazy_Sequence.list_of_lazy_sequence @ V2))))))))))
(TLazy_Sequence.hb_if_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.hb_if_seq @ V0)) @ (((cHOL.If @ V0) @ (cLazy_Sequence.hb_single @ cProduct_Type.Unity)) @ cLazy_Sequence.empty)))))
(TLazy_Sequence.hb_single_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.hb_single @ V0)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V1]: (cOption.option.Some @ ((cProduct_Type.Pair @ (cOption.option.Some @ V0)) @ cLazy_Sequence.empty))))))))
(TLazy_Sequence.hit_bound_def,((cHOL.eq @ cLazy_Sequence.hit_bound) @ (cLazy_Sequence.Lazy_Sequence @ (^[V0]: (cOption.option.Some @ ((cProduct_Type.Pair @ cOption.option.None) @ cLazy_Sequence.empty))))))
(TLifting.Quotient_abs_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((V0 @ V6) @ V6)) @ (V4 @ (V1 @ V6)))))) @ (V4 @ V5))))))))))))))))
(TLifting.Quotient_to_Domainp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (cRelation.Domainp @ V3)) @ (^[V4]: ((V0 @ V4) @ V4)))))))))))))
(TLifting.bi_total_left_total,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ (cLifting.left_total @ V0)))))
(TLifting.functional_relation,(call @ (^[V0]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((c==> @ (cLifting.left_total @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Ex1 @ (^[V2]: ((V0 @ V1) @ V2))))))))))
(TLifting.invariant_same_args,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (((cLifting.invariant @ V0) @ V1) @ V1)) @ (V0 @ V1)))))))
(TLifting.typedef_left_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ (cLifting.left_unique @ V3))))))))))))
(TLifting.typedef_right_total,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ (cTransfer.right_total @ V3))))))))))))
(TLifting.typedef_to_Quotient,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ ((((cLifting.Quotient @ (cLifting.invariant @ (^[V4]: ((cSet.member @ V4) @ V2)))) @ V1) @ V0) @ V3))))))))))))
(TLifting_Product.prod_rel_OO,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cRelation.relcompp @ ((cLifting_Product.prod_rel @ V0) @ V1)) @ ((cLifting_Product.prod_rel @ V2) @ V3))) @ ((cLifting_Product.prod_rel @ ((cRelation.relcompp @ V0) @ V2)) @ ((cRelation.relcompp @ V1) @ V3))))))))))))
(TLifting_Product.prod_rel_eq,((cHOL.eq @ ((cLifting_Product.prod_rel @ cHOL.eq) @ cHOL.eq)) @ cHOL.eq))
(TLifting_Set.SUPR_parametric,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq)) @ cComplete_Lattices.complete_lattice_class.SUPR) @ cComplete_Lattices.complete_lattice_class.SUPR))))
(TLifting_Set.filter_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V0))) @ cSet.filter) @ cSet.filter)))))
(TLifting_Set.finite_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ cHOL.eq) @ cFinite_Set.finite) @ cFinite_Set.finite)))))
(TLifting_Set.insert_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V0))) @ cSet.insert) @ cSet.insert))))
(TLifting_Set.member_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ cHOL.eq)) @ cSet.member) @ cSet.member)))))
(TLifting_Set.subset_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ cHOL.eq)) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq)))))
(TLimited_Sequence.if_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.if_seq @ V0)) @ (((cHOL.If @ V0) @ (cLimited_Sequence.single @ cProduct_Type.Unity)) @ cLimited_Sequence.empty)))))
(TLimited_Sequence.single_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.single @ V0)) @ (^[V1]: (^[V2]: (cOption.option.Some @ (cLazy_Sequence.single @ V0))))))))
(TList.append_butlast_last_id,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ ((cList.append @ (cList.butlast @ V0)) @ ((cList.list.Cons @ (cList.last @ V0)) @ cList.list.Nil))) @ V0)))))
(TList.append_eq_append_conv2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ ((cList.append @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ V4))) @ ((cHOL.eq @ ((cList.append @ V4) @ V1)) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ ((cList.append @ V0) @ V4)) @ V2)) @ ((cHOL.eq @ V1) @ ((cList.append @ V4) @ V3))))))))))))))))
(TList.distinct_length_filter,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ (cNat.size_class.size @ ((cList.filter @ V1) @ V0))) @ (cFinite_Set.card @ ((cLattices.inf_class.inf @ (cSet.Collect @ (^[V2]: (V1 @ V2)))) @ (cList.set @ V0))))))))))
(TList.distinct_product_lists,(call @ (^[V0]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V1]: (cList.distinct @ V1)))) @ (cList.distinct @ (cList.product_lists @ V0))))))
(TList.dropWhile_eq_Cons_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.dropWhile @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ ((cList.takeWhile @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ V3)))) @ (cHOL.Not @ (V0 @ V2)))))))))))))
(TList.enumerate_replicate_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.enumerate @ V0) @ ((cList.replicate @ V1) @ V2))) @ ((cList.map @ (^[V3]: ((cProduct_Type.Pair @ V3) @ V2))) @ ((cList.upt @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)))))))))))
(TList.finite_lists_length_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ V0)) @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ V1)))))))))))
(TList.finite_lists_length_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V2)) @ V1)))))))))))
(TList.fold_append_concat_rev,(call @ (^[V0]: ((cHOL.eq @ ((cList.fold @ cList.append) @ V0)) @ (cList.append @ (cList.concat @ (cList.rev @ V0)))))))
(TList.greaterThanAtMost_upto,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ (cList.set @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1))))))))
(TList.in_set_butlast_appendI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.disj @ ((cSet.member @ V0) @ (cList.set @ (cList.butlast @ V1)))) @ ((cSet.member @ V0) @ (cList.set @ (cList.butlast @ V2))))) @ ((cSet.member @ V0) @ (cList.set @ (cList.butlast @ ((cList.append @ V1) @ V2))))))))))))
(TList.lexord_take_index_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.lexord @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ ((cList.take @ (cNat.size_class.size @ V0)) @ V1)) @ V0))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V3) @ ((cOrderings.ord_class.min @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ ((cList.take @ V3) @ V0)) @ ((cList.take @ V3) @ V1))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.nth @ V0) @ V3)) @ ((cList.nth @ V1) @ V3))) @ V2))))))))))))))
(TList.linorder.distinct_sort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cList.distinct @ (((cList.linorder.sort_key @ V0) @ V2) @ V3))) @ (cList.distinct @ V3))))))))))))
(TList.linorder.filter_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ V3))) @ ((c==> @ (V4 @ V5)) @ ((cHOL.eq @ ((cList.filter @ V4) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V5) @ V3))) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V5) @ ((cList.filter @ V4) @ V3)))))))))))))))))))
(TList.linorder.length_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cNat.size_class.size @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4))) @ (cNat.Suc @ (cNat.size_class.size @ V4)))))))))))))))
(TList.linorder.sorted.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((c==> @ (V3 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: ((V0 @ V5) @ V6)))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V4)) @ ((c==> @ (V3 @ V4)) @ (V3 @ ((cList.list.Cons @ V5) @ V4)))))))))) @ (V3 @ V2))))))))))))))
(TList.linorder.sorted.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: ((V0 @ V3) @ V4)))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V3) @ V2))))))))))))))
(TList.linorder.sorted.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cList.linorder.sorted @ V0) @ cList.list.Nil)))))))
(TList.linorder.sorted_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted @ V0) @ ((cList.append @ V2) @ V3))) @ ((cHOL.conj @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cHOL.conj @ ((cList.linorder.sorted @ V0) @ V3)) @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: ((cSet.Ball @ (cList.set @ V3)) @ (^[V5]: ((V0 @ V4) @ V5))))))))))))))))))
(TList.linorder.sorted_filter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ V3))) @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ ((cList.filter @ V4) @ V3))))))))))))))))
(TList.linorder.sorted_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted @ V0) @ ((((cList.linorder.insort_key @ V0) @ (^[V4]: V4)) @ V2) @ V3))) @ ((cList.linorder.sorted @ V0) @ V3))))))))))))
(TList.linorder.sorted_single,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V2) @ cList.list.Nil))))))))))
(TList.list_all2_conv_all_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.list_all2 @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V1)) @ (cNat.size_class.size @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V1))) @ ((V0 @ ((cList.nth @ V1) @ V3)) @ ((cList.nth @ V2) @ V3))))))))))))))
(TList.list_invariant_commute,(call @ (^[V0]: ((cHOL.eq @ (cList.list_all2 @ (cLifting.invariant @ V0))) @ (cLifting.invariant @ (cList.list_all @ V0))))))
(TList.map_tailrec_rev.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (((V0 @ V4) @ cList.list.Nil) @ V5)))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((V0 @ V4) @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7))) @ (((V0 @ V4) @ ((cList.list.Cons @ V5) @ V6)) @ V7))))))))))) @ (((V0 @ V1) @ V2) @ V3))))))))))))
(TList.map_tailrec_rev.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cList.map_tailrec_rev @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ V6)) @ ((c==> @ ((cHOL.eq @ V3) @ V6)) @ ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V6)))) @ V4)))))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ V2) @ V8)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cList.map_tailrec_rev @ V5) @ V7) @ ((cList.list.Cons @ (V5 @ V6)) @ V8)))) @ ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V7)) @ V8)))) @ V4)))))))))))))) @ V4)))))))))))))))
(TList.map_tailrec_rev.psimps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V1) @ V2)) @ V3)))) @ ((cHOL.eq @ (((cList.map_tailrec_rev @ V0) @ ((cList.list.Cons @ V1) @ V2)) @ V3)) @ (((cList.map_tailrec_rev @ V0) @ V2) @ ((cList.list.Cons @ (V0 @ V1)) @ V3)))))))))))))
(TList.map_tailrec_rev.psimps_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V1)))) @ ((cHOL.eq @ (((cList.map_tailrec_rev @ V0) @ cList.list.Nil) @ V1)) @ V1)))))))
(TList.monoid_add.listsum_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ V2)) @ (((cList.foldr @ V0) @ V2) @ V1))))))))))
(TList.nth_append_length_plus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.nth @ ((cList.append @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ V0)) @ V2))) @ ((cList.nth @ V1) @ V2)))))))))
(TList.nth_non_equal_first_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.nth @ ((cList.list.Cons @ V0) @ V2)) @ V3)) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ ((cList.nth @ V2) @ ((cNat.minus_nat_inst.minus_nat @ V3) @ cNat.one_nat_inst.one_nat))) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V3)))))))))))))
(TList.product_lists_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ (cList.list_all2 @ (cList.list_all2 @ V0))) @ (cList.list_all2 @ (cList.list_all2 @ V0))) @ cList.product_lists) @ cList.product_lists))))
(TList.remdups_adj_append_two,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.remdups_adj @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ ((cList.list.Cons @ V2) @ cList.list.Nil))))) @ ((cList.append @ (cList.remdups_adj @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ V2)) @ cList.list.Nil) @ ((cList.list.Cons @ V2) @ cList.list.Nil)))))))))))
(TList.remdups_adj_length_ge1,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ (cNat.size_class.size @ (cList.remdups_adj @ V0)))))))
(TList.remdups_adj_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.remdups_adj_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V3) @ V4)) @ ((V2 @ ((cList.list.Cons @ V3) @ V5)) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((V2 @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.remdups_adj_rel.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cList.remdups_adj_rel @ ((cList.list.Cons @ V1) @ V2)) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2)))))))))))
(TList.remdups_adj_rel.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cList.remdups_adj_rel @ ((cList.list.Cons @ V0) @ V2)) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2)))))))))))
(TList.replicate_eq_replicate,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.replicate @ V0) @ V1)) @ ((cList.replicate @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ V1) @ V3)))))))))))))
(TList.right_unique_list_all2,(call @ (^[V0]: ((c==> @ (cTransfer.right_unique @ V0)) @ (cTransfer.right_unique @ (cList.list_all2 @ V0))))))
(TList.snoc_listrel1_snoc_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.append @ V0) @ ((cList.list.Cons @ V1) @ cList.list.Nil))) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ cList.list.Nil)))) @ (cList.listrel1 @ V4))) @ ((cHOL.disj @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ (cList.listrel1 @ V4))) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V4)))))))))))))))
(TList.split_list_first_propE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V3]: (V1 @ V3)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.append @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ (V1 @ V4)) @ ((c==> @ ((cSet.Ball @ (cList.set @ V3)) @ (^[V6]: (cHOL.Not @ (V1 @ V6))))) @ V2)))))))))) @ V2)))))))))
(TList.takeWhile_dropWhile_id,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.append @ ((cList.takeWhile @ V0) @ V1)) @ ((cList.dropWhile @ V0) @ V1))) @ V1))))))
(TList.transpose_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.transpose_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ cList.list.Nil) @ cList.list.Nil)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cList.transpose_graph @ V4) @ (V3 @ V4))) @ ((c==> @ ((V2 @ V4) @ (V3 @ V4))) @ ((V2 @ ((cList.list.Cons @ cList.list.Nil) @ V4)) @ (V3 @ V4))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cList.transpose_graph @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))))) @ ((c==> @ ((V2 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))))) @ ((V2 @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ V5)) @ V6)) @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))))
(TList.transpose_graph.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cList.transpose_graph @ ((cList.list.Cons @ V0) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V4]: (^[V5]: ((cList.list.Cons @ V5) @ cList.list.Nil))))) @ V1)))) @ (V2 @ ((cList.list.Cons @ V0) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V4]: (^[V5]: ((cList.list.Cons @ V5) @ cList.list.Nil))))) @ V1)))))) @ ((cList.transpose_graph @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ V0)) @ V1)) @ ((cList.list.Cons @ ((cList.list.Cons @ V3) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V4]: (^[V5]: ((cList.list.Cons @ V4) @ cList.list.Nil))))) @ V1)))) @ (V2 @ ((cList.list.Cons @ V0) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V4]: (^[V5]: ((cList.list.Cons @ V5) @ cList.list.Nil))))) @ V1))))))))))))))))
(TList.transpose_graph.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cList.transpose_graph @ V0) @ (V1 @ V0))) @ ((cList.transpose_graph @ ((cList.list.Cons @ cList.list.Nil) @ V0)) @ (V1 @ V0))))))))
(TList.transpose_graph.intros_1,((cList.transpose_graph @ cList.list.Nil) @ cList.list.Nil))
(TList.upd_conv_take_nth_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ ((cHOL.eq @ (((cList.list_update @ V1) @ V0) @ V2)) @ ((cList.append @ ((cList.take @ V0) @ V1)) @ ((cList.list.Cons @ V2) @ ((cList.drop @ (cNat.Suc @ V0)) @ V1))))))))))))
(TList.zip_obtain_same_length,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V3)) @ (cNat.size_class.size @ V4))) @ ((c==> @ ((cHOL.eq @ V5) @ ((cOrderings.ord_class.min @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1)))) @ ((c==> @ ((cHOL.eq @ V3) @ ((cList.take @ V5) @ V0))) @ ((c==> @ ((cHOL.eq @ V4) @ ((cList.take @ V5) @ V1))) @ (V2 @ ((cList.zip @ V3) @ V4))))))))))))) @ (V2 @ ((cList.zip @ V0) @ V1))))))))))
(TMain.random_aux_sumbool_def,((c== @ cMain.random_aux_sumbool) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cExtraction.sumbool.Left) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cExtraction.sumbool.Right) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cExtraction.sumbool.Left) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cExtraction.sumbool.Right) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))) @ V4)))))) @ V0))))
(TMeson.make_refined_neg_rule,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TNat.dvd.order.strict_trans1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.dvd.order.strict_trans2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TNat.mult_eq_self_implies_10,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cNat.one_nat_inst.one_nat)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))))))))
(TNat.semiring_1.of_nat_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ (cNat.Suc @ V4))) @ ((V2 @ V0) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)))))))))))))))
(TNat.semiring_1.of_nat_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ cNat.zero_nat_inst.zero_nat)) @ V3)))))))))))
(TNat.semiring_1_class.Nats_0,((cSet.member @ cGroups.zero_class.zero) @ cNat.semiring_1_class.Nats))
(TNat.semiring_1_class.Nats_1,((cSet.member @ cGroups.one_class.one) @ cNat.semiring_1_class.Nats))
(TNitpick.arity_equal_fun_box,(cHOL.equal_class @ cTYPE))
(TNitpick.arity_type_pair_box,(cHOL.type_class @ cTYPE))
(TNitpick.fold_graph'.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNitpick.fold_graph' @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((((V4 @ V5) @ V6) @ cOrderings.bot_class.bot) @ V6)))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cSet.member @ V5) @ V6)) @ ((c==> @ ((((cNitpick.fold_graph' @ V7) @ V8) @ ((cGroups.minus_class.minus @ V6) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ V9)) @ ((c==> @ ((((V4 @ V7) @ V8) @ ((cGroups.minus_class.minus @ V6) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ V9)) @ ((((V4 @ V7) @ V8) @ V6) @ ((V7 @ V5) @ V9)))))))))))))))) @ ((((V4 @ V0) @ V1) @ V2) @ V3)))))))))))))))
(TNitpick.fun_box.Rep_fun_box,(call @ (^[V0]: ((cSet.member @ (cNitpick.Rep_fun_box @ V0)) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set)))))
(TNitpick.nat_gcd.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V2) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V2))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cNitpick.nat_gcd_rel) @ V1))))))))
(TNitpick.nat_gcd_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.nat_gcd_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat)) @ V4) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat))) @ ((cNitpick.nat_gcd_graph @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))) @ V2)))))))))) @ V2)))))))))
(TNitpick.nat_gcd_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.nat_gcd_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat)) @ V3) @ (V2 @ ((cProduct_Type.Pair @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4)))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))) @ ((cNitpick.nat_gcd_graph @ ((cProduct_Type.Pair @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4))) @ (V2 @ ((cProduct_Type.Pair @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4)))))))))))))))))))
(TNitpick.nat_gcd_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.nat_gcd_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cDivides.div_nat_inst.mod_nat @ V3) @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.norm_frac_graph_def,((c== @ cNitpick.norm_frac_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V4) @ V5)) @ (^[V6]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V4) @ V6)) @ ((cDivides.div_int_inst.div_int @ V5) @ V6)))))))) @ ((cHOL.induct_implies @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((V0 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))))))))))))))))))
(TNitpick.norm_frac_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.norm_frac_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ V2)))))))) @ V2)))))))))
(TNitpick.norm_frac_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.norm_frac_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V2)) @ (cInt.uminus_int_inst.uminus_int @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int)))))))))))))
(TNitpick.random_aux_word_def,((c== @ cNitpick.random_aux_word) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.word.Word) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.word.Word) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TNitpick.random_pair_box_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cNitpick.random_aux_pair_box @ V0) @ V0)))))
(TNitpick.typerep_fun_box_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TNitpick.word.Abs_word_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.Abs_word @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNitpick.word.word_rep_set))) @ V1))))) @ V1))))))
(TNitpick.word.Rep_word_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.word.word_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.Rep_word @ V2))) @ V1)))) @ V1)))))))
(TNitpick.word.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cNitpick.word.word_case @ V2) @ V0)) @ ((cNitpick.word.word_case @ V2) @ V1))))))))))
(TNum.class.neg_numeral.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cNum.class.numeral @ V1)) @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3))))))))))))
(TNum.class.ring_char_0.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TNum.neg_numeral.dbl_dec_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNum.neg_numeral.dbl_dec @ V0) @ V1) @ V4) @ V5)) @ ((V0 @ ((V1 @ V5) @ V5)) @ V4))))))))))))))))
(TNum.neg_numeral.dbl_inc_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNum.neg_numeral.dbl_inc @ V1) @ V4) @ V5)) @ ((V1 @ ((V1 @ V5) @ V5)) @ V4))))))))))))))))
(TNum.neg_numeral_class.intro,((c==> @ (cGroups.group_add_class @ cTYPE)) @ ((c==> @ (cNum.numeral_class @ cTYPE)) @ (cNum.neg_numeral_class @ cTYPE))))
(TNum.neg_numeral_class.super_2,((c==> @ (cNum.neg_numeral_class @ cTYPE)) @ (cNum.numeral_class @ cTYPE)))
(TNum.neg_numeral_class.super_1,((c==> @ (cNum.neg_numeral_class @ cTYPE)) @ (cGroups.group_add_class @ cTYPE)))
(TNum.num.num_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.num.num_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNum.num.num_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ V2)))))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNum.num.num_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ V2)))))))) @ (V1 @ V0))))))))))
(TNum.num_of_nat_plus_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cHOL.eq @ (cNum.num_of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ ((cNum.plus_num_inst.plus_num @ (cNum.num_of_nat @ V0)) @ (cNum.num_of_nat @ V1))))))))))
(TNum.ring_1_class.iszero_def,(call @ (^[V0]: ((cHOL.eq @ (cNum.ring_1_class.iszero @ V0)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TNum.ring_char_0_class.intro,((c==> @ (cNat.semiring_char_0_class @ cTYPE)) @ ((c==> @ (cRings.ring_1_class @ cTYPE)) @ (cNum.ring_char_0_class @ cTYPE))))
(TNum.ring_char_0_class.super_2,((c==> @ (cNum.ring_char_0_class @ cTYPE)) @ (cRings.ring_1_class @ cTYPE)))
(TNum.ring_char_0_class.super_1,((c==> @ (cNum.ring_char_0_class @ cTYPE)) @ (cNat.semiring_char_0_class @ cTYPE)))
(TNum.semiring_numeral.mult_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ (((cNum.numeral.numeral @ V0) @ V2) @ (cNum.num.Bit0 @ cNum.num.One))) @ V3)) @ ((V2 @ V3) @ V3))))))))))))
(TOption.map.compositionality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOption.map @ V0) @ ((cOption.map @ V1) @ V2))) @ ((cOption.map @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TOrderings.class.order.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ (cOrderings.class.order_axioms @ V0)) @ ((cOrderings.class.order @ V0) @ V1))))))))
(TOrderings.dense_order.dense,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.dense_order @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V1 @ V2) @ V4)) @ ((V1 @ V4) @ V3)))))))))))))))
(TOrderings.linorder.le_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((c==> @ ((V0 @ V2) @ V3)) @ V4)) @ ((c==> @ ((c==> @ ((V0 @ V3) @ V2)) @ V4)) @ V4))))))))))))))
(TOrderings.linorder.not_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((V1 @ V2) @ V3))) @ ((V0 @ V3) @ V2))))))))))))
(TOrderings.linorder_le_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ V2)) @ V2)))))))))
(TOrderings.linorder_not_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TOrderings.ord_class.max_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ V1) @ V0)))))))
(TOrderings.ord_class.min_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ V0) @ V1)))))))
(TOrderings.ord_eq_less_subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.ord_less_eq_subst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_class.intro,((c==> @ (cOrderings.preorder_class @ cTYPE)) @ ((c==> @ (cOrderings.class.order_axioms @ cOrderings.ord_class.less_eq)) @ (cOrderings.order_class @ cTYPE))))
(TOrderings.order_class.monoD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TOrderings.order_class.monoE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2))) @ V3)) @ V3))))))))))))
(TOrderings.order_class.monoI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2)))))))) @ (cOrderings.order_class.mono @ V0)))))
(TOrderings.order_class.super,((c==> @ (cOrderings.order_class @ cTYPE)) @ (cOrderings.preorder_class @ cTYPE)))
(TOrderings.order_less_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TOrderings.order_less_irrefl,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V0)))))
(TOrderings.order_less_subst1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_less_subst2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_trans_rules_29,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.eq @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_28,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_27,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_26,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_25,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_24,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_trans_rules_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)))))))))
(TOrderings.order_trans_rules_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_trans_rules_18,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.order_trans_rules_17,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.order_trans_rules_16,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.implies @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TOrderings.order_trans_rules_15,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ V0) @ ((c==> @ ((cHOL.implies @ V0) @ V1)) @ V1)))))))
(TOrderings.order_trans_rules_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ (V0 @ V2))))))))))
(TOrderings.order_trans_rules_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (V2 @ V1)) @ (V2 @ V0))))))))))
(TOrderings.order_trans_rules_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_trans_rules_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_trans_rules_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_trans_rules_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_trans_rules_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_trans_rules_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_trans_rules_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_trans_rules_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_trans_rules_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_trans_rules_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_trans_rules_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_trans_rules_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.wellorder.LeastI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V2 @ V5)) @ (V4 @ V5))))) @ (V4 @ ((cOrderings.ord.Least @ V0) @ V2))))))))))))))))
(TPower.monoid_mult.power_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V4))) @ ((V1 @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3)) @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V4)))))))))))))))
(TPower.monoid_mult.power_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V0) @ V2)) @ V0)))))))))
(TPower.power.power.power_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNat.Suc @ V3))) @ ((V1 @ V2) @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3))))))))))))
(TPower.power_class.power_def,((c== @ cPower.power_class.power) @ (^[V0]: (^[V1]: ((((cNat.nat.nat_rec @ (^[V2]: cGroups.one_class.one)) @ (^[V2]: (^[V3]: (^[V4]: ((cGroups.times_class.times @ V4) @ (V3 @ V4)))))) @ V1) @ V0)))))
(TPower.semiring_1.one_power2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ V0)))))))))))
(TPredicate.contained_less_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.contained @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cPredicate.pred_of_seq @ V0)) @ V1)))))))
(TPredicate.less_eq_pred_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cPredicate.Seq @ V0)) @ V1)) @ ((((cPredicate.seq.seq_case @ cHOL.True) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cPredicate.eval @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V3) @ V1))))) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cPredicate.contained @ V3) @ V1))))) @ (V0 @ cProduct_Type.Unity))))))))
(TPredicate.member_set_of_seq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cPredicate.set_of_seq @ V1))) @ ((cPredicate.member @ V1) @ V0)))))))
(TPredicate.pred.pred_rec_def,((c== @ cPredicate.pred.pred_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cPredicate.pred.pred_rec_set @ V0) @ V1) @ V2)))))))
(TPredicate.pred_of_seq.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.pred_of_seq @ ((cPredicate.seq.Join @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ (cPredicate.pred_of_seq @ V1))))))))
(TPredicate.pred_of_seq.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cPredicate.pred_of_seq @ ((cPredicate.seq.Insert @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cPredicate.single @ V0)) @ V1)))))))
(TPredicate.pred_of_seq.simps_1,((cHOL.eq @ (cPredicate.pred_of_seq @ cPredicate.seq.Empty)) @ cOrderings.bot_class.bot))
(TPredicate.seq.Abs_seq_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cPredicate.Abs_seq @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cPredicate.seq.seq_rep_set))) @ V1))))) @ V1))))))
(TPredicate.seq.Rep_seq_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.seq.seq_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cPredicate.Rep_seq @ V2))) @ V1)))) @ V1)))))))
(TPredicate.singleton_sup_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.singleton @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ ((cPredicate.singleton @ V0) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)) @ ((cPredicate.singleton @ V0) @ V1)) @ ((cPredicate.singleton @ V0) @ ((cLattices.sup_class.sup @ (cPredicate.single @ ((cPredicate.singleton @ V0) @ V1))) @ (cPredicate.single @ ((cPredicate.singleton @ V0) @ V2))))))))))))))
(TPredicate_Compile.containsE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate_Compile.contains @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ V2)))))))) @ V2)))))))))
(TPredicate_Compile.containsI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cPredicate_Compile.contains @ V1) @ V0)))))))
(TProduct_Type.bool.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cHOL.True)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cHOL.False)) @ ((cHOL.eq @ V4) @ V5))) @ ((cHOL.eq @ (((cProduct_Type.bool.bool_case @ V2) @ V4) @ V0)) @ (((cProduct_Type.bool.bool_case @ V3) @ V5) @ V1))))))))))))))))))
(TProduct_Type.bool.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cProduct_Type.bool.bool_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cHOL.True)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cHOL.False)) @ (cHOL.Not @ (V0 @ V2)))))))))))))))
(TProduct_Type.cond_split_eta,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((V0 @ V2) @ V3)) @ (V1 @ ((cProduct_Type.Pair @ V2) @ V3)))))))) @ ((cHOL.eq @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((V0 @ V2) @ V3))))) @ V1)))))))
(TProduct_Type.equal_bool_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TProduct_Type.equal_prod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TProduct_Type.equal_unit_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TProduct_Type.fst_comp_apfst,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ cProduct_Type.fst) @ (cProduct_Type.apfst @ V0))) @ ((cFun.comp @ V0) @ cProduct_Type.fst)))))
(TProduct_Type.fst_comp_apsnd,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ cProduct_Type.fst) @ (cProduct_Type.apsnd @ V0))) @ cProduct_Type.fst))))
(TProduct_Type.map_pair_ident,((cHOL.eq @ ((cProduct_Type.map_pair @ (^[V0]: V0)) @ (^[V0]: V0))) @ (^[V0]: V0)))
(TProduct_Type.member_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cProduct_Type.product @ V1) @ V2))) @ ((cSet.member @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: V2)))))))))))
(TProduct_Type.prod.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))) @ ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V2) @ V0)) @ ((cProduct_Type.prod.prod_case @ V3) @ V1)))))))))))))
(TProduct_Type.prod.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TProduct_Type.prod_case_beta,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V0) @ V1)) @ ((V0 @ (cProduct_Type.fst @ V1)) @ (cProduct_Type.snd @ V1))))))))
(TProduct_Type.snd_comp_apfst,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ cProduct_Type.snd) @ (cProduct_Type.apfst @ V0))) @ cProduct_Type.snd))))
(TProduct_Type.snd_comp_apsnd,(call @ (^[V0]: ((cHOL.eq @ ((cFun.comp @ cProduct_Type.snd) @ (cProduct_Type.apsnd @ V0))) @ ((cFun.comp @ V0) @ cProduct_Type.snd)))))
(TProduct_Type.unit.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cProduct_Type.Unity)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cProduct_Type.unit.unit_case @ V2) @ V0)) @ ((cProduct_Type.unit.unit_case @ V3) @ V1)))))))))))))
(TProduct_Type.unit.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.unit.unit_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cProduct_Type.Unity)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TQuotient.ball_reg_eqv_range,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((cHOL.eq @ ((cSet.Ball @ (cLifting.Respects @ ((cTransfer.fun_rel @ V1) @ V0))) @ (^[V4]: (V2 @ (V4 @ V3))))) @ (cHOL.All @ (^[V4]: (V2 @ (V4 @ V3)))))))))))))))
(TQuotient.bex1_bexeq_reg_eqv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((cHOL.implies @ (cHOL.Ex1 @ (^[V2]: (V1 @ V2)))) @ ((cQuotient.Bex1_rel @ V0) @ V1))))))))
(TQuotient.identity_quotient3,(((cQuotient.Quotient3 @ cHOL.eq) @ cFun.id) @ cFun.id))
(TQuotient.quot_type.Quotient,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ (((cQuotient.Quotient3 @ V0) @ ((cQuotient.quot_type.abs @ V0) @ V1)) @ (cQuotient.quot_type.rep @ V2))))))))))
(TQuotient.quot_type.rep_prop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V2 @ V3)) @ (cSet.Collect @ (V0 @ V4))))))))))))))))
(TRandom.iterate_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.iterate_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom.iterate_graph @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V6)) @ ((cProduct_Type.scomp @ (V5 @ V6)) @ (^[V7]: (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom.iterate_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom.iterate_graph @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V1) @ V4))) @ (V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V1) @ V4)))))))) @ ((cRandom.iterate_graph @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V3))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V3)) @ ((cProduct_Type.scomp @ (V1 @ V3)) @ (^[V4]: (V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V1) @ V4)))))))))))))))))
(TRandom.select_weight_member,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ (cList.monoid_add_class.listsum @ ((cList.map @ cProduct_Type.fst) @ V0)))) @ ((cSet.member @ (cProduct_Type.fst @ ((cRandom.select_weight @ V0) @ V1))) @ (cList.set @ ((cList.map @ cProduct_Type.snd) @ V0)))))))))
(TRandom.select_weight_select,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ (cRandom.select_weight @ ((cList.map @ (cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural)) @ V0))) @ (cRandom.select @ V0))))))
(TRandom_Pred.iter'_graph_def,((c== @ cRandom_Pred.iter'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V6) @ V7)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cPredicate.Seq @ (^[V11]: ((cPredicate.seq.Insert @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V10)))))))))))))))) @ (cHOL.induct_forall @ (^[V8]: (cHOL.induct_forall @ (^[V9]: (cHOL.induct_forall @ (^[V10]: (cHOL.induct_forall @ (^[V11]: (cHOL.induct_forall @ (^[V12]: (cHOL.induct_forall @ (^[V13]: (cHOL.induct_forall @ (^[V14]: ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.induct_implies @ ((cHOL.eq @ V8) @ ((cQuickcheck_Random.random_class.random @ V6) @ V7))) @ ((cHOL.induct_implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((cHOL.induct_implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))))))))))))))))))))))))))))))))))))))))
(TRandom_Pred.iter'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Pred.iter'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V12))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V7) @ ((cQuickcheck_Random.random_class.random @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ V2))))))))))))))))))))))))))))) @ V2)))))))))
(TRandom_Pred.iter'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Pred.iter'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: (cHOL.Ex @ (^[V12]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V4) @ V11))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ ((cQuickcheck_Random.random_class.random @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ ((cProduct_Type.Pair @ V7) @ V8)) @ V6)) @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V7))))))))))))))))))))))))))))))))))
(TRandom_Sequence.iter.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ (((V0 @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13)))))))))))))))))))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TRandom_Sequence.iter.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cRandom_Sequence.iter @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.iter_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cHOL.eq @ V6) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V8]: ((cHOL.Let @ (V5 @ V7)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V9]: (^[V10]: (^[V11]: (cOption.option.Some @ ((cProduct_Type.Pair @ V9) @ (((cRandom_Sequence.iter @ V5) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V11)))))))))))))) @ ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.iter_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TRandom_Sequence.iter.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.iter_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cRandom_Sequence.iter @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V3]: ((cHOL.Let @ (V0 @ V2)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (^[V6]: (cOption.option.Some @ ((cProduct_Type.Pair @ V4) @ (((cRandom_Sequence.iter @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))))))))))))))
(TRandom_Sequence.neg_map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.neg_map @ V0) @ V1)) @ ((cRandom_Sequence.neg_bind @ V1) @ ((cFun.comp @ cRandom_Sequence.neg_single) @ V0))))))))
(TRandom_Sequence.pos_map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.pos_map @ V0) @ V1)) @ ((cRandom_Sequence.pos_bind @ V1) @ ((cFun.comp @ cRandom_Sequence.pos_single) @ V0))))))))
(TRecord.isomorphic_tuple_def,(call @ (^[V0]: ((c== @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.conj @ (cHOL.All @ (^[V1]: ((cHOL.eq @ ((cRecord.abst @ V0) @ ((cRecord.repr @ V0) @ V1))) @ V1)))) @ (cHOL.All @ (^[V1]: ((cHOL.eq @ ((cRecord.repr @ V0) @ ((cRecord.abst @ V0) @ V1))) @ V1))))))))
(TRelation.Domain_Diff_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ (cRelation.Domain @ V0)) @ (cRelation.Domain @ V1))) @ (cRelation.Domain @ ((cGroups.minus_class.minus @ V0) @ V1))))))))
(TRelation.Id_on_subset_Times,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cRelation.Id_on @ V0)) @ ((cProduct_Type.Sigma @ V0) @ (^[V1]: V0))))))
(TRelation.converse_inv_image,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRelation.converse @ ((cRelation.inv_image @ V0) @ V1))) @ ((cRelation.inv_image @ (cRelation.converse @ V0)) @ V1)))))))
(TRings.class.comm_ring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cRings.class.comm_semiring @ V0) @ V4)) @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TRings.class.comm_ring_1_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cHOL.conj @ (((((cRings.class.comm_ring @ V2) @ V3) @ V4) @ V5) @ V0)) @ ((cRings.class.zero_neq_one @ V1) @ V3)))))))))))))))))
(TRings.class.mult_zero.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V1)))) @ ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V1)))) @ ((cRings.class.mult_zero @ V0) @ V1))))))))
(TRings.class.semiring.axioms_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.semiring @ V0) @ V1)) @ ((cRings.class.semiring_axioms @ V0) @ V1)))))))
(TRings.class.semiring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.semiring @ V0) @ V1)) @ (cGroups.class.semigroup_mult @ V1)))))))
(TRings.class.semiring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.semiring @ V0) @ V1)) @ (cGroups.class.ab_semigroup_add @ V0)))))))
(TRings.comm_ring_1_class_def,((c== @ (cRings.comm_ring_1_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_ring_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))))
(TRings.comm_ring_class.intro,((c==> @ (cGroups.ab_group_add_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_class @ cTYPE)) @ (cRings.comm_ring_class @ cTYPE))))
(TRings.comm_ring_class.super_2,((c==> @ (cRings.comm_ring_class @ cTYPE)) @ (cRings.comm_semiring_class @ cTYPE)))
(TRings.comm_ring_class.super_1,((c==> @ (cRings.comm_ring_class @ cTYPE)) @ (cGroups.ab_group_add_class @ cTYPE)))
(TRings.comm_semiring.distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cRings.class.comm_semiring @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ ((V0 @ V2) @ V3)) @ V4)) @ ((V0 @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))))))))
(TRings.mult_zero_class.intro,((c==> @ (cGroups.times_class @ cTYPE)) @ ((c==> @ (cGroups.zero_class @ cTYPE)) @ ((c==> @ ((cRings.class.mult_zero @ cGroups.times_class.times) @ cGroups.zero_class.zero)) @ (cRings.mult_zero_class @ cTYPE)))))
(TRings.mult_zero_class.super_2,((c==> @ (cRings.mult_zero_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TRings.mult_zero_class.super_1,((c==> @ (cRings.mult_zero_class @ cTYPE)) @ (cGroups.times_class @ cTYPE)))
(TRings.ring.minus_mult_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ (V3 @ V5)) @ (V3 @ V6))) @ ((V4 @ V5) @ V6))))))))))))))))))
(TRings.ring.minus_mult_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ (V3 @ ((V4 @ V5) @ V6))) @ ((V4 @ V5) @ (V3 @ V6)))))))))))))))))))
(TRings.ring.mult_minus_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ V5) @ (V3 @ V6))) @ (V3 @ ((V4 @ V5) @ V6)))))))))))))))))))
(TRings.semiring.distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cRings.class.semiring @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V2) @ ((V0 @ V3) @ V4))) @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V1 @ V2) @ V4)))))))))))))))
(TRings.semiring_class.axioms,((cRings.class.semiring_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times))
(TSMT.arity_narrowing_pattern,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TSMT.pattern.pattern_rec_def,((c== @ cSMT.pattern.pattern_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cSMT.pattern.pattern_rec_set @ V0) @ V1) @ V2)))))))
(TSMT.type_definition_pattern,(((cTypedef.type_definition @ cSMT.Rep_pattern) @ cSMT.Abs_pattern) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set)))
(TSet.singleton_insert_inj_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cSet.insert @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))))))))
(TSet_Interval.Compl_lessThan,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cSet_Interval.ord_class.lessThan @ V0))) @ (cSet_Interval.ord_class.atLeast @ V0)))))
(TSet_Interval.UN_atMost_UNIV,((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V0]: (cSet_Interval.ord_class.atMost @ V0)))) @ cOrderings.top_class.top))
(TSet_Interval.atLeast0AtMost,(call @ (^[V0]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (cSet_Interval.ord_class.atMost @ V0)))))
(TSet_Interval.atLeast_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet_Interval.card_less_Suc2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cSet.member @ cNat.zero_nat_inst.zero_nat) @ V0))) @ ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ (cNat.Suc @ V2)) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ V2) @ V1)))))) @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.Suc @ V1)))))))))))))
(TSet_Interval.dvd.Icc_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V2) @ V3))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.conj @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V3))))))))))))))
(TSet_Interval.dvd.atMost_def,(call @ (^[V0]: ((c== @ ((cSet_Interval.ord.atMost @ cRings.dvd_class.dvd) @ V0)) @ (cSet.Collect @ (^[V1]: ((cRings.dvd_class.dvd @ V1) @ V0)))))))
(TSet_Interval.dvd.atMost_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.atMost @ cRings.dvd_class.dvd) @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TSet_Interval.finite_less_ub,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cNat.ord_nat_inst.less_eq_nat @ V2) @ (V0 @ V2))))) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cNat.ord_nat_inst.less_eq_nat @ (V0 @ V2)) @ V1))))))))))
(TSet_Interval.ord.atMost_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord.atMost @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TSet_Interval.ord.atMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.atMost @ V1) @ V2))) @ ((V1 @ V0) @ V2)))))))))
(TString.char.Abs_char_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cString.char.char_rep_set))) @ (V0 @ (cString.Abs_char @ V2)))))) @ (V0 @ V1)))))))
(TString.char.Abs_char_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.char.char_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cString.char.char_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cString.Abs_char @ V0)) @ (cString.Abs_char @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TString.char.Rep_char_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.char.char_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cString.Rep_char @ V2))))) @ (V1 @ V0))))))))
(TString.char.Rep_char_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cString.Rep_char @ V0)) @ (cString.Rep_char @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.char.arity_size_char,(cNat.size_class @ cTYPE))
(TString.nat_of_char_less_256,(call @ (^[V0]: ((cNat.ord_nat_inst.less_nat @ (cString.nat_of_char @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))
(TString.nat_of_nibble_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cString.nat_of_nibble @ V0)) @ (cString.nat_of_nibble @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.nat_of_nibble_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cString.nat_of_nibble @ (cString.nibble_of_nat @ V0))) @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TString.nibble_of_nat_mod_16,(call @ (^[V0]: ((cHOL.eq @ (cString.nibble_of_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))) @ (cString.nibble_of_nat @ V0)))))
(TString.type_definition_char,(((cTypedef.type_definition @ cString.Rep_char) @ cString.Abs_char) @ (cSet.Collect @ cString.char.char_rep_set)))
(TSum_Type.Plus_eq_empty_conv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cSum_Type.Plus @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))))))
(TSum_Type.sum.Abs_sum_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ cSum_Type.sum)) @ (V0 @ (cSum_Type.Abs_sum @ V2)))))) @ (V0 @ V1)))))))
(TSum_Type.sum.Abs_sum_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cSum_Type.sum)) @ ((c==> @ ((cSet.member @ V1) @ cSum_Type.sum)) @ ((cHOL.eq @ ((cHOL.eq @ (cSum_Type.Abs_sum @ V0)) @ (cSum_Type.Abs_sum @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TSum_Type.sum.Rep_sum_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cSum_Type.sum)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cSum_Type.Rep_sum @ V2))))) @ (V1 @ V0))))))))
(TSum_Type.sum.Rep_sum_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSum_Type.Rep_sum @ V0)) @ (cSum_Type.Rep_sum @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSum_Type.sum.arity_size_sum,(cNat.size_class @ cTYPE))
(TSum_Type.sum.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cSum_Type.sum.sum_case @ V2) @ V3) @ V0)) @ (((cSum_Type.sum.sum_case @ V2) @ V3) @ V1))))))))))))
(TSum_Type.sum_case_weak_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cSum_Type.sum.sum_case @ V2) @ V3) @ V0)) @ (((cSum_Type.sum.sum_case @ V2) @ V3) @ V1))))))))))))
(TTransfer.bi_total_conversep,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_total @ (cRelation.conversep @ V0))) @ (cTransfer.bi_total @ V0)))))
(TTransfer.transfer_forall_eq,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: (V0 @ V1)))))))
(TTransitive_Closure.acyclicI,(call @ (^[V0]: ((c==> @ (cHOL.All @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ (cTransitive_Closure.trancl @ V0)))))) @ (cTransitive_Closure.acyclic @ V0)))))
(TTransitive_Closure.relpow_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.compow @ cNat.one_nat_inst.one_nat) @ V0)) @ V0))))
(TTransitive_Closure.relpow_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V2) @ (cNat.Suc @ V6))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V5)) @ ((cNat.compow @ V6) @ V3))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ V3)) @ V4)))))))) @ V4))))))))))))))
(TTransitive_Closure.rtranclD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))))))))))))
(TTransitive_Closure.rtranclE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V1)) @ V2)) @ V3))))) @ V3))))))))))))
(TTransitive_Closure.tranclD2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V1)) @ V2))))))))))))
(TTransitive_Closure.tranclpD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((V0 @ V1) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V3) @ V2))))))))))))
(TTypedef.type_definition.Rep,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((cSet.member @ (V0 @ V3)) @ V2)))))))))))
(TTypedef.type_definition_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cSet.member @ (V0 @ V3)) @ V2)))) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.eq @ (V1 @ (V0 @ V3))) @ V3)))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cSet.member @ V3) @ V2)) @ ((cHOL.eq @ (V0 @ (V1 @ V3))) @ V3))))))))))))))
(TTyperep.arity_equal_typerep,(cHOL.equal_class @ cTYPE))
(TTyperep.typerep.Rep_typerep,(call @ (^[V0]: ((cSet.member @ (cTyperep.Rep_typerep @ V0)) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1)))))
(TTyperep.typerep.Typerep_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cTyperep.typerep.Typerep @ V0) @ V1)) @ (cTyperep.Abs_typerep @ ((cDatatype.Scons @ (cDatatype.Leaf @ V0)) @ (cTyperep.typerep.typerep_Rep_1 @ V1)))))))))
(TTyperep.typerep_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cTyperep.typerep_class @ cTYPE)))
(TTyperep.typerep_class.super,((c==> @ (cTyperep.typerep_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TTyperep.typerep_integer_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_integer_inst.typerep_integer @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_literal_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_literal_inst.typerep_literal @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_natural_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_natural_inst.typerep_natural @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_typerep_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_typerep_inst.typerep_typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)))))
(TWellfounded.acc_induct_rule,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cWellfounded.acc @ V1))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V1)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V0))))))))))
(TWellfounded.max_ext.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.max_ext @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V4)) @ ((cSet.Bex @ V5) @ (^[V7]: ((cSet.member @ ((cProduct_Type.Pair @ V6) @ V7)) @ V2))))))) @ ((V3 @ V4) @ V5)))))))))) @ ((V3 @ V0) @ V1))))))))))))
(TWellfounded.max_extp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cWellfounded.max_extp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ (cSet.Collect @ (^[V6]: (cOrderings.bot_class.bot @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V4)) @ ((cSet.Bex @ V5) @ (V0 @ V6)))))) @ ((V3 @ V4) @ V5)))))))))) @ ((V3 @ V1) @ V2))))))))))))
(TWellfounded.max_extp.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ (cSet.Collect @ (^[V3]: (cOrderings.bot_class.bot @ V3)))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cSet.Bex @ V1) @ (V2 @ V3)))))) @ (((cWellfounded.max_extp @ V2) @ V0) @ V1))))))))))))
(TWellfounded.trans_less_than,(cRelation.trans @ cWellfounded.less_than))
(TWellfounded.wfP_induct_rule,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cWellfounded.wfP @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))))))
(TBig_Operators.abs_setsum_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cGroups.abs_class.abs @ (V0 @ V2)))) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cGroups.abs_class.abs @ (V0 @ V2)))) @ V1)))))))
(TBig_Operators.card_eq_setsum,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V1]: cNat.one_nat_inst.one_nat)) @ V0)))))
(TBig_Operators.setprod_Un_Int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1)))) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1))))))))))))
(TBig_Operators.setprod_Un_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)))))))))))))
(TBig_Operators.setprod_delta',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V1) @ V3)) @ (V2 @ V3)) @ cGroups.one_class.one))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.one_class.one))))))))))
(TBig_Operators.setprod_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cSet.insert @ V1) @ V0))) @ ((cGroups.times_class.times @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))))
(TBig_Operators.setprod_nonneg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V1 @ V2)))))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0))))))))
(TBig_Operators.setprod_timesf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cGroups.times_class.times @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V2))))))))))
(TBig_Operators.setsum_Un_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)))))))))))))
(TBig_Operators.setsum_bounded,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V2))))) @ ((cOrderings.ord_class.less_eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ (cFinite_Set.card @ V0))) @ V2))))))))))
(TBig_Operators.setsum_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V3))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V5]: ((cGroups.times_class.times @ (V0 @ V4)) @ (V2 @ V5)))) @ V3))) @ V1)))))))))))
(TBig_Operators.setsum_reindex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet.image @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ ((cFun.comp @ V2) @ V0)) @ V1))))))))))
(TCode_Evaluation.term.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TCode_Evaluation.term.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cCode_Evaluation.term.dummy_term)) @ V1)) @ V1))))))
(TCode_Evaluation.term.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cCode_Evaluation.term.dummy_term)) @ (V0 @ V1)))))))
(TCode_Evaluation.term_of_char,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_char_inst.term_of_char @ V0)) @ ((cString.char.char_case @ (^[V1]: (^[V2]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (cCode_Evaluation.term_of_nibble_inst.term_of_nibble @ V1))) @ (cCode_Evaluation.term_of_nibble_inst.term_of_nibble @ V2))))) @ V0)))))
(TCode_Numeral.abs_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cInt.abs_int_inst.abs_int) @ cInt.abs_int_inst.abs_int))
(TCode_Numeral.abs_integer_def,((c== @ cCode_Numeral.abs_integer_inst.abs_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int) @ cInt.abs_int_inst.abs_int)))
(TCode_Numeral.div_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cDivides.div_int_inst.div_int) @ cDivides.div_int_inst.div_int))
(TCode_Numeral.div_integer_def,((c== @ cCode_Numeral.div_integer_inst.div_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int)) @ cDivides.div_int_inst.div_int)))
(TCode_Numeral.div_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cDivides.div_nat_inst.div_nat) @ cDivides.div_nat_inst.div_nat))
(TCode_Numeral.div_natural_def,((c== @ cCode_Numeral.div_natural_inst.div_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.natural_of_nat)) @ cDivides.div_nat_inst.div_nat)))
(TCode_Numeral.divmod_abs_code_6,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.divmod_abs @ cCode_Numeral.zero_integer_inst.zero_integer) @ V0)) @ ((cProduct_Type.Pair @ cCode_Numeral.zero_integer_inst.zero_integer) @ cCode_Numeral.zero_integer_inst.zero_integer)))))
(TCode_Numeral.divmod_abs_code_5,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.divmod_abs @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ ((cProduct_Type.Pair @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.abs_integer_inst.abs_integer @ V0))))))
(TCode_Numeral.divmod_abs_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.divmod_abs @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Neg @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TCode_Numeral.divmod_abs_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.divmod_abs @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Pos @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TCode_Numeral.divmod_abs_code_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.divmod_abs @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Neg @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TCode_Numeral.divmod_abs_code_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.divmod_abs @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Pos @ V1))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)))))))
(TCode_Numeral.mod_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cDivides.div_int_inst.mod_int) @ cDivides.div_int_inst.mod_int))
(TCode_Numeral.mod_integer_def,((c== @ cCode_Numeral.div_integer_inst.mod_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int)) @ cDivides.div_int_inst.mod_int)))
(TCode_Numeral.mod_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cDivides.div_nat_inst.mod_nat) @ cDivides.div_nat_inst.mod_nat))
(TCode_Numeral.mod_natural_def,((c== @ cCode_Numeral.div_natural_inst.mod_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.natural_of_nat)) @ cDivides.div_nat_inst.mod_nat)))
(TCode_Numeral.natural.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cCode_Numeral.Suc @ V2))) @ V1)))) @ V1)))))))
(TCode_Numeral.natural.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cCode_Numeral.Suc @ V2)))))) @ (V0 @ V1))))))))
(TCode_Numeral.one_integer.rsp,((cHOL.eq @ cInt.one_int_inst.one_int) @ cInt.one_int_inst.one_int))
(TCode_Numeral.one_integer_def,((c== @ cCode_Numeral.one_integer_inst.one_integer) @ (cCode_Numeral.integer_of_int @ cInt.one_int_inst.one_int)))
(TCode_Numeral.one_natural.rsp,((cHOL.eq @ cNat.one_nat_inst.one_nat) @ cNat.one_nat_inst.one_nat))
(TCode_Numeral.one_natural_def,((c== @ cCode_Numeral.one_natural_inst.one_natural) @ (cCode_Numeral.natural_of_nat @ cNat.one_nat_inst.one_nat)))
(TCode_Numeral.pcr_integer_def,((c== @ cCode_Numeral.pcr_integer) @ ((cRelation.relcompp @ cHOL.eq) @ cCode_Numeral.cr_integer)))
(TCode_Numeral.pcr_natural_def,((c== @ cCode_Numeral.pcr_natural) @ ((cRelation.relcompp @ cHOL.eq) @ cCode_Numeral.cr_natural)))
(TCode_Numeral.sgn_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cInt.sgn_int_inst.sgn_int) @ cInt.sgn_int_inst.sgn_int))
(TCode_Numeral.sgn_integer_def,((c== @ cCode_Numeral.sgn_integer_inst.sgn_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int) @ cInt.sgn_int_inst.sgn_int)))
(TComplete_Lattices.INT_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.INT_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cSet.insert @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.inf_class.inf @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ V2))))))))))
(TComplete_Lattices.Int_Union2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cLattices.inf_class.inf @ V2) @ V1)))))))))
(TComplete_Lattices.Inter_UNIV,((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ cOrderings.top_class.top)) @ cOrderings.bot_class.bot))
(TComplete_Lattices.Pow_INT_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Pow @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (cSet.Pow @ (V1 @ V2))))))))))
(TComplete_Lattices.UN_bool_eq,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1)))) @ ((cLattices.sup_class.sup @ (V0 @ cHOL.True)) @ (V0 @ cHOL.False))))))
(TComplete_Lattices.Union_UNIV,((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(TComplete_Lattices.Union_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.bind_UNION,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.bind @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)))))))
(TComplete_Lattices.vimage_INT,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.vimage @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cSet.vimage @ V0) @ (V2 @ V3))))))))))))
(TDatatype.Scons_inject_lemma1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cDatatype.Scons @ V0) @ V1)) @ ((cDatatype.Scons @ V2) @ V3))) @ ((cOrderings.ord_class.less_eq @ V0) @ V2)))))))))))
(TDatatype.Scons_inject_lemma2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cDatatype.Scons @ V0) @ V1)) @ ((cDatatype.Scons @ V2) @ V3))) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))
(TDatatype.dprod_subset_Sigma2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cOrderings.ord_class.less_eq @ ((cDatatype.dprod @ ((cProduct_Type.Sigma @ V0) @ V1)) @ ((cProduct_Type.Sigma @ V2) @ V3))) @ ((cProduct_Type.Sigma @ ((cDatatype.uprod @ V0) @ V2)) @ (cDatatype.Split @ (^[V4]: (^[V5]: ((cDatatype.uprod @ (V1 @ V4)) @ (V3 @ V5))))))))))))))))
(TDatatype.node.Abs_Node_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cDatatype.Abs_Node @ V2))) @ ((c==> @ ((cSet.member @ V2) @ cDatatype.Node)) @ V1))))) @ V1))))))
(TDatatype.node.Rep_Node_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cDatatype.Node)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cDatatype.Rep_Node @ V2))) @ V1)))) @ V1)))))))
(TDivides.class.ring_div.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V5) @ V3) @ V4) @ V6) @ V7)) @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7))))))))))))))))))))
(TDivides.div_int_inst.div_int,((c== @ cDivides.div_int_inst.div_int) @ cDivides.div_int_inst.div_int))
(TDivides.div_int_inst.mod_int,((c== @ cDivides.div_int_inst.mod_int) @ cDivides.div_int_inst.mod_int))
(TDivides.div_nat_inst.div_nat,((c== @ cDivides.div_nat_inst.div_nat) @ cDivides.div_nat_inst.div_nat))
(TDivides.div_nat_inst.mod_nat,((c== @ cDivides.div_nat_inst.mod_nat) @ cDivides.div_nat_inst.mod_nat))
(TDivides.divmod_nat_zero_left,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.divmod_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cProduct_Type.Pair @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))))
(TDivides.dvd_neg_numeral_left,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ V1)) @ ((cRings.dvd_class.dvd @ (cNum.numeral_class.numeral @ V0)) @ V1)))))))
(TDivides.mod_less_eq_dividend,(call @ (^[V0]: (call @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1)) @ V0))))))
(TDivides.negDivAlg_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.negDivAlg_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.negDivAlg_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.negDivAlg_rel @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cProduct_Type.Pair @ V0) @ V1))))))))
(TDivides.neg_imp_zdiv_neg_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ ((cDivides.div_int_inst.div_int @ V1) @ V0)) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1))))))))
(TDivides.posDivAlg_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.posDivAlg_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.posDivAlg_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.posDivAlg_rel @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cProduct_Type.Pair @ V0) @ V1))))))))
(TDivides.pos_imp_zdiv_neg_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ ((cDivides.div_int_inst.div_int @ V1) @ V0)) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.pos_imp_zdiv_pos_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1))))))))
(TDivides.ring_div.dvd_div_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V8) @ V9)) @ ((cHOL.eq @ ((V1 @ V9) @ (V7 @ V8))) @ (V7 @ ((V1 @ V9) @ V8))))))))))))))))))))))))))
(TDivides.ring_div.dvd_neg_div,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V8) @ V9)) @ ((cHOL.eq @ ((V1 @ (V7 @ V9)) @ V8)) @ (V7 @ ((V1 @ V9) @ V8))))))))))))))))))))))))))
(TDivides.ring_div.mod_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ ((V6 @ V8) @ V9)) @ V10)) @ ((V2 @ ((V6 @ ((V2 @ V8) @ V10)) @ ((V2 @ V9) @ V10))) @ V10))))))))))))))))))))))))))
(TDivides.ring_div_class.intro,((c==> @ (cDivides.semiring_div_class @ cTYPE)) @ ((c==> @ (cRings.comm_ring_1_class @ cTYPE)) @ (cDivides.ring_div_class @ cTYPE))))
(TDivides.ring_div_class.super_2,((c==> @ (cDivides.ring_div_class @ cTYPE)) @ (cRings.comm_ring_1_class @ cTYPE)))
(TDivides.ring_div_class.super_1,((c==> @ (cDivides.ring_div_class @ cTYPE)) @ (cDivides.semiring_div_class @ cTYPE)))
(TDivides.semiring_div.div_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)) @ ((cHOL.eq @ ((V1 @ ((V3 @ V7) @ V8)) @ V6)) @ ((V3 @ ((V1 @ V7) @ V6)) @ ((V1 @ V8) @ V6)))))))))))))))))))))))))
(TDivides.semiring_div.dvd_mod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)) @ (((cRings.dvd.dvd @ V0) @ V6) @ ((V2 @ V7) @ V8))))))))))))))))))))))))
(TDivides.zdiv_mono2_neg_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V2)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V3) @ V4)) @ V5))) @ ((c==> @ ((cInt.ord_int_inst.less_int @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V3) @ V4)) @ V5)) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V2) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V5)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V3)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ V1))))))))))))))))))))
(TEnum.arity_linorder_finite_1,(cOrderings.linorder_class @ cTYPE))
(TEnum.arity_linorder_finite_2,(cOrderings.linorder_class @ cTYPE))
(TEnum.arity_linorder_finite_3,(cOrderings.linorder_class @ cTYPE))
(TEnum.enum_class.enum_ex_UNIV,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_ex @ V0)) @ ((cSet.Bex @ cOrderings.top_class.top) @ V0)))))
(TEnum.finite_1.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cEnum.finite_1.finite_1_case @ V2) @ V0)) @ ((cEnum.finite_1.finite_1_case @ V2) @ V1))))))))))
(TEnum.finite_2.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cEnum.finite_2.finite_2_case @ V2) @ V3) @ V0)) @ (((cEnum.finite_2.finite_2_case @ V2) @ V3) @ V1))))))))))))
(TEnum.finite_3.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((((cEnum.finite_3.finite_3_case @ V2) @ V3) @ V4) @ V0)) @ ((((cEnum.finite_3.finite_3_case @ V2) @ V3) @ V4) @ V1))))))))))))))
(TEnum.finite_4.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((((cEnum.finite_4.finite_4_case @ V2) @ V3) @ V4) @ V5) @ V0)) @ (((((cEnum.finite_4.finite_4_case @ V2) @ V3) @ V4) @ V5) @ V1))))))))))))))))
(TEnum.finite_5.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((((((cEnum.finite_5.finite_5_case @ V2) @ V3) @ V4) @ V5) @ V6) @ V0)) @ ((((((cEnum.finite_5.finite_5_case @ V2) @ V3) @ V4) @ V5) @ V6) @ V1))))))))))))))))))
(TEnum.map_of_zip_enum_is_Some,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ cEnum.enum_class.enum))) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ ((cMap.map_of @ ((cList.zip @ cEnum.enum_class.enum) @ V0)) @ V1)) @ (cOption.option.Some @ V2))))))))))
(TEquiv_Relations.congruent2I',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V1)) @ ((cHOL.eq @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V6))))))))))))) @ (((cEquiv_Relations.congruent2 @ V0) @ V1) @ V2)))))))))
(TEquiv_Relations.equivp_equiv,(call @ (^[V0]: ((cHOL.eq @ ((cEquiv_Relations.equiv @ cOrderings.top_class.top) @ V0)) @ (cEquiv_Relations.equivp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))))))
(TEquiv_Relations.equivp_reflp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((V0 @ V1) @ V1)))))))
(TEquiv_Relations.part_equivpE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEquiv_Relations.part_equivp @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((V0 @ V2) @ V2)) @ ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ (cRelation.transp @ V0)) @ V1)))))) @ V1)))))))
(TEquiv_Relations.part_equivpI,(call @ (^[V0]: ((c==> @ (cHOL.Ex @ (^[V1]: ((V0 @ V1) @ V1)))) @ ((c==> @ (cRelation.symp @ V0)) @ ((c==> @ (cRelation.transp @ V0)) @ (cEquiv_Relations.part_equivp @ V0)))))))
(TEquiv_Relations.quotient_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEquiv_Relations.quotient @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cSet.insert @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)))))))))
(TEquiv_Relations.quotient_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ ((cSet.member @ V3) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ ((c==> @ ((cSet.member @ V5) @ V3)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1)) @ ((cHOL.eq @ V2) @ V3))))))))))))))))))))
(TExtraction.equal_sumbool_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TExtraction.sumbool.Right_def,((c== @ cExtraction.sumbool.Right) @ (cExtraction.Abs_sumbool @ (cDatatype.In1 @ cHOL.undefined))))
(TExtraction.sumbool.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cExtraction.sumbool.Left)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cExtraction.sumbool.Right)) @ ((cHOL.eq @ V4) @ V5))) @ ((cHOL.eq @ (((cExtraction.sumbool.sumbool_case @ V2) @ V4) @ V0)) @ (((cExtraction.sumbool.sumbool_case @ V3) @ V5) @ V1))))))))))))))))))
(TExtraction.sumbool.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cExtraction.sumbool.sumbool_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Left)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Right)) @ (cHOL.Not @ (V0 @ V2)))))))))))))))
(TFields.field.times_divide_eq_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ ((V1 @ V8) @ V9)) @ V10)) @ ((V1 @ ((V2 @ V8) @ V10)) @ V9))))))))))))))))))))))))))
(TFields.field.times_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V8) @ ((V1 @ V9) @ V10))) @ ((V1 @ ((V2 @ V8) @ V9)) @ V10))))))))))))))))))))))))))
(TFinite_Set.arity_finite_bool,(cFinite_Set.finite_class @ cTYPE))
(TFinite_Set.arity_finite_prod,(cFinite_Set.finite_class @ cTYPE))
(TFinite_Set.arity_finite_unit,(cFinite_Set.finite_class @ cTYPE))
(TFinite_Set.card_Plus_conv_if,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSum_Type.Plus @ V0) @ V1))) @ (((cHOL.If @ ((cHOL.conj @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))) @ cNat.zero_nat_inst.zero_nat)))))))
(TFinite_Set.comp_fun_idem_def,(call @ (^[V0]: ((c== @ (cFinite_Set.comp_fun_idem @ V0)) @ ((cHOL.conj @ (cFinite_Set.comp_fun_commute @ V0)) @ (cFinite_Set.comp_fun_idem_axioms @ V0))))))
(TFinite_Set.empty_fold_graphE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ cOrderings.bot_class.bot) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ V1)) @ V3)) @ V3)))))))))))
(TFinite_Set.finite_fun_UNIVD2,((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TFinite_Set.finite_set_choice,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cHOL.Ex @ (^[V3]: ((V1 @ V2) @ V3)))))) @ (cHOL.Ex @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((V1 @ V3) @ (V2 @ V3)))))))))))))
(TFinite_Set.finite_vimage_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (cFinite_Set.finite @ ((cSet.vimage @ V0) @ V1))) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.fold_graph.emptyI,(call @ (^[V0]: (call @ (^[V1]: ((((cFinite_Set.fold_graph @ V0) @ V1) @ cOrderings.bot_class.bot) @ V1))))))
(TFinite_Set.fold_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V4 @ cOrderings.bot_class.bot) @ V1)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cSet.member @ V5) @ V6))) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V6) @ V7)) @ ((c==> @ ((V4 @ V6) @ V7)) @ ((V4 @ ((cSet.insert @ V5) @ V6)) @ ((V0 @ V5) @ V7)))))))))))) @ ((V4 @ V2) @ V3)))))))))))))))
(TFinite_Set.fold_graph.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((c==> @ ((((cFinite_Set.fold_graph @ V2) @ V3) @ V1) @ V4)) @ ((((cFinite_Set.fold_graph @ V2) @ V3) @ ((cSet.insert @ V0) @ V1)) @ ((V2 @ V0) @ V4)))))))))))))))
(TFinite_Set.fold_graph.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cFinite_Set.fold_graph @ V0) @ V1) @ cOrderings.bot_class.bot) @ V1))))))
(TFinite_Set.image_fold_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cSet.image @ V1) @ V0)) @ (((cFinite_Set.fold @ (^[V2]: (^[V3]: ((cSet.insert @ (V1 @ V2)) @ V3)))) @ cOrderings.bot_class.bot) @ V0))))))))
(TFinite_Set.infinite_UNIV_nat,(cHOL.Not @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TFinite_Set.minus_fold_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V1) @ V0)) @ (((cFinite_Set.fold @ cSet.remove) @ V1) @ V0))))))))
(TFinite_Set.psubset_card_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V0)))))))))
(TFinite_Set.rev_finite_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.union_fold_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (((cFinite_Set.fold @ cSet.insert) @ V1) @ V0))))))))
(TFun.map_fun.compositionality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cFun.map_fun @ V0) @ V1) @ (((cFun.map_fun @ V2) @ V3) @ V4))) @ (((cFun.map_fun @ ((cFun.comp @ V2) @ V0)) @ ((cFun.comp @ V1) @ V3)) @ V4)))))))))))))
(TFunDef.THE_default1_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Ex1 @ (^[V3]: (V0 @ V3)))) @ ((c==> @ (V0 @ V1)) @ ((cHOL.eq @ ((cFunDef.THE_default @ V2) @ V0)) @ V1))))))))))
(TFunDef.fundef_ex1_uniqueness,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c== @ V0) @ (^[V5]: ((cFunDef.THE_default @ (V1 @ V5)) @ (^[V6]: ((V2 @ V5) @ V6)))))) @ ((c==> @ (cHOL.Ex1 @ (^[V5]: ((V2 @ V3) @ V5)))) @ ((c==> @ ((V2 @ V3) @ (V4 @ V3))) @ ((cHOL.eq @ (V4 @ V3)) @ (V0 @ V3))))))))))))))))
(TGroups.abel_semigroup.axioms_2,(call @ (^[V0]: ((c==> @ (cGroups.abel_semigroup @ V0)) @ (cGroups.abel_semigroup_axioms @ V0)))))
(TGroups.abel_semigroup.axioms_1,(call @ (^[V0]: ((c==> @ (cGroups.abel_semigroup @ V0)) @ (cGroups.semigroup @ V0)))))
(TGroups.class.group_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((c==> @ ((((cGroups.class.group_add_axioms @ V2) @ V0) @ V1) @ V3)) @ ((((cGroups.class.group_add @ V2) @ V0) @ V1) @ V3))))))))))))
(TGroups.class.monoid_mult_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.class.semigroup_mult @ V1)) @ ((cGroups.class.monoid_mult_axioms @ V0) @ V1))))))))
(TGroups.comm_monoid_add.add_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))))))))
(TGroups.group_add.add_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V1 @ V4) @ V5)) @ V6))))))))))))))))))
(TGroups.group_add.minus_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ (V3 @ V4))) @ V4)))))))))))))
(TGroups.group_add.right_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ V4) @ (V3 @ V4))) @ V2)))))))))))))
(TGroups.group_add_class.intro,((c==> @ (cGroups.minus_class @ cTYPE)) @ ((c==> @ (cGroups.monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.uminus_class @ cTYPE)) @ ((c==> @ ((((cGroups.class.group_add_axioms @ cGroups.minus_class.minus) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus)) @ (cGroups.group_add_class @ cTYPE))))))
(TGroups.group_add_class.super_3,((c==> @ (cGroups.group_add_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE)))
(TGroups.group_add_class.super_2,((c==> @ (cGroups.group_add_class @ cTYPE)) @ (cGroups.monoid_add_class @ cTYPE)))
(TGroups.group_add_class.super_1,((c==> @ (cGroups.group_add_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TGroups.monoid_add.add_0_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))))))))
(TGroups.monoid_mult_class_def,((c== @ (cGroups.monoid_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.one_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.semigroup_mult_class @ cTYPE)) @ ((cGroups.class.monoid_mult_axioms @ cGroups.one_class.one) @ cGroups.times_class.times)))))
(THOL.equal_class.equal_axioms,(cHOL.class.equal @ cHOL.eq))
(THilbert_Choice.GreatestM_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHilbert_Choice.GreatestM @ V0) @ V1)) @ (cHilbert_Choice.Eps @ (^[V2]: ((cHOL.conj @ (V1 @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V1 @ V3)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V3)) @ (V0 @ V2))))))))))))))
(THilbert_Choice.LeastM_nat_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ ((cHilbert_Choice.LeastM @ V2) @ V0))) @ (V2 @ V1))))))))))
(THilbert_Choice.image_inv_f_f,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ ((cSet.image @ V0) @ V1))) @ V1)))))))
(THilbert_Choice.inv_into_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ ((cSet.image @ V1) @ V2))) @ ((c==> @ ((cFun.inj_on @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ ((cSet.image @ V0) @ ((cSet.image @ V1) @ V2)))) @ ((cHOL.eq @ (((cHilbert_Choice.inv_into @ V2) @ ((cFun.comp @ V0) @ V1)) @ V3)) @ (((cFun.comp @ ((cHilbert_Choice.inv_into @ V2) @ V1)) @ ((cHilbert_Choice.inv_into @ ((cSet.image @ V1) @ V2)) @ V0)) @ V3))))))))))))))
(THilbert_Choice.inv_into_f_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cHOL.eq @ (V0 @ V2)) @ V3)) @ ((cHOL.eq @ (((cHilbert_Choice.inv_into @ V1) @ V0) @ V3)) @ V2)))))))))))))
(THilbert_Choice.inv_into_into,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cSet.image @ V1) @ V2))) @ ((cSet.member @ (((cHilbert_Choice.inv_into @ V2) @ V1) @ V0)) @ V2)))))))))
(THilbert_Choice.o_inv_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((c==> @ (((cFun.bij_betw @ V1) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ ((cFun.comp @ V0) @ V1))) @ ((cFun.comp @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V1)) @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0))))))))))
(THilbert_Choice.some_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cHOL.eq @ V2) @ V1))))) @ ((cHOL.eq @ (cHilbert_Choice.Eps @ (^[V2]: (V0 @ V2)))) @ V1))))))))
(TInductive.def_lfp_induct_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.lfp @ V1))) @ ((c==> @ (cOrderings.order_class.mono @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ (V1 @ ((cLattices.inf_class.inf @ V0) @ (cSet.Collect @ (^[V5]: (V3 @ V5))))))) @ (V3 @ V4))))) @ (V3 @ V2))))))))))))))
(TInductive.lfp_ordinal_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V1 @ V2)) @ (V1 @ (V0 @ V2)))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.Ball @ V2) @ (^[V3]: (V1 @ V3)))) @ (V1 @ (cComplete_Lattices.Sup_class.Sup @ V2)))))) @ (V1 @ (cInductive.complete_lattice_class.lfp @ V0))))))))))
(TInt.equal_int_inst.equal_int,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TInt.int_one_le_iff_zero_less,(call @ (^[V0]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ cInt.one_int_inst.one_int) @ V0)) @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)))))
(TInt.minus_int_inst.minus_int,((c== @ cInt.minus_int_inst.minus_int) @ cInt.minus_int_inst.minus_int))
(TInt.ord_int_inst.less_eq_int,((c== @ cInt.ord_int_inst.less_eq_int) @ cInt.ord_int_inst.less_eq_int))
(TInt.pos_zmult_eq_1_iff_lemma,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ cInt.one_int_inst.one_int)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cInt.one_int_inst.one_int)) @ ((cHOL.eq @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))))))))
(TInt.ring_1_class.Ints_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cInt.ring_1_class.Ints)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cInt.ring_1_class.of_int @ V2))))) @ (V1 @ V0))))))))
(TInt.ring_1_class.Ints_of_int,(call @ (^[V0]: ((cSet.member @ (cInt.ring_1_class.of_int @ V0)) @ cInt.ring_1_class.Ints))))
(TInt.ring_1_class.Ints_of_nat,(call @ (^[V0]: ((cSet.member @ (cNat.semiring_1_class.of_nat @ V0)) @ cInt.ring_1_class.Ints))))
(TInt.ring_1_class.of_int_code_3,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cInt.Pos @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TInt.ring_1_class.of_int_code_2,((cHOL.eq @ (cInt.ring_1_class.of_int @ cInt.zero_int_inst.zero_int)) @ cGroups.zero_class.zero))
(TInt.ring_1_class.of_int_code_1,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cInt.Neg @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TInt.ring_1_class.of_int_diff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cInt.minus_int_inst.minus_int @ V0) @ V1))) @ ((cGroups.minus_class.minus @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))))))))
(TInt.ring_1_class.of_int_mult,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cInt.times_int_inst.times_int @ V0) @ V1))) @ ((cGroups.times_class.times @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))))))))
(TInt.times_int_inst.times_int,((c== @ cInt.times_int_inst.times_int) @ cInt.times_int_inst.times_int))
(TLattices.class.lattice.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ (((cLattices.class.semilattice_sup @ V3) @ V1) @ V2)) @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3))))))))))))
(TLattices.lattice.inf_sup_aci_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ V4) @ ((V3 @ V4) @ V5))) @ ((V3 @ V4) @ V5))))))))))))))))
(TLattices.lattice.inf_sup_aci_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ V4) @ ((V3 @ V5) @ V6))) @ ((V3 @ V5) @ ((V3 @ V4) @ V6)))))))))))))))))))
(TLattices.lattice.inf_sup_aci_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ ((V3 @ V4) @ V5)) @ V6)) @ ((V3 @ V4) @ ((V3 @ V5) @ V6)))))))))))))))))))
(TLattices.lattice.inf_sup_aci_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ V4) @ V5)) @ ((V3 @ V5) @ V4))))))))))))))))
(TLattices.lattice.inf_sup_aci_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V0 @ V4) @ V5))) @ ((V0 @ V4) @ V5))))))))))))))))
(TLattices.lattice.inf_sup_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ V5) @ ((V0 @ V4) @ V6)))))))))))))))))))
(TLattices.lattice.inf_sup_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V4) @ V5)) @ V6)) @ ((V0 @ V4) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TLattices.lattice.inf_sup_aci_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V0 @ V5) @ V4))))))))))))))))
(TLattices.lattice.inf_sup_ord_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ V4) @ ((V3 @ V5) @ V4))))))))))))))))
(TLattices.lattice.inf_sup_ord_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ V4) @ ((V3 @ V4) @ V5))))))))))))))))
(TLattices.lattice.inf_sup_ord_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ ((V0 @ V4) @ V5)) @ V5)))))))))))))))
(TLattices.lattice.inf_sup_ord_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ ((V0 @ V4) @ V5)) @ V4)))))))))))))))
(TLattices.lattice_class.intro,((c==> @ (cLattices.semilattice_inf_class @ cTYPE)) @ ((c==> @ (cLattices.semilattice_sup_class @ cTYPE)) @ (cLattices.lattice_class @ cTYPE))))
(TLattices.lattice_class.super_2,((c==> @ (cLattices.lattice_class @ cTYPE)) @ (cLattices.semilattice_sup_class @ cTYPE)))
(TLattices.lattice_class.super_1,((c==> @ (cLattices.lattice_class @ cTYPE)) @ (cLattices.semilattice_inf_class @ cTYPE)))
(TLazy_Sequence.hb_not_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.hb_not_seq @ V0)) @ (((cOption.option.option_case @ (cLazy_Sequence.single @ cProduct_Type.Unity)) @ (^[V1]: ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: cLazy_Sequence.empty))) @ V1))) @ (cLazy_Sequence.yield @ V0))))))
(TLifting.Quotient_part_equivp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ (cEquiv_Relations.part_equivp @ V0)))))))))))
(TLifting.Quotient_right_total,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ (cTransfer.right_total @ V3)))))))))))
(TLifting.Quotient_to_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V4)) @ ((c==> @ ((c== @ V5) @ (V1 @ V4))) @ ((V3 @ V4) @ V5)))))))))))))))))
(TLifting.fun_rel_eq_invariant,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cTransfer.fun_rel @ (cLifting.invariant @ V0)) @ V1)) @ (^[V2]: (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((V1 @ (V2 @ V4)) @ (V3 @ V4)))))))))))))
(TLifting.invariant_to_Domainp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ (cLifting.invariant @ V0)) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (cRelation.Domainp @ V3)) @ V0)))))))))))
(TLifting.left_total_conversep,(call @ (^[V0]: ((cHOL.eq @ (cLifting.left_total @ (cRelation.conversep @ V0))) @ (cTransfer.right_total @ V0)))))
(TLifting.left_unique_transfer,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_total @ V0)) @ ((c==> @ (cTransfer.right_total @ V1)) @ ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq))) @ cHOL.implies) @ cLifting.left_unique) @ cLifting.left_unique)))))))))
(TLifting.typedef_rep_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ ((((cTransfer.fun_rel @ V3) @ cHOL.eq) @ (^[V4]: V4)) @ V0))))))))))))
(TLifting.typedef_right_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ (cTransfer.right_unique @ V3))))))))))))
(TLifting_Option.None_transfer,(call @ (^[V0]: (((cLifting_Option.option_rel @ V0) @ cOption.option.None) @ cOption.option.None))))
(TLifting_Option.Some_transfer,(call @ (^[V0]: ((((cTransfer.fun_rel @ V0) @ (cLifting_Option.option_rel @ V0)) @ cOption.option.Some) @ cOption.option.Some))))
(TLifting_Option.option_rel_OO,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcompp @ (cLifting_Option.option_rel @ V0)) @ (cLifting_Option.option_rel @ V1))) @ (cLifting_Option.option_rel @ ((cRelation.relcompp @ V0) @ V1))))))))
(TLifting_Option.option_rel_eq,((cHOL.eq @ (cLifting_Option.option_rel @ cHOL.eq)) @ cHOL.eq))
(TLifting_Product.Domainp_prod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V2)) @ V3)) @ ((cHOL.eq @ (cRelation.Domainp @ ((cLifting_Product.prod_rel @ V0) @ V2))) @ ((cLifting_Product.prod_pred @ V1) @ V3)))))))))))))
(TLifting_Product.fst_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cLifting_Product.prod_rel @ V0) @ V1)) @ V0) @ cProduct_Type.fst) @ cProduct_Type.fst))))))
(TLifting_Product.prod_rel_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLifting_Product.prod_rel @ V0) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cHOL.conj @ ((V0 @ V2) @ V4)) @ ((V1 @ V3) @ V5))))))))))))))
(TLifting_Product.snd_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cLifting_Product.prod_rel @ V0) @ V1)) @ V1) @ cProduct_Type.snd) @ cProduct_Type.snd))))))
(TLifting_Set.Collect_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ (cLifting_Set.set_rel @ V0)) @ cSet.Collect) @ cSet.Collect)))))
(TLifting_Set.bi_total_set_rel,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ (cTransfer.bi_total @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Set.set_rel_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq))) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V1)) @ cHOL.eq))) @ cLifting_Set.set_rel) @ cLifting_Set.set_rel))))))
(TLifting_Sum.bi_total_sum_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((c==> @ (cTransfer.bi_total @ V1)) @ (cTransfer.bi_total @ ((cLifting_Sum.sum_rel @ V0) @ V1)))))))))
(TLimited_Sequence.map_seq_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLimited_Sequence.map_seq @ V0) @ V1) @ V2) @ V3)) @ ((cOption.map @ cLazy_Sequence.flat) @ (cLazy_Sequence.those @ ((cLazy_Sequence.map @ (^[V4]: (((V0 @ V4) @ V2) @ V3))) @ V1)))))))))))))
(TLimited_Sequence.neg_map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.neg_map @ V0) @ V1)) @ (^[V2]: ((cLazy_Sequence.hb_map @ V0) @ (V1 @ V2)))))))))
(TLimited_Sequence.not_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.not_seq @ V0)) @ (^[V1]: (^[V2]: (((cOption.option.option_case @ (cOption.option.Some @ cLazy_Sequence.empty)) @ (^[V3]: (((cOption.option.option_case @ (cOption.option.Some @ (cLazy_Sequence.single @ cProduct_Type.Unity))) @ (^[V4]: (cOption.option.Some @ cLazy_Sequence.empty))) @ (cLazy_Sequence.yield @ V3)))) @ ((V0 @ V1) @ (cHOL.Not @ V2)))))))))
(TLimited_Sequence.pos_map_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.pos_map @ V0) @ V1)) @ (^[V2]: ((cLazy_Sequence.map @ V0) @ (V1 @ V2)))))))))
(TList.can_select_set_list_ex1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.can_select @ V0) @ (cList.set @ V1))) @ ((cList.list_ex1 @ V0) @ V1)))))))
(TList.greaterThanLessThan_upt,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ (cList.set @ ((cList.upt @ (cNat.Suc @ V0)) @ V1))))))))
(TList.in_set_conv_decomp_last,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V2) @ ((cList.list.Cons @ V0) @ V3)))) @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V3))))))))))))))
(TList.length_filter_conv_card,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.filter @ V0) @ V1))) @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V1))) @ (V0 @ ((cList.nth @ V1) @ V2))))))))))))
(TList.length_transpose_sorted,(call @ (^[V0]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ ((cList.map @ cNat.size_class.size) @ V0)))) @ ((cHOL.eq @ (cNat.size_class.size @ (cList.transpose @ V0))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ ((cList.nth @ V0) @ cNat.zero_nat_inst.zero_nat))))))))
(TList.linorder.insort_is_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V5]: ((V0 @ (V3 @ V4)) @ (V3 @ V5))))) @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ V3) @ V4) @ V2)) @ ((cList.list.Cons @ V4) @ V2)))))))))))))))
(TList.linorder.insort_key_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c== @ (cList.linorder.insort_key @ V0)) @ (^[V2]: (^[V3]: (^[V4]: (((((cList.list.list_rec @ (^[V5]: (^[V6]: ((cList.list.Cons @ V6) @ cList.list.Nil)))) @ (^[V5]: (^[V6]: (^[V7]: (^[V8]: (^[V9]: (((cHOL.If @ ((V0 @ (V8 @ V9)) @ (V8 @ V5))) @ ((cList.list.Cons @ V9) @ ((cList.list.Cons @ V5) @ V6))) @ ((cList.list.Cons @ V5) @ ((V7 @ V8) @ V9))))))))) @ V4) @ V2) @ V3)))))))))))
(TList.linorder.insort_not_Nil,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4)) @ cList.list.Nil))))))))))))))
(TList.linorder.insort_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (cList.set @ V3))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V3)) @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ (^[V4]: V4)) @ V2) @ ((cList.remove1 @ V2) @ V3))) @ V3)))))))))))))
(TList.linorder.remove1_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.remove1 @ V2) @ ((((cList.linorder.insort_key @ V0) @ (^[V4]: V4)) @ V2) @ V3))) @ V3)))))))))))
(TList.linorder.set_insort_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cList.set @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4))) @ ((cSet.insert @ V3) @ (cList.set @ V4)))))))))))))))
(TList.linorder.sort_conv_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cList.linorder.sort_key @ V0) @ (^[V3]: V3)) @ V2)) @ (((cList.fold @ ((cList.linorder.insort_key @ V0) @ (^[V3]: V3))) @ V2) @ cList.list.Nil))))))))))
(TList.linorder.sort_key_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cList.linorder.sort_key @ V0) @ V2) @ ((cList.list.Cons @ V3) @ V4))) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ (((cList.linorder.sort_key @ V0) @ V2) @ V4)))))))))))))))
(TList.linorder.sort_key_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cList.linorder.sort_key @ V0) @ V2) @ cList.list.Nil)) @ cList.list.Nil)))))))))
(TList.linorder.sorted.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((c==> @ (V3 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V6]: ((V0 @ V5) @ V6)))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V4)) @ ((c==> @ (V3 @ V4)) @ (V3 @ ((cList.list.Cons @ V5) @ V4)))))))))) @ (V3 @ V2))))))))))))))
(TList.linorder.sorted_butlast,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cList.list.Nil))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ (cList.butlast @ V2))))))))))))
(TList.linorder.sorted_many_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ ((cHOL.conj @ ((V0 @ V2) @ V3)) @ ((cList.linorder.sorted @ V0) @ ((cList.list.Cons @ V3) @ V4))))))))))))))))
(TList.linorder.sorted_remdups,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ (cList.remdups @ V2)))))))))))
(TList.linorder.sorted_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((cList.remove1 @ V3) @ V2)))))))))))))
(TList.linorder.sorted_sort_id,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cHOL.eq @ (((cList.linorder.sort_key @ V0) @ (^[V3]: V3)) @ V2)) @ V2))))))))))
(TList.linorder_class.set_sort,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ ((cList.linorder_class.sort_key @ V0) @ V1))) @ (cList.set @ V1)))))))
(TList.list.list_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cList.list.list_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V7) @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ (((V1 @ V7) @ V5) @ V6))) @ ((c==> @ ((((cList.list.list_rec_set @ V0) @ V1) @ V5) @ V6)) @ V4)))))))))) @ V4))))))))))))))
(TList.list.list_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cList.list.list_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ ((cHOL.eq @ V3) @ V0))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cList.list.Cons @ V6) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ (((V1 @ V6) @ V4) @ V5))) @ ((((cList.list.list_rec_set @ V0) @ V1) @ V4) @ V5))))))))))))))))))))
(TList.listrel1_subset_listrel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cRelation.refl_on @ cOrderings.top_class.top) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.listrel1 @ V0)) @ (cList.listrel @ V1)))))))))
(TList.map_tailrec_rev.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V5)))) @ (((V3 @ V4) @ cList.list.Nil) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V6)) @ V7)))) @ ((c==> @ (((V3 @ V4) @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7))) @ (((V3 @ V4) @ ((cList.list.Cons @ V5) @ V6)) @ V7)))))))))))) @ (((V3 @ V0) @ V1) @ V2)))))))))))))
(TList.map_tailrec_rev_rel_def,((c== @ cList.map_tailrec_rev_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V5) @ ((cList.list.Cons @ (V3 @ V4)) @ V6))))) @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ V6))))))))))))))))))
(TList.monoid_add.listsum_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V4]: V2)) @ V3))) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ (cNat.size_class.size @ V3))) @ V2))))))))))))
(TList.remdups_adj.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V1) @ V3)) @ ((cList.list.Cons @ V1) @ ((cList.list.Cons @ V2) @ V3)))) @ V0))))))))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V3)) @ ((cList.list.Cons @ V1) @ ((cList.list.Cons @ V2) @ V3)))) @ V0))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cList.remdups_adj_rel) @ V1)))))))))
(TList.remdups_adj_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.remdups_adj_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ V2))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V4) @ cList.list.Nil))) @ V2))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ V5)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))) @ ((cList.list.Cons @ V4) @ (V3 @ ((cList.list.Cons @ V5) @ V6)))))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ V5)) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V4) @ V6)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V5) @ V6)) @ (V3 @ ((cList.list.Cons @ V5) @ V6))))) @ V2))))))))))))) @ V2)))))))))))
(TList.remdups_adj_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.remdups_adj_graph @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ ((cHOL.eq @ V1) @ cList.list.Nil))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ cList.list.Nil))) @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ cList.list.Nil)))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V3) @ V4)) @ (V2 @ ((cList.list.Cons @ V3) @ V5))) @ ((cList.list.Cons @ V3) @ (V2 @ ((cList.list.Cons @ V4) @ V5)))))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ V4)) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V3) @ V5)) @ (V2 @ ((cList.list.Cons @ V3) @ V5))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V4) @ V5)) @ (V2 @ ((cList.list.Cons @ V4) @ V5)))))))))))))))))))))))
(TList.remdups_adj_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.remdups_adj_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V3) @ V4)) @ ((V2 @ ((cList.list.Cons @ V3) @ V5)) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((V2 @ ((cList.list.Cons @ V4) @ V5)) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.remdups_id_iff_distinct,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.remdups @ V0)) @ V0)) @ (cList.distinct @ V0)))))
(TList.removeAll_filter_not_eq,(call @ (^[V0]: ((cHOL.eq @ (cList.removeAll @ V0)) @ (cList.filter @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))))
(TList.replicate.replicate_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.replicate @ (cNat.Suc @ V0)) @ V1)) @ ((cList.list.Cons @ V1) @ ((cList.replicate @ V0) @ V1))))))))
(TList.replicate_app_Cons_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.append @ ((cList.replicate @ V0) @ V1)) @ ((cList.list.Cons @ V1) @ V2))) @ ((cList.list.Cons @ V1) @ ((cList.append @ ((cList.replicate @ V0) @ V1)) @ V2))))))))))
(TList.replicate_length_filter,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.replicate @ (cNat.size_class.size @ ((cList.filter @ (^[V2]: ((cHOL.eq @ V0) @ V2))) @ V1))) @ V0)) @ ((cList.filter @ (^[V2]: ((cHOL.eq @ V0) @ V2))) @ V1)))))))
(TList.rtrancl_listrel1_ConsI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V2)))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V0)) @ ((cList.list.Cons @ V3) @ V1))) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V2)))))))))))))
(TList.rtrancl_listrel1_ConsI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V2)))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V0) @ V3)) @ ((cList.list.Cons @ V1) @ V4))) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V2))))))))))))))))
(TList.rtrancl_listrel1_eq_len,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V2)))) @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))))
(TList.sublist_shift_lemma_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.map @ cProduct_Type.fst) @ ((cList.filter @ (^[V3]: (V0 @ (cNat.Suc @ (cProduct_Type.snd @ V3))))) @ ((cList.zip @ V1) @ V2)))) @ ((cList.map @ cProduct_Type.fst) @ ((cList.filter @ (^[V3]: (V0 @ (cProduct_Type.snd @ V3)))) @ ((cList.zip @ V1) @ ((cList.map @ cNat.Suc) @ V2))))))))))))
(TList.sum_length_filter_compl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ ((cList.filter @ V0) @ V1))) @ (cNat.size_class.size @ ((cList.filter @ (^[V2]: (cHOL.Not @ (V0 @ V2)))) @ V1)))) @ (cNat.size_class.size @ V1)))))))
(TList.takeWhile_eq_take_P_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V1))) @ (V2 @ ((cList.nth @ V1) @ V3))))))) @ ((c==> @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cNat.size_class.size @ V1))) @ (cHOL.Not @ (V2 @ ((cList.nth @ V1) @ V0))))) @ ((cHOL.eq @ ((cList.takeWhile @ V2) @ V1)) @ ((cList.take @ V0) @ V1)))))))))))
(TList.transpose_column_length,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ ((cList.map @ cNat.size_class.size) @ V0)))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V0))) @ ((cHOL.eq @ (cNat.size_class.size @ ((cList.filter @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V2)))) @ (cList.transpose @ V0)))) @ (cNat.size_class.size @ ((cList.nth @ V0) @ V1))))))))))
(TList.transpose_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.transpose_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ cList.list.Nil) @ cList.list.Nil)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cList.transpose_graph @ V4) @ (V3 @ V4))) @ ((c==> @ ((V2 @ V4) @ (V3 @ V4))) @ ((V2 @ ((cList.list.Cons @ cList.list.Nil) @ V4)) @ (V3 @ V4))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cList.transpose_graph @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))))) @ ((c==> @ ((V2 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6)))))) @ ((V2 @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ V5)) @ V6)) @ ((cList.list.Cons @ ((cList.list.Cons @ V4) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V7) @ cList.list.Nil))))) @ V6)))) @ (V3 @ ((cList.list.Cons @ V5) @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V7]: (^[V8]: ((cList.list.Cons @ V8) @ cList.list.Nil))))) @ V6))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))))
(TMain.arity_narrowing_sumbool,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TNat.equal_nat_inst.equal_nat,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TNat.infinite_descent_measure,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.Not @ (V0 @ V3))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ (V1 @ V4)) @ (V1 @ V3))) @ (cHOL.Not @ (V0 @ V4))))))))) @ (V0 @ V2)))))))))
(TNat.minus_nat_inst.minus_nat,((c== @ cNat.minus_nat_inst.minus_nat) @ cNat.minus_nat_inst.minus_nat))
(TNat.nat_add_left_cancel_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)))))))))
(TNat.ord_nat_inst.less_eq_nat,((c== @ cNat.ord_nat_inst.less_eq_nat) @ cNat.ord_nat_inst.less_eq_nat))
(TNat.order.lift_Suc_mono_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (call @ (^[V5]: ((V1 @ (V2 @ V5)) @ (V2 @ (cNat.Suc @ V5)))))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V4)) @ ((V1 @ (V2 @ V3)) @ (V2 @ V4))))))))))))))))
(TNat.ring_1_class.of_nat_diff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0))) @ ((cGroups.minus_class.minus @ (cNat.semiring_1_class.of_nat @ V1)) @ (cNat.semiring_1_class.of_nat @ V0)))))))))
(TNat.times_nat_inst.times_nat,((c== @ cNat.times_nat_inst.times_nat) @ cNat.times_nat_inst.times_nat))
(TNitpick.arity_equal_pair_box,(cHOL.equal_class @ cTYPE))
(TNitpick.arity_narrowing_word,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TNitpick.arity_random_fun_box,(cQuickcheck_Random.random_class @ cTYPE))
(TNitpick.nat_gcd_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.nat_gcd_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat))) @ ((cNitpick.nat_gcd_graph @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat))) @ ((V2 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat)) @ V4) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.nat_gcd_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat))) @ ((cNitpick.nat_gcd_graph @ ((cProduct_Type.Pair @ V0) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0))) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0)))))) @ ((cNitpick.nat_gcd_graph @ ((cProduct_Type.Pair @ V1) @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V1) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cDivides.div_nat_inst.mod_nat @ V1) @ V0)))))))))))))
(TNitpick.norm_frac_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.norm_frac_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.norm_frac_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac_rel @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V1)) @ (cInt.uminus_int_inst.uminus_int @ V0))) @ ((cProduct_Type.Pair @ V1) @ V0))))))))
(TNitpick.pair_box.PairBox_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cNitpick.pair_box.PairBox @ V0) @ V1)) @ (cNitpick.Abs_pair_box @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1))))))))))
(TNitpick.term_of_fun_box_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TNitpick.type_definition_word,(((cTypedef.type_definition @ cNitpick.Rep_word) @ cNitpick.Abs_word) @ (cSet.Collect @ cNitpick.word.word_rep_set)))
(TNitpick.typerep_pair_box_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TNitpick.word.Abs_word_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNitpick.word.word_rep_set))) @ (V0 @ (cNitpick.Abs_word @ V2)))))) @ (V0 @ V1)))))))
(TNitpick.word.Abs_word_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.word.word_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cNitpick.word.word_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cNitpick.Abs_word @ V0)) @ (cNitpick.Abs_word @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TNitpick.word.Rep_word_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.word.word_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cNitpick.Rep_word @ V2))))) @ (V1 @ V0))))))))
(TNitpick.word.Rep_word_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNitpick.Rep_word @ V0)) @ (cNitpick.Rep_word @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.word.arity_size_word,(cNat.size_class @ cTYPE))
(TNum.class.neg_numeral.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ (cNum.class.numeral @ V1)))))))))))
(TNum.class.neg_numeral.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)))))))))))
(TNum.class.ring_char_0.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))
(TNum.class.ring_char_0.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)))))))))))))))
(TNum.equal_num_inst.equal_num,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TNum.neg_numeral.is_num.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ V4)) @ V6)) @ ((c==> @ (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V5) @ (V3 @ V7))) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V7)) @ V6))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V5) @ ((V1 @ V7) @ V8))) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V7)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V8)) @ V6)))))))) @ V6))))))))))))))))))))
(TNum.neg_numeral.is_num.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((cHOL.disj @ ((cHOL.eq @ V5) @ V4)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V5) @ (V3 @ V6))) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6))))) @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V5) @ ((V1 @ V6) @ V7))) @ ((cHOL.conj @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V7))))))))))))))))))))))))
(TNum.neg_numeral.numeral_BitM,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.BitM @ V5))) @ ((V0 @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.num.Bit0 @ V5))) @ V4))))))))))))))))
(TNum.numeral.numeral_plus_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ V1)) @ (((cNum.numeral.numeral @ V1) @ V0) @ ((cNum.plus_num_inst.plus_num @ V2) @ cNum.num.One)))))))))))
(TNum.numeral.one_plus_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ (((cNum.numeral.numeral @ V1) @ V0) @ V2))) @ (((cNum.numeral.numeral @ V1) @ V0) @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V2)))))))))))
(TNum.ord_num_inst.less_eq_num,((c== @ cNum.ord_num_inst.less_eq_num) @ cNum.ord_num_inst.less_eq_num))
(TNum.ring_1.mult_minus1_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ V6) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ cNum.num.One))) @ (V5 @ V6))))))))))))))))))
(TNum.ring_1_class.mult_minus1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ V0)) @ (cGroups.uminus_class.uminus @ V0)))))
(TNum.times_num_inst.times_num,((c== @ cNum.times_num_inst.times_num) @ cNum.times_num_inst.times_num))
(TOption.option.option_rec_def,((c== @ cOption.option.option_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cOption.option.option_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TOption.option.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cOption.option.option_case @ V2) @ V3) @ V0)) @ (((cOption.option.option_case @ V2) @ V3) @ V1))))))))))))
(TOption.option_map_o_sum_case,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ (cOption.map @ V0)) @ ((cSum_Type.sum.sum_case @ V1) @ V2))) @ ((cSum_Type.sum.sum_case @ ((cFun.comp @ (cOption.map @ V0)) @ V1)) @ ((cFun.comp @ (cOption.map @ V0)) @ V2))))))))))
(TOrderings.arity_preorder_fun,(cOrderings.preorder_class @ cTYPE))
(TOrderings.class.linorder_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.order @ V0) @ V1)) @ (cOrderings.class.linorder_axioms @ V0))))))))
(TOrderings.class.no_bot.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (cOrderings.class.no_bot_axioms @ V1)) @ ((cOrderings.class.no_bot @ V0) @ V1))))))))
(TOrderings.class.no_top.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (cOrderings.class.no_top_axioms @ V1)) @ ((cOrderings.class.no_top @ V0) @ V1))))))))
(TOrderings.class.order.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ (cOrderings.class.order_axioms @ V0)))))))
(TOrderings.class.order.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cOrderings.class.preorder @ V0) @ V1)))))))
(TOrderings.class.preorder_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V2) @ V3)) @ (cHOL.Not @ ((V0 @ V3) @ V2))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: ((V0 @ V2) @ V2)))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((V0 @ V2) @ V4)))))))))))))))))
(TOrderings.linorder.mono_invE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.mono @ V0) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ (V2 @ V3)) @ (V2 @ V4))) @ ((c==> @ ((c==> @ ((V0 @ V3) @ V4)) @ V5)) @ V5)))))))))))))))))
(TOrderings.linorder.split_max,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (V2 @ (((cOrderings.ord.max @ V0) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((V0 @ V3) @ V4)) @ (V2 @ V4))) @ ((cHOL.implies @ (cHOL.Not @ ((V0 @ V3) @ V4))) @ (V2 @ V3))))))))))))))))
(TOrderings.linorder.split_min,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (V2 @ (((cOrderings.ord.min @ V0) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((V0 @ V3) @ V4)) @ (V2 @ V3))) @ ((cHOL.implies @ (cHOL.Not @ ((V0 @ V3) @ V4))) @ (V2 @ V4))))))))))))))))
(TOrderings.linorder_class.leD,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.linorder_class.leI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TOrderings.linorder_class_def,((c== @ (cOrderings.linorder_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ (cOrderings.class.linorder_axioms @ cOrderings.ord_class.less_eq))))
(TOrderings.no_bot_class.intro,((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ (cOrderings.class.no_bot_axioms @ cOrderings.ord_class.less)) @ (cOrderings.no_bot_class @ cTYPE))))
(TOrderings.no_bot_class.lt_ex,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0))))))
(TOrderings.no_bot_class.super,((c==> @ (cOrderings.no_bot_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TOrderings.no_top_class.gt_ex,(call @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cOrderings.ord_class.less @ V0) @ V1))))))
(TOrderings.no_top_class.intro,((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ (cOrderings.class.no_top_axioms @ cOrderings.ord_class.less)) @ (cOrderings.no_top_class @ cTYPE))))
(TOrderings.no_top_class.super,((c==> @ (cOrderings.no_top_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TOrderings.order.antisym_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V3) @ V2)))))))))))))
(TOrderings.order.le_neq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((V1 @ V2) @ V3)))))))))))))
(TOrderings.order.less_imp_neq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.order.neq_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V1 @ V2) @ V3)))))))))))))
(TOrderings.order.strict_monoD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.strict_mono @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((cOrderings.ord_class.less @ (V2 @ V3)) @ (V2 @ V4))))))))))))))))
(TOrderings.order.strict_monoI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V1 @ V3) @ V4)) @ ((cOrderings.ord_class.less @ (V2 @ V3)) @ (V2 @ V4)))))))) @ ((cOrderings.order.strict_mono @ V1) @ V2))))))))))
(TOrderings.order_antisym_conv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.order_bot.bot_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V3) @ V0))) @ ((V2 @ V0) @ V3))))))))))))
(TOrderings.order_class.axioms,(cOrderings.class.order_axioms @ cOrderings.ord_class.less_eq))
(TOrderings.order_class.eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TOrderings.order_le_neq_trans,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.order_less_not_sym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.order_neq_le_trans,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.order_top.less_top,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V3) @ V2))) @ ((V1 @ V3) @ V2))))))))))))
(TOrderings.ordering_top.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((cOrderings.ordering_top_axioms @ V0) @ V2)) @ (((cOrderings.ordering_top @ V0) @ V1) @ V2))))))))))
(TOrderings.preorder.less_asym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((c==> @ (cHOL.Not @ V4)) @ ((V1 @ V3) @ V2))) @ V4))))))))))))))
(TOrderings.preorder_class_def,((c== @ (cOrderings.preorder_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.ord_class @ cTYPE)) @ ((cOrderings.class.preorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))))
(TOrderings.wellorder.Least_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ ((V0 @ ((cOrderings.ord.Least @ V0) @ (^[V4]: (V2 @ V4)))) @ V3))))))))))))
(TPartial_Function.fun_lub_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPartial_Function.fun_lub @ V0) @ V1)) @ (^[V2]: (V0 @ (cSet.Collect @ (^[V3]: ((cSet.Bex @ V1) @ (^[V4]: ((cHOL.eq @ V3) @ (V4 @ V2))))))))))))))
(TPartial_Function.fun_ord_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cPartial_Function.fun_ord @ V0) @ V1) @ V2)) @ (cHOL.All @ (^[V3]: ((V0 @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TPartial_Function.img_lub_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cPartial_Function.img_lub @ V0) @ V1) @ V2)) @ (^[V3]: (V1 @ (V2 @ ((cSet.image @ V0) @ V3))))))))))))
(TPartial_Function.img_ord_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPartial_Function.img_ord @ V0) @ V1)) @ (^[V2]: (^[V3]: ((V1 @ (V0 @ V2)) @ (V0 @ V3))))))))))
(TPartial_Function.mk_less_def,(call @ (^[V0]: ((cHOL.eq @ (cPartial_Function.mk_less @ V0)) @ (^[V1]: (^[V2]: ((cHOL.conj @ ((V0 @ V1) @ V2)) @ (cHOL.Not @ ((V0 @ V2) @ V1)))))))))
(TPartial_Function.option.ccpo,(((cComplete_Partial_Order.class.ccpo @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.mk_less @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None)))))
(TPower.field_class.power_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V1))) @ ((cFields.inverse_class.divide @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V0) @ V1))))))))))))
(TPower.monoid_mult.power_Suc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNat.Suc @ V3))) @ ((V1 @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3)) @ V2))))))))))))
(TPower.monoid_mult.power_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ ((cNat.times_nat_inst.times_nat @ V3) @ V4))) @ ((((cPower.power.power @ V0) @ V1) @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3)) @ V4))))))))))))))
(TPower.nat_power_eq_Suc_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V0) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TPower.semiring_1.zero_power2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V3) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ V3)))))))))))
(TPredicate.iterate_upto.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TPredicate.iterate_upto.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cPredicate.iterate_upto @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (cPredicate.Seq @ (^[V8]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V7) @ V6)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V5 @ V6)) @ (((cPredicate.iterate_upto @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7))))))) @ V4))))))))))) @ V4)))))))))))))
(TPredicate.iterate_upto.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cPredicate.iterate_upto @ V0) @ V1) @ V2)) @ (cPredicate.Seq @ (^[V3]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ V1)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V0 @ V1)) @ (((cPredicate.iterate_upto @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)))))))))))))
(TPredicate.member_set_of_pred,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cPredicate.set_of_pred @ V1))) @ ((cPredicate.eval @ V1) @ V0)))))))
(TPredicate.pred.pred_case_def,((c== @ cPredicate.pred.pred_case) @ (^[V0]: (cPredicate.pred.pred_rec @ (^[V1]: (V0 @ V1))))))
(TPredicate.pred.pred_size_def,(call @ (^[V0]: ((c== @ (cPredicate.pred.pred_size @ V0)) @ (cPredicate.pred.pred_rec @ (^[V1]: cNat.zero_nat_inst.zero_nat))))))
(TPredicate.seq.Abs_seq_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cPredicate.seq.seq_rep_set))) @ (V0 @ (cPredicate.Abs_seq @ V2)))))) @ (V0 @ V1)))))))
(TPredicate.seq.Abs_seq_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.seq.seq_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cPredicate.seq.seq_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cPredicate.Abs_seq @ V0)) @ (cPredicate.Abs_seq @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TPredicate.seq.Rep_seq_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.seq.seq_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cPredicate.Rep_seq @ V2))))) @ (V1 @ V0))))))))
(TPredicate.seq.Rep_seq_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cPredicate.Rep_seq @ V0)) @ (cPredicate.Rep_seq @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.seq.arity_size_seq,(cNat.size_class @ cTYPE))
(TPredicate.seq.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((((cPredicate.seq.seq_case @ V2) @ V3) @ V4) @ V0)) @ ((((cPredicate.seq.seq_case @ V2) @ V3) @ V4) @ V1))))))))))))))
(TPredicate.the_only_singleton,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.the_only @ V0) @ V1)) @ ((cPredicate.singleton @ V0) @ (cPredicate.pred_of_seq @ V1))))))))
(TProduct_Type.Pair_fst_snd_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ (cProduct_Type.fst @ V0)) @ (cProduct_Type.fst @ V1))) @ ((cHOL.eq @ (cProduct_Type.snd @ V0)) @ (cProduct_Type.snd @ V1)))))))))
(TProduct_Type.UNIV_Times_UNIV,((cHOL.eq @ ((cProduct_Type.Sigma @ cOrderings.top_class.top) @ (^[V0]: cOrderings.top_class.top))) @ cOrderings.top_class.top))
(TProduct_Type.arity_type_prod,(cHOL.type_class @ cTYPE))
(TProduct_Type.arity_type_unit,(cHOL.type_class @ cTYPE))
(TProduct_Type.fst_image_times,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cProduct_Type.fst) @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1)))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ V0)))))))
(TProduct_Type.map_pair_imageI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ (V3 @ V0)) @ (V4 @ V1))) @ ((cSet.image @ ((cProduct_Type.map_pair @ V3) @ V4)) @ V2))))))))))))))
(TProduct_Type.map_pair_inj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ V3)) @ ((cFun.inj_on @ ((cProduct_Type.map_pair @ V0) @ V2)) @ ((cProduct_Type.Sigma @ V1) @ (^[V4]: V3))))))))))))))
(TProduct_Type.prod_fun_imageE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V0) @ ((cSet.image @ ((cProduct_Type.map_pair @ V1) @ V2)) @ V3))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (V1 @ V5)) @ (V2 @ V6)))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V3)) @ V4))))))) @ V4)))))))))))))
(TProduct_Type.snd_image_times,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cProduct_Type.snd) @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ V1)))))))
(TProduct_Type.split_paired_Ex,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TProduct_Type.split_split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.prod.prod_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TProduct_Type.split_weak_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V2) @ V0)) @ ((cProduct_Type.prod.prod_case @ V2) @ V1))))))))))
(TProduct_Type.times_Int_times,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cProduct_Type.Sigma @ V0) @ (^[V4]: V1))) @ ((cProduct_Type.Sigma @ V2) @ (^[V4]: V3)))) @ ((cProduct_Type.Sigma @ ((cLattices.inf_class.inf @ V0) @ V2)) @ (^[V4]: ((cLattices.inf_class.inf @ V1) @ V3)))))))))))))
(TQuickcheck_Narrowing.all_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.all @ V0)) @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ (^[V1]: (^[V2]: (((cQuickcheck_Narrowing.property.Universal @ V1) @ (^[V3]: (V0 @ ((cQuickcheck_Narrowing.conv @ V2) @ V3)))) @ (cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ cTYPE))))) @ (cQuickcheck_Narrowing.narrowing_class.narrowing @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))
(TQuickcheck_Narrowing.sum_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.sum @ V0) @ V1) @ V2)) @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ (^[V3]: (^[V4]: ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ (^[V5]: ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ (^[V6]: (^[V7]: ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ (^[V8]: ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ ((cList.append @ V5) @ V8))) @ ((cList.append @ V4) @ V7)))) @ V6)))) @ (V1 @ V2)))) @ V3)))) @ (V0 @ V2))))))))))
(TQuickcheck_Random.beyond_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Random.beyond @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1)) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)))))))
(TQuotient.Quotient3_rep_reflp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((V0 @ (V2 @ V3)) @ (V2 @ V3))))))))))))
(TRandom.iterate_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom.iterate_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom.iterate_graph @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ V6)) @ ((cProduct_Type.scomp @ (V5 @ V6)) @ (^[V7]: (V3 @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V7)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Pred.iter'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Pred.iter'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V7) @ ((cQuickcheck_Random.random_class.random @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V12)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))))))))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Pred.iter'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Random.random_class.random @ V2) @ V3))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V6) @ V7)) @ V4)) @ ((cRandom_Pred.iter'_rel @ ((cProduct_Type.Pair @ V8) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V2) @ V9)))) @ ((cProduct_Type.Pair @ V8) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V2) @ V3)))))))))))))))))))))))))))))
(TRandom_Pred.iterate_upto_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRandom_Pred.iterate_upto @ V0) @ V1) @ V2)) @ (cProduct_Type.Pair @ (((cPredicate.iterate_upto @ V0) @ V1) @ V2))))))))))
(TRandom_Sequence.Random.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TRandom_Sequence.Random.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cRandom_Sequence.Random @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V4 @ V6)) @ (^[V7]: ((cProduct_Type.scomp @ (((cRandom_Sequence.Random @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)) @ (^[V8]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V7))) @ V8)))))))))) @ V3)))))))) @ V3)))))))))))
(TRandom_Sequence.Random.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.Random @ V0) @ V1)) @ (^[V2]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V0 @ V2)) @ (^[V3]: ((cProduct_Type.scomp @ (((cRandom_Sequence.Random @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)) @ (^[V4]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V3))) @ V4))))))))))))))
(TRandom_Sequence.iter.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.iter_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.iter_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ (((V3 @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13)))))))))))))))))))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TRandom_Sequence.iter_rel_def,((c== @ cRandom_Sequence.iter_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: (cHOL.Ex @ (^[V12]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V12)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.conj @ ((cHOL.eq @ V7) @ (V3 @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8))))))))))))))))))))))))))))))))
(TRandom_Sequence.neg_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.neg_bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cLimited_Sequence.neg_bind @ (((V0 @ V2) @ V3) @ V4)) @ (^[V5]: ((((V1 @ V5) @ V2) @ V3) @ V4))))))))))))
(TRandom_Sequence.pos_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.pos_bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cLimited_Sequence.pos_bind @ (((V0 @ V2) @ V3) @ V4)) @ (^[V5]: ((((V1 @ V5) @ V2) @ V3) @ V4))))))))))))
(TRecord.update_accessor_noopE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ (V1 @ V3))) @ (V1 @ V3))) @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ V3))))))))))))
(TRelation.Image_Collect_split,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.Image @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((V0 @ V2) @ V3)))))) @ V1)) @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V1) @ (^[V3]: ((V0 @ V3) @ V2)))))))))))
(TRelation.Image_singleton_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V0)) @ V1)))))))))
(TRelation.Range_Collect_split,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Range @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2))))))) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TRelation.conversep_conversep,(call @ (^[V0]: ((cHOL.eq @ (cRelation.conversep @ (cRelation.conversep @ V0))) @ V0))))
(TRelation.insert_relcomp_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cRelation.relcomp @ ((cSet.insert @ V1) @ V2)) @ V0)) @ (((cFinite_Set.fold @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ ((cHOL.eq @ (cProduct_Type.snd @ V1)) @ V3)) @ ((cSet.insert @ ((cProduct_Type.Pair @ (cProduct_Type.fst @ V1)) @ V4)) @ V5)) @ V5)))))) @ ((cRelation.relcomp @ V2) @ V0)) @ V0))))))))))
(TRelation.relcompp_relcomp_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcompp @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V0)))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cRelation.relcomp @ V0) @ V1))))))))))
(TRelation.simgle_valued_empty,(cRelation.single_valued @ cOrderings.bot_class.bot))
(TRelation.single_valued_Id_on,(call @ (^[V0]: (cRelation.single_valued @ (cRelation.Id_on @ V0)))))
(TRings.class.comm_ring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cRings.class.comm_semiring @ V0) @ V4)))))))))))))
(TRings.class.comm_ring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)))))))))))))
(TRings.class.ordered_ring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c== @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.conj @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cRings.class.ring @ V0) @ V1) @ V5) @ V6) @ V4))))))))))))))))))
(TRings.class.semiring_0.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cRings.class.mult_zero @ V2) @ V1)) @ ((c==> @ ((cRings.class.semiring @ V0) @ V2)) @ (((cRings.class.semiring_0 @ V0) @ V1) @ V2)))))))))))
(TRings.class.semiring_1.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((c==> @ (((cRings.class.semiring_0 @ V2) @ V3) @ V1)) @ ((c==> @ ((cRings.class.zero_neq_one @ V0) @ V3)) @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)))))))))))))
(TRings.class.zero_neq_one_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.class.zero_neq_one @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))))))))
(TRings.idom_class.idom_axioms,((((((cRings.class.idom @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TRings.mult_zero_class.axioms,((cRings.class.mult_zero @ cGroups.times_class.times) @ cGroups.zero_class.zero))
(TRings.ordered_ring_class_def,((c== @ (cRings.ordered_ring_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.ordered_cancel_semiring_class @ cTYPE)) @ (cRings.ring_class @ cTYPE))))
(TRings.ring.left_diff_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ ((V2 @ V5) @ V6)) @ V7)) @ ((V2 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V7)))))))))))))))))))))
(TRings.ring_class.eq_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V1)) @ V4))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V3)) @ V1)) @ V2)) @ V4)))))))))))))
(TRings.ring_class.eq_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V1)) @ V4))) @ ((cHOL.eq @ V2) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V3) @ V0)) @ V1)) @ V4))))))))))))))
(TRings.ring_class.ring_axioms,(((((cRings.class.ring @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.times_class.times))
(TRings.semiring.distrib_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cRings.class.semiring @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ ((V0 @ V2) @ V3)) @ V4)) @ ((V0 @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))))))))
(TRings.semiring_0_class.intro,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cRings.mult_zero_class @ cTYPE)) @ ((c==> @ (cRings.semiring_class @ cTYPE)) @ (cRings.semiring_0_class @ cTYPE)))))
(TRings.semiring_0_class.super_3,((c==> @ (cRings.semiring_0_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))
(TRings.semiring_0_class.super_2,((c==> @ (cRings.semiring_0_class @ cTYPE)) @ (cRings.mult_zero_class @ cTYPE)))
(TRings.semiring_0_class.super_1,((c==> @ (cRings.semiring_0_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TRings.semiring_1_class.intro,((c==> @ (cGroups.monoid_mult_class @ cTYPE)) @ ((c==> @ (cRings.semiring_0_class @ cTYPE)) @ ((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cRings.semiring_1_class @ cTYPE)))))
(TRings.semiring_1_class.super_3,((c==> @ (cRings.semiring_1_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))
(TRings.semiring_1_class.super_2,((c==> @ (cRings.semiring_1_class @ cTYPE)) @ (cRings.semiring_0_class @ cTYPE)))
(TRings.semiring_1_class.super_1,((c==> @ (cRings.semiring_1_class @ cTYPE)) @ (cGroups.monoid_mult_class @ cTYPE)))
(TRings.zero_neq_one_class_def,((c== @ (cRings.zero_neq_one_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.one_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.zero_class @ cTYPE)) @ ((cRings.class.zero_neq_one @ cGroups.one_class.one) @ cGroups.zero_class.zero)))))
(TSMT.pattern.pattern_case_def,((c== @ cSMT.pattern.pattern_case) @ (^[V0]: (cSMT.pattern.pattern_rec @ V0))))
(TSMT.pattern.pattern_size_def,((c== @ cSMT.pattern.pattern_size) @ (cSMT.pattern.pattern_rec @ cNat.zero_nat_inst.zero_nat)))
(TSMT.pattern.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSMT.random_aux_pattern @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cSMT.pattern.Pattern) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))))))))
(TSet.disjoint_eq_subset_Compl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cOrderings.ord_class.less_eq @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TSet.equal_set_inst.equal_set,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TSet.minus_set_inst.minus_set,((c== @ cSet.minus_set_inst.minus_set) @ cSet.minus_set_inst.minus_set))
(TSet.ord_set_inst.less_eq_set,((c== @ cSet.ord_set_inst.less_eq_set) @ cSet.ord_set_inst.less_eq_set))
(TSet.singleton_insert_inj_eq',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cSet.insert @ V0) @ V1)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))
(TSet_Interval.Inf_greaterThan,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ (cSet_Interval.ord_class.greaterThan @ V0))) @ V0))))
(TSet_Interval.UN_UN_finite_eq,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V1)) @ (^[V2]: (V0 @ V2)))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1)))))))
(TSet_Interval.UN_atLeast_UNIV,((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V0]: (cSet_Interval.ord_class.atLeast @ V0)))) @ cOrderings.top_class.top))
(TSet_Interval.UN_le_add_shift,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet_Interval.ord_class.atMost @ V0)) @ (^[V3]: (V1 @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2))) @ (^[V3]: (V1 @ V3)))))))))))
(TSet_Interval.dvd.atLeast_def,(call @ (^[V0]: ((c== @ ((cSet_Interval.ord.atLeast @ cRings.dvd_class.dvd) @ V0)) @ (cSet.Collect @ (^[V1]: ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TSet_Interval.dvd.atLeast_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.atLeast @ cRings.dvd_class.dvd) @ V1))) @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))
(TSet_Interval.finite_lessThan,(call @ (^[V0]: (cFinite_Set.finite @ (cSet_Interval.ord_class.lessThan @ V0)))))
(TSet_Interval.greaterThan_Suc,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.greaterThan @ (cNat.Suc @ V0))) @ ((cGroups.minus_class.minus @ (cSet_Interval.ord_class.greaterThan @ V0)) @ ((cSet.insert @ (cNat.Suc @ V0)) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_un_one_8,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ (cSet_Interval.ord_class.atLeast @ V0))))))))
(TSet_Interval.ivl_disj_un_one_7,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ (cSet_Interval.ord_class.atLeast @ V0))))))))
(TSet_Interval.ivl_disj_un_one_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ (cSet_Interval.ord_class.greaterThan @ V0))))))))
(TSet_Interval.ivl_disj_un_one_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ (cSet_Interval.ord_class.greaterThan @ V0))))))))
(TSet_Interval.ivl_disj_un_one_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.ivl_disj_un_one_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.ivl_disj_un_one_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ (cSet_Interval.ord_class.lessThan @ V1))))))))
(TSet_Interval.ivl_disj_un_one_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ (cSet_Interval.ord_class.lessThan @ V1))))))))
(TSet_Interval.ivl_disj_un_two_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_two_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_two_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_two_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_two_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_two_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_two_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V2)))))))))))
(TSet_Interval.ivl_disj_un_two_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V2)))))))))))
(TSet_Interval.lessThan_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSet_Interval.ord_class.lessThan @ V0)) @ (cSet_Interval.ord_class.lessThan @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet_Interval.ord.atLeast_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord.atLeast @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TSet_Interval.ord.atLeast_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.atLeast @ V1) @ V2))) @ ((V1 @ V2) @ V0)))))))))
(TSet_Interval.setsum_head_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (V2 @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cNat.Suc @ V0)) @ V1))))))))))))
(TSet_Interval.setsum_ivl_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V6)) @ ((c==> @ ((cOrderings.ord_class.less @ V6) @ V3)) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V4) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V5) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V3)))))))))))))))))))
(TString.char.Abs_char_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.char.char_rep_set))) @ ((cHOL.eq @ (cString.Rep_char @ (cString.Abs_char @ V0))) @ V0)))))
(TString.char.Rep_char_inverse,(call @ (^[V0]: ((cHOL.eq @ (cString.Abs_char @ (cString.Rep_char @ V0))) @ V0))))
(TString.char.char_rec_set_def,((c== @ cString.char.char_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cString.char.Char @ V4) @ V5))) @ ((cHOL.eq @ V3) @ ((V0 @ V4) @ V5))))))))))))))
(TString.char.char_rep_set_def,((c== @ cString.char.char_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V1) @ ((cDatatype.Scons @ (cDatatype.Leaf @ V2)) @ (cDatatype.Leaf @ V3))))))))))))
(TString.literal.explode_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cString.explode @ V2))) @ V1)))) @ V1)))))))
(TString.nat_of_nibble_less_16,(call @ (^[V0]: ((cNat.ord_nat_inst.less_nat @ (cString.nat_of_nibble @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TString.nibble.nibble_rec_def,((c== @ cString.nibble.nibble_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (^[V6]: (^[V7]: (^[V8]: (^[V9]: (^[V10]: (^[V11]: (^[V12]: (^[V13]: (^[V14]: (^[V15]: (^[V16]: (cHOL.The @ (^[V17]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17))))))))))))))))))))))
(TString.nibble.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((((((((((((((((cString.nibble.nibble_case @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17) @ V0)) @ (((((((((((((((((cString.nibble.nibble_case @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17) @ V1))))))))))))))))))))))))))))))))))))))))
(TSum_Type.Inl_Rep_not_Inr_Rep,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSum_Type.Inl_Rep @ V0)) @ (cSum_Type.Inr_Rep @ V1))))))))
(TSum_Type.sum.Abs_sum_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cSum_Type.sum)) @ ((cHOL.eq @ (cSum_Type.Rep_sum @ (cSum_Type.Abs_sum @ V0))) @ V0)))))
(TSum_Type.sum.Rep_sum_inverse,(call @ (^[V0]: ((cHOL.eq @ (cSum_Type.Abs_sum @ (cSum_Type.Rep_sum @ V0))) @ V0))))
(TSum_Type.sum.sum_rec_set_def,((c== @ cSum_Type.sum.sum_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cSum_Type.Inl @ V5))) @ ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cSum_Type.Inr @ V5))) @ ((cHOL.eq @ V4) @ (V1 @ V5))))))))))))))
(TSum_Type.type_definition_sum,(((cTypedef.type_definition @ cSum_Type.Rep_sum) @ cSum_Type.Abs_sum) @ cSum_Type.sum))
(TTransfer.bi_unique_conversep,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_unique @ (cRelation.conversep @ V0))) @ (cTransfer.bi_unique @ V0)))))
(TTransfer.right_total_alt_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.implies)) @ cHOL.implies) @ cHOL.All) @ cHOL.All)))))
(TTransfer.transfer_forall_def,((c== @ cHOL.All) @ cHOL.All))
(TTransfer.transfer_implies_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((c==> @ V0) @ V1)) @ ((cHOL.implies @ V0) @ V1)))))))
(TTransitive_Closure.relpow_E2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ V2) @ V3))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V2) @ (cNat.Suc @ V6))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V5)) @ V3)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ ((cNat.compow @ V6) @ V3))) @ V4)))))))) @ V4))))))))))))))
(TTransitive_Closure.relpowp_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.compow @ cNat.one_nat_inst.one_nat) @ V0)) @ V0))))
(TTransitive_Closure.relpowp_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.compow @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.Suc @ V6))) @ ((c==> @ ((((cNat.compow @ V6) @ V1) @ V2) @ V5)) @ ((c==> @ ((V1 @ V5) @ V3)) @ V4)))))))) @ V4))))))))))))))
(TTransitive_Closure.rtranclpD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2))) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)))))))))))
(TTransitive_Closure.trancl_id,(call @ (^[V0]: ((c==> @ (cRelation.trans @ V0)) @ ((cHOL.eq @ (cTransitive_Closure.trancl @ V0)) @ V0)))))
(TTyperep.arity_typerep_itself,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_nibble,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_option,(cTyperep.typerep_class @ cTYPE))
(TTyperep.typerep_finite_1_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_finite_1_inst.typerep_finite_1 @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_finite_2_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_finite_2_inst.typerep_finite_2 @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_finite_3_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_finite_3_inst.typerep_finite_3 @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_finite_4_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_finite_4_inst.typerep_finite_4 @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))
(TTyperep.typerep_finite_5_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_finite_5_inst.typerep_finite_5 @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))
(TWellfounded.accp_induct_rule,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ V0) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ (V2 @ V4))))) @ (V2 @ V3)))))) @ (V2 @ V1))))))))))
(TWellfounded.max_ext.max_extI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cSet.Bex @ V1) @ (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V2))))))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.max_ext @ V2)))))))))))))
(TWellfounded.max_ext_additive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cWellfounded.max_ext @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (cWellfounded.max_ext @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cLattices.sup_class.sup @ V0) @ V3)) @ ((cLattices.sup_class.sup @ V1) @ V4))) @ (cWellfounded.max_ext @ V2)))))))))))))))
(TWellfounded.max_extp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cWellfounded.max_extp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ (cSet.Collect @ (^[V6]: (cOrderings.bot_class.bot @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V4)) @ ((cSet.Bex @ V5) @ (V0 @ V6)))))) @ ((V3 @ V4) @ V5)))))))))) @ ((V3 @ V1) @ V2))))))))))))
(TBig_Operators.linorder.Max_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.linorder.Max @ V0) @ ((cLattices.sup_class.sup @ V2) @ V3))) @ (((cOrderings.ord.max @ V0) @ ((cBig_Operators.linorder.Max @ V0) @ V2)) @ ((cBig_Operators.linorder.Max @ V0) @ V3)))))))))))))))))
(TBig_Operators.linorder.Max_ge,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((V0 @ V3) @ ((cBig_Operators.linorder.Max @ V0) @ V2))))))))))))))
(TBig_Operators.linorder.Max_in,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cSet.member @ ((cBig_Operators.linorder.Max @ V0) @ V2)) @ V2)))))))))))
(TBig_Operators.linorder.Min_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.linorder.Min @ V0) @ ((cLattices.sup_class.sup @ V2) @ V3))) @ (((cOrderings.ord.min @ V0) @ ((cBig_Operators.linorder.Min @ V0) @ V2)) @ ((cBig_Operators.linorder.Min @ V0) @ V3)))))))))))))))))
(TBig_Operators.linorder.Min_in,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cSet.member @ ((cBig_Operators.linorder.Min @ V0) @ V2)) @ V2)))))))))))
(TBig_Operators.linorder.Min_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((V0 @ ((cBig_Operators.linorder.Min @ V0) @ V2)) @ V3)))))))))))))
(TBig_Operators.linorder.max_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cOrderings.ord.max @ V0) @ V2) @ (((cOrderings.ord.max @ V0) @ V3) @ V4))) @ (((cOrderings.ord.max @ V0) @ V3) @ (((cOrderings.ord.max @ V0) @ V2) @ V4)))))))))))))))
(TBig_Operators.linorder.max_ac_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cOrderings.ord.max @ V0) @ V2) @ V3)) @ (((cOrderings.ord.max @ V0) @ V3) @ V2))))))))))))
(TBig_Operators.linorder.max_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cOrderings.ord.max @ V0) @ (((cOrderings.ord.max @ V0) @ V2) @ V3)) @ V4)) @ (((cOrderings.ord.max @ V0) @ V2) @ (((cOrderings.ord.max @ V0) @ V3) @ V4)))))))))))))))
(TBig_Operators.linorder.min_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cOrderings.ord.min @ V0) @ V2) @ (((cOrderings.ord.min @ V0) @ V3) @ V4))) @ (((cOrderings.ord.min @ V0) @ V3) @ (((cOrderings.ord.min @ V0) @ V2) @ V4)))))))))))))))
(TBig_Operators.linorder.min_ac_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cOrderings.ord.min @ V0) @ V2) @ V3)) @ (((cOrderings.ord.min @ V0) @ V3) @ V2))))))))))))
(TBig_Operators.linorder.min_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (((cOrderings.ord.min @ V0) @ (((cOrderings.ord.min @ V0) @ V2) @ V3)) @ V4)) @ (((cOrderings.ord.min @ V0) @ V2) @ (((cOrderings.ord.min @ V0) @ V3) @ V4)))))))))))))))
(TBig_Operators.setprod_dividef,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cFields.inverse_class.divide @ (V1 @ V3)) @ (V2 @ V3)))) @ V0)) @ ((cFields.inverse_class.divide @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)))))))))))
(TBig_Operators.setprod_pos_nat,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (V1 @ V2))))) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)))))))))
(TBig_Operators.setprod_reindex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cSet.image @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ ((cFun.comp @ V2) @ V0)) @ V1))))))))))
(TBig_Operators.setsum_constant,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: V0)) @ V1)) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ (cFinite_Set.card @ V1))) @ V0)))))))
(TBig_Operators.setsum_diff_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cNat.minus_nat_inst.minus_nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.setsum_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cNat.zero_nat_inst.zero_nat))))))))))
(TBig_Operators.setsum_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ cNat.one_nat_inst.one_nat)) @ ((cSet.Bex @ V0) @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ cNat.one_nat_inst.one_nat)) @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ (V1 @ V3)) @ cNat.zero_nat_inst.zero_nat))))))))))))))
(TBig_Operators.setsum_infinite,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ cGroups.zero_class.zero)))))))
(TBig_Operators.setsum_nonneg_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V1 @ V3)))))) @ ((c==> @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V1 @ V3))) @ V0)) @ cGroups.zero_class.zero)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cHOL.eq @ (V1 @ V2)) @ cGroups.zero_class.zero))))))))))))
(TCode_Evaluation.term.Rep_term,(call @ (^[V0]: ((cSet.member @ (cCode_Evaluation.Rep_term @ V0)) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set)))))
(TCode_Evaluation.term.eq.simps,((c== @ ((cHOL.equal_class.equal @ cCode_Evaluation.term.dummy_term) @ cCode_Evaluation.term.dummy_term)) @ cHOL.True))
(TCode_Evaluation.term.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.eq @ V0) @ cCode_Evaluation.term.dummy_term))))
(TCode_Numeral.Quotient_integer,((((cLifting.Quotient @ cHOL.eq) @ cCode_Numeral.integer_of_int) @ cCode_Numeral.int_of_integer) @ cCode_Numeral.cr_integer))
(TCode_Numeral.Quotient_natural,((((cLifting.Quotient @ cHOL.eq) @ cCode_Numeral.natural_of_nat) @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.cr_natural))
(TCode_Numeral.abs_integer_code,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.abs_integer_inst.abs_integer @ V0)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ V0)) @ V0)))))
(TCode_Numeral.div_integer_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.div_integer_inst.div_integer @ V0) @ V1)) @ (cProduct_Type.fst @ ((cCode_Numeral.divmod_integer @ V0) @ V1))))))))
(TCode_Numeral.integer.bi_total,(cTransfer.bi_total @ cCode_Numeral.pcr_integer))
(TCode_Numeral.less_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cInt.ord_int_inst.less_int) @ cInt.ord_int_inst.less_int))
(TCode_Numeral.less_integer_def,((c== @ cCode_Numeral.ord_integer_inst.less_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cFun.id)) @ cInt.ord_int_inst.less_int)))
(TCode_Numeral.less_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cNat.ord_nat_inst.less_nat) @ cNat.ord_nat_inst.less_nat))
(TCode_Numeral.less_natural_def,((c== @ cCode_Numeral.ord_natural_inst.less_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cFun.id)) @ cNat.ord_nat_inst.less_nat)))
(TCode_Numeral.mod_integer_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.div_integer_inst.mod_integer @ V0) @ V1)) @ (cProduct_Type.snd @ ((cCode_Numeral.divmod_integer @ V0) @ V1))))))))
(TCode_Numeral.natural.bi_total,(cTransfer.bi_total @ cCode_Numeral.pcr_natural))
(TCode_Numeral.natural.distinct_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cCode_Numeral.Suc @ V0)) @ cCode_Numeral.zero_natural_inst.zero_natural)))))
(TCode_Numeral.natural.distinct_1,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cCode_Numeral.zero_natural_inst.zero_natural) @ (cCode_Numeral.Suc @ V0))))))
(TCode_Numeral.natural.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cCode_Numeral.Suc @ V1))))))))
(TCode_Numeral.one_integer_code,((cHOL.eq @ cCode_Numeral.one_integer_inst.one_integer) @ (cCode_Numeral.Pos @ cNum.num.One)))
(TCode_Numeral.plus_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cInt.plus_int_inst.plus_int) @ cInt.plus_int_inst.plus_int))
(TCode_Numeral.plus_integer_def,((c== @ cCode_Numeral.plus_integer_inst.plus_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int)) @ cInt.plus_int_inst.plus_int)))
(TCode_Numeral.plus_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cNat.plus_nat_inst.plus_nat) @ cNat.plus_nat_inst.plus_nat))
(TCode_Numeral.plus_natural_def,((c== @ cCode_Numeral.plus_natural_inst.plus_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.natural_of_nat)) @ cNat.plus_nat_inst.plus_nat)))
(TCode_Numeral.sgn_integer_code,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.sgn_integer_inst.sgn_integer @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cCode_Numeral.zero_integer_inst.zero_integer) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ cCode_Numeral.one_integer_inst.one_integer)) @ cCode_Numeral.one_integer_inst.one_integer))))))
(TCode_Numeral.zero_integer.rsp,((cHOL.eq @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int))
(TCode_Numeral.zero_integer_def,((c== @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.integer_of_int @ cInt.zero_int_inst.zero_int)))
(TCode_Numeral.zero_natural.rsp,((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat))
(TCode_Numeral.zero_natural_def,((c== @ cCode_Numeral.zero_natural_inst.zero_natural) @ (cCode_Numeral.natural_of_nat @ cNat.zero_nat_inst.zero_nat)))
(TComplete_Lattices.INF_bool_eq,((cHOL.eq @ cComplete_Lattices.complete_lattice_class.INFI) @ cSet.Ball))
(TComplete_Lattices.INT_bool_eq,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1)))) @ ((cLattices.inf_class.inf @ (V0 @ cHOL.True)) @ (V0 @ cHOL.False))))))
(TComplete_Lattices.Inf_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (^[V1]: ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V2 @ V1))))))))
(TComplete_Lattices.Inf_set_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cSet.Collect @ (^[V1]: (cComplete_Lattices.Inf_bool_inst.Inf_bool @ ((cSet.image @ (^[V2]: ((cSet.member @ V1) @ V2))) @ V0))))))))
(TComplete_Lattices.Inter_empty,((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top))
(TComplete_Lattices.Inter_lower,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V1)) @ V0)))))))
(TComplete_Lattices.SUP_bool_eq,((cHOL.eq @ cComplete_Lattices.complete_lattice_class.SUPR) @ cSet.Bex))
(TComplete_Lattices.Sup_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V1]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V2 @ V1))))))))
(TComplete_Lattices.Sup_set_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cSet.Collect @ (^[V1]: (cComplete_Lattices.Sup_bool_inst.Sup_bool @ ((cSet.image @ (^[V2]: ((cSet.member @ V1) @ V2))) @ V0))))))))
(TComplete_Lattices.UN_constant,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: V1))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ V1)))))))
(TComplete_Lattices.Union_empty,((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TComplete_Lattices.Union_least,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)))))))
(TComplete_Lattices.Union_upper,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.image_Union,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: ((cSet.image @ V0) @ V2)))))))))
(TComplete_Lattices.image_eq_UN,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: ((cSet.insert @ (V0 @ V2)) @ cOrderings.bot_class.bot)))))))))
(TComplete_Lattices.member_bind,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet.bind @ V1) @ V2))) @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V2))))))))))
(TComplete_Partial_Order.chainD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cHOL.disj @ ((V0 @ V2) @ V3)) @ ((V0 @ V3) @ V2))))))))))))))
(TComplete_Partial_Order.chainE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((c==> @ ((c==> @ ((V0 @ V2) @ V3)) @ V4)) @ ((c==> @ ((c==> @ ((V0 @ V3) @ V2)) @ V4)) @ V4))))))))))))))))
(TComplete_Partial_Order.chainI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.disj @ ((V1 @ V2) @ V3)) @ ((V1 @ V3) @ V2))))))))) @ ((cComplete_Partial_Order.chain @ V1) @ V0)))))))
(TDatatype.ndepth_Push_Node_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.implies @ ((cHOL.eq @ (((cNat.nat.nat_case @ (cSum_Type.Inr @ (cNat.Suc @ V0))) @ V1) @ V2)) @ (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat))) @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.Suc @ (cOrderings.ord_class.Least @ (^[V3]: ((cHOL.eq @ (V1 @ V3)) @ (cSum_Type.Inr @ cNat.zero_nat_inst.zero_nat)))))) @ V2)))))))))
(TDatatype.node.Abs_Node_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ cDatatype.Node)) @ (V0 @ (cDatatype.Abs_Node @ V2)))))) @ (V0 @ V1)))))))
(TDatatype.node.Abs_Node_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cDatatype.Node)) @ ((c==> @ ((cSet.member @ V1) @ cDatatype.Node)) @ ((cHOL.eq @ ((cHOL.eq @ (cDatatype.Abs_Node @ V0)) @ (cDatatype.Abs_Node @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TDatatype.node.Rep_Node_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cDatatype.Node)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Rep_Node @ V2))))) @ (V1 @ V0))))))))
(TDatatype.node.Rep_Node_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cDatatype.Rep_Node @ V0)) @ (cDatatype.Rep_Node @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TDatatype.type_definition_node,(((cTypedef.type_definition @ cDatatype.Rep_Node) @ cDatatype.Abs_Node) @ cDatatype.Node))
(TDivides.class.ring_div.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cRings.class.comm_ring_1 @ V0) @ V5) @ V3) @ V4) @ V6) @ V7)))))))))))))))))))
(TDivides.class.ring_div.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))))))
(TDivides.div_pos_neg_1_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ cInt.one_int_inst.one_int) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cProduct_Type.fst @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.negDivAlg @ (cInt.uminus_int_inst.uminus_int @ cInt.one_int_inst.one_int)) @ (cInt.uminus_int_inst.uminus_int @ (cNum.neg_numeral_class.neg_numeral @ V0)))))))))
(TDivides.div_pos_pos_1_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0))) @ (cProduct_Type.fst @ ((cDivides.posDivAlg @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0)))))))
(TDivides.divmod_int_divmod_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.divmod_int @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cProduct_Type.apsnd @ (cInt.times_int_inst.times_int @ (cInt.sgn_int_inst.sgn_int @ V1))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0))) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.divmod_abs @ V0) @ V1)) @ ((cHOL.Let @ ((cDivides.divmod_abs @ V0) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V2)) @ cInt.zero_int_inst.zero_int)) @ ((cProduct_Type.Pair @ ((cInt.minus_int_inst.minus_int @ (cInt.uminus_int_inst.uminus_int @ V2)) @ cInt.one_int_inst.one_int)) @ ((cInt.minus_int_inst.minus_int @ (cInt.abs_int_inst.abs_int @ V1)) @ V3)))))))))))))))))
(TDivides.divmod_nat_rel_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ V2)) @ ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TDivides.dvd_neg_numeral_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ (cNum.numeral_class.numeral @ V1))))))))
(TDivides.mod_pos_neg_1_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ cInt.one_int_inst.one_int) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cProduct_Type.snd @ ((cProduct_Type.apsnd @ cInt.uminus_int_inst.uminus_int) @ ((cDivides.negDivAlg @ (cInt.uminus_int_inst.uminus_int @ cInt.one_int_inst.one_int)) @ (cInt.uminus_int_inst.uminus_int @ (cNum.neg_numeral_class.neg_numeral @ V0)))))))))
(TDivides.mod_pos_pos_1_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0))) @ (cProduct_Type.snd @ ((cDivides.posDivAlg @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0)))))))
(TDivides.negDivAlg.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V1) @ V2))) @ ((cInt.ord_int_inst.less_eq_int @ V2) @ cInt.zero_int_inst.zero_int)))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V2))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cDivides.negDivAlg_rel) @ V1))))))))
(TDivides.negDivAlg_eqn_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.negDivAlg @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))) @ ((cDivides.adjust @ (cNum.numeral_class.numeral @ V1)) @ ((cDivides.negDivAlg @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNum.numeral_class.numeral @ V1)))))))))))
(TDivides.negDivAlg_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.negDivAlg_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.negDivAlg_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ V2)))))))))) @ V2)))))))))
(TDivides.negDivAlg_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.negDivAlg_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cDivides.adjust @ V4) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.negDivAlg_graph @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))))))))))))))))))
(TDivides.negDivAlg_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.negDivAlg_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V3) @ V4))) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.posDivAlg.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ V2) @ cInt.zero_int_inst.zero_int)))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V2))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cDivides.posDivAlg_rel) @ V1))))))))
(TDivides.posDivAlg_eqn_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.posDivAlg @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ (cNum.numeral_class.numeral @ V0))) @ ((cDivides.adjust @ (cNum.numeral_class.numeral @ V1)) @ ((cDivides.posDivAlg @ (cNum.numeral_class.numeral @ V0)) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNum.numeral_class.numeral @ V1)))))))))))
(TDivides.posDivAlg_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.posDivAlg_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.posDivAlg_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ V2)))))))))) @ V2)))))))))
(TDivides.posDivAlg_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.posDivAlg_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V3)) @ ((cDivides.adjust @ V4) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.posDivAlg_graph @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4)))))))))))))))))))
(TDivides.posDivAlg_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.posDivAlg_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.ring_div.mod_minus_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ (V7 @ V8)) @ V9)) @ ((V2 @ (V7 @ ((V2 @ V8) @ V9))) @ V9))))))))))))))))))))))))
(TDivides.semiring_div.div_by_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ V6) @ V4)) @ V4)))))))))))))))))
(TDivides.semiring_div.div_by_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ V6) @ V5)) @ V6)))))))))))))))))
(TDivides.semiring_div.div_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ V6) @ V6)) @ V5))))))))))))))))))
(TDivides.semiring_div.mod_by_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ V6) @ V4)) @ V6)))))))))))))))))
(TDivides.semiring_div.mod_by_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ V6) @ V5)) @ V4)))))))))))))))))
(TDivides.semiring_div.mod_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ V6) @ V6)) @ V4)))))))))))))))))
(TDivides.unique_quotient_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V2)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V3)) @ V4))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V2) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V4) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V3))))))))))))))))
(TDivides.zmod_zminus1_not_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cInt.uminus_int_inst.uminus_int @ V0)) @ V1)) @ cInt.zero_int_inst.zero_int))) @ (cHOL.Not @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.zmod_zminus2_not_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ (cInt.uminus_int_inst.uminus_int @ V1))) @ cInt.zero_int_inst.zero_int))) @ (cHOL.Not @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ cInt.zero_int_inst.zero_int))))))))
(TEnum.enum_bool_inst.enum_bool,((c== @ cEnum.enum_bool_inst.enum_bool) @ cEnum.enum_bool_inst.enum_bool))
(TEnum.enum_class.enum_all_UNIV,(call @ (^[V0]: ((cHOL.eq @ (cEnum.enum_class.enum_all @ V0)) @ ((cSet.Ball @ cOrderings.top_class.top) @ V0)))))
(TEnum.enum_class.enum_distinct,(cList.distinct @ cEnum.enum_class.enum))
(TEnum.enum_prod_inst.enum_prod,((c== @ cEnum.enum_prod_inst.enum_prod) @ cEnum.enum_prod_inst.enum_prod))
(TEnum.enum_unit_inst.enum_unit,((c== @ cEnum.enum_unit_inst.enum_unit) @ cEnum.enum_unit_inst.enum_unit))
(TEnum.equal_fun_inst.equal_fun,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TEnum.type_definition_finite_1,(((cTypedef.type_definition @ cEnum.Rep_finite_1) @ cEnum.Abs_finite_1) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set)))
(TEnum.type_definition_finite_2,(((cTypedef.type_definition @ cEnum.Rep_finite_2) @ cEnum.Abs_finite_2) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set)))
(TEnum.type_definition_finite_3,(((cTypedef.type_definition @ cEnum.Rep_finite_3) @ cEnum.Abs_finite_3) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set)))
(TEnum.type_definition_finite_4,(((cTypedef.type_definition @ cEnum.Rep_finite_4) @ cEnum.Abs_finite_4) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set)))
(TEnum.type_definition_finite_5,(((cTypedef.type_definition @ cEnum.Rep_finite_5) @ cEnum.Abs_finite_5) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set)))
(TEquiv_Relations.congruent_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEquiv_Relations.congruent @ V0) @ V1)) @ ((cSet.Ball @ V0) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.eq @ (V1 @ V2)) @ (V1 @ V3))))))))))))
(TEquiv_Relations.equiv_comp_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((cHOL.eq @ ((cRelation.relcomp @ (cRelation.converse @ V1)) @ V1)) @ V1)))))))
(TEquiv_Relations.equivp_transp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V0 @ V1) @ V3)))))))))))))
(TEquiv_Relations.quotient_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ ((cSet.member @ V3) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ V3)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))))))))))
(TExtraction.arity_type_sumbool,(cHOL.type_class @ cTYPE))
(TFields.class.field_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cFields.class.field_axioms @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ V4))) @ ((cHOL.eq @ ((V2 @ (V0 @ V5)) @ V5)) @ V3))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.eq @ ((V1 @ V5) @ V6)) @ ((V2 @ V5) @ (V0 @ V6))))))))))))))))))))
(TFields.division_ring.divide_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ V2)) @ V8)))))))))))))))))))))
(TFields.field_class.frac_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V2) @ V0)) @ ((cFields.inverse_class.divide @ V3) @ V1))) @ ((cHOL.eq @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V3) @ V0))))))))))))))
(TFinite_Set.bij_betw_same_card,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V2))))))))))
(TFinite_Set.card.insert_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.insert @ V1) @ V0))) @ (cNat.Suc @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))
(TFinite_Set.class.finite.intro,((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ (cFinite_Set.class.finite @ cTYPE)))
(TFinite_Set.eq_card_imp_inj_on,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.image @ V1) @ V0))) @ (cFinite_Set.card @ V0))) @ ((cFun.inj_on @ V1) @ V0))))))))
(TFinite_Set.finite.finite_UNIV,((c==> @ (cFinite_Set.class.finite @ cTYPE)) @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TFinite_Set.finite.finite_code,(call @ (^[V0]: ((c==> @ (cFinite_Set.class.finite @ cTYPE)) @ ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ cHOL.True)))))
(TFinite_Set.finite_Collect_bex,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V0) @ (^[V3]: ((V1 @ V2) @ V3))))))) @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ (cSet.Collect @ (^[V3]: ((V1 @ V3) @ V2)))))))))))))
(TFinite_Set.finite_Collect_not,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ (cSet.Collect @ (^[V1]: (V0 @ V1))))) @ ((cHOL.eq @ (cFinite_Set.finite @ (cSet.Collect @ (^[V1]: (cHOL.Not @ (V0 @ V1)))))) @ (cFinite_Set.finite @ cOrderings.top_class.top))))))
(TFinite_Set.finite_Diff_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cFinite_Set.finite @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ V2)))) @ (cFinite_Set.finite @ ((cGroups.minus_class.minus @ V0) @ V2))))))))))
(TFinite_Set.finite_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ ((c==> @ (cFinite_Set.class.finite @ cTYPE)) @ (cFinite_Set.finite_class @ cTYPE))))
(TFinite_Set.finite_class.super,((c==> @ (cFinite_Set.finite_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TFinite_Set.finite_option_UNIV,((cHOL.eq @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TFinite_Set.finite_vimage_IntI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cFun.inj_on @ V1) @ V2)) @ (cFinite_Set.finite @ ((cLattices.inf_class.inf @ ((cSet.vimage @ V1) @ V0)) @ V2)))))))))))
(TFinite_Set.fold_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V4 @ cOrderings.bot_class.bot) @ V1)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cSet.member @ V5) @ V6))) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V6) @ V7)) @ ((c==> @ ((V4 @ V6) @ V7)) @ ((V4 @ ((cSet.insert @ V5) @ V6)) @ ((V0 @ V5) @ V7)))))))))))) @ ((V4 @ V2) @ V3)))))))))))))))
(TFinite_Set.fold_graph.insertI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ V1))) @ ((c==> @ ((((cFinite_Set.fold_graph @ V2) @ V3) @ V1) @ V4)) @ ((((cFinite_Set.fold_graph @ V2) @ V3) @ ((cSet.insert @ V0) @ V1)) @ ((V2 @ V0) @ V4)))))))))))))))
(TFinite_Set.folding_idem.intro,(call @ (^[V0]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((c==> @ (cFinite_Set.folding_idem_axioms @ V0)) @ (cFinite_Set.folding_idem @ V0))))))
(TFinite_Set.inj_on_iff_eq_card,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cFun.inj_on @ V1) @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.image @ V1) @ V0))) @ (cFinite_Set.card @ V0)))))))))
(TGroebner_Basis.weak_dnf_simps_38,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ ((cHOL.disj @ V0) @ V1))) @ ((cHOL.disj @ V0) @ V1)))))))
(TGroebner_Basis.weak_dnf_simps_37,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V0)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_36,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ cHOL.False) @ V0)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_35,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ cHOL.False)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_34,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ cHOL.True) @ V0)) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_33,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ cHOL.True)) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_32,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ (cHOL.Not @ V0)) @ V0)) @ cHOL.False))))
(TGroebner_Basis.weak_dnf_simps_31,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ (cHOL.Not @ V0))) @ cHOL.False))))
(TGroebner_Basis.weak_dnf_simps_30,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.conj @ V0) @ V1))) @ ((cHOL.conj @ V0) @ V1)))))))
(TGroebner_Basis.weak_dnf_simps_29,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V0)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_28,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ cHOL.False) @ V0)) @ cHOL.False))))
(TGroebner_Basis.weak_dnf_simps_27,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ cHOL.False)) @ cHOL.False))))
(TGroebner_Basis.weak_dnf_simps_26,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ cHOL.True) @ V0)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_25,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.conj @ V0) @ cHOL.True)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_24,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ (cHOL.Not @ V0))) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.weak_dnf_simps_23,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.weak_dnf_simps_22,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ V0)) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_21,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ V0) @ cHOL.True)) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_20,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ cHOL.False) @ V0)) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_19,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.implies @ cHOL.True) @ V0)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_18,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.False)) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.weak_dnf_simps_17,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cHOL.False) @ V0)) @ (cHOL.Not @ V0)))))
(TGroebner_Basis.weak_dnf_simps_16,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ cHOL.True)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_15,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cHOL.True) @ V0)) @ V0))))
(TGroebner_Basis.weak_dnf_simps_14,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ V0) @ (cHOL.Not @ V0))))))
(TGroebner_Basis.weak_dnf_simps_13,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cHOL.Not @ V0)) @ V0)))))
(TGroebner_Basis.weak_dnf_simps_12,((cHOL.eq @ (cHOL.Not @ cHOL.False)) @ cHOL.True))
(TGroebner_Basis.weak_dnf_simps_11,((cHOL.eq @ (cHOL.Not @ cHOL.True)) @ cHOL.False))
(TGroebner_Basis.weak_dnf_simps_10,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V0)) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_9,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ (cHOL.Not @ V0)) @ V0)) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_8,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.disj @ V0) @ (cHOL.Not @ V0))) @ cHOL.True))))
(TGroebner_Basis.weak_dnf_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.eq @ V0) @ (cHOL.Not @ V1))))))))
(TGroebner_Basis.weak_dnf_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cHOL.Not @ V0)) @ (cHOL.Not @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TGroebner_Basis.weak_dnf_simps_5,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cHOL.Not @ V0))) @ V0))))
(TGroebner_Basis.weak_dnf_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.disj @ V0) @ V1)) @ ((cHOL.disj @ V1) @ V0)))))))
(TGroebner_Basis.weak_dnf_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V1) @ V0)))))))
(TGroebner_Basis.weak_dnf_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ ((cHOL.disj @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V2)) @ ((cHOL.conj @ V1) @ V2))))))))))
(TGroebner_Basis.weak_dnf_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.conj @ V0) @ ((cHOL.disj @ V1) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ V0) @ V1)) @ ((cHOL.conj @ V0) @ V2))))))))))
(TGroups.ab_group_add_class_def,((c== @ (cGroups.ab_group_add_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.comm_monoid_add_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE))) @ ((cPure.conjunction @ (cGroups.uminus_class @ cTYPE)) @ ((((cGroups.class.ab_group_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus)))))
(TGroups.abel_semigroup.commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cGroups.abel_semigroup @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.class.ab_group_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((((cGroups.class.ab_group_add_axioms @ V0) @ V1) @ V2) @ V3))))))))))))
(TGroups.class.group_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((((cGroups.class.group_add_axioms @ V0) @ V1) @ V2) @ V3)))))))))))
(TGroups.class.group_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.monoid_add @ V1) @ V2)))))))))))
(TGroups.class.monoid_add.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.class.semigroup_add @ V0)) @ ((c==> @ ((cGroups.class.monoid_add_axioms @ V0) @ V1)) @ ((cGroups.class.monoid_add @ V0) @ V1))))))))
(TGroups.comm_monoid_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.comm_monoid_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))))))))
(TGroups.group_add.add_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V4) @ V5)) @ V2)) @ ((cHOL.eq @ V5) @ (V3 @ V4)))))))))))))))))
(TGroups.group_add.diff_0_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V2)) @ V4)))))))))))))
(TGroups.group_add.minus_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ ((V1 @ V4) @ V5)) @ V2)) @ ((cHOL.eq @ (V3 @ V4)) @ V5))))))))))))))))
(TGroups.group_add_class.axioms,((((cGroups.class.group_add_axioms @ cGroups.minus_class.minus) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus))
(TGroups.group_add_class.diff_0,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.zero_class.zero) @ V0)) @ (cGroups.uminus_class.uminus @ V0)))))
(TGroups.monoid_add.add_0_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))))))))
(TGroups.monoid_add_class.intro,((c==> @ (cGroups.semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.zero_class @ cTYPE)) @ ((c==> @ ((cGroups.class.monoid_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)) @ (cGroups.monoid_add_class @ cTYPE)))))
(TGroups.monoid_add_class.super_2,((c==> @ (cGroups.monoid_add_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TGroups.monoid_add_class.super_1,((c==> @ (cGroups.monoid_add_class @ cTYPE)) @ (cGroups.semigroup_add_class @ cTYPE)))
(THilbert_Choice.GreatestM_natI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V4)) @ V3))))) @ (V0 @ ((cHilbert_Choice.GreatestM @ V2) @ V0)))))))))))))
(THilbert_Choice.inj_imp_inv_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (cHOL.All @ (^[V2]: ((cHOL.eq @ (V0 @ (V1 @ V2))) @ V2)))) @ ((cHOL.eq @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ V1))))))))
(THilbert_Choice.inv_image_comp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ ((cSet.image @ V0) @ V1))) @ V1)))))))
(THilbert_Choice.o_inv_o_cancel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0))) @ V0)) @ V1)))))))
(THilbert_Choice.some1_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex1 @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (V0 @ V1)) @ ((cHOL.eq @ (cHilbert_Choice.Eps @ (^[V2]: (V0 @ V2)))) @ V1))))))))
(TInductive.weak_coinduct_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V2) @ V1)) @ (V3 @ ((cSet.image @ V2) @ V1)))) @ ((cSet.member @ (V2 @ V0)) @ (cInductive.complete_lattice_class.gfp @ V3)))))))))))))
(TInt.arity_distrib_lattice_int,(cLattices.distrib_lattice_class @ cTYPE))
(TInt.arity_linordered_idom_int,(cRings.linordered_idom_class @ cTYPE))
(TInt.divide_less_0_iff_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)))))))))
(TInt.inverse_eq_divide_numeral,(call @ (^[V0]: ((cHOL.eq @ (cFields.inverse_class.inverse @ (cNum.numeral_class.numeral @ V0))) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))))))
(TInt.left_diff_distrib_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (cNum.numeral_class.numeral @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ V2))) @ ((cGroups.times_class.times @ V1) @ (cNum.numeral_class.numeral @ V2)))))))))))
(TInt.ring_1.of_int_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ (cNum.neg_numeral_class.neg_numeral @ V6))) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6))))))))))))))))))
(TInt.ring_1_class.of_int_minus,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cInt.uminus_int_inst.uminus_int @ V0))) @ (cGroups.uminus_class.uminus @ (cInt.ring_1_class.of_int @ V0))))))
(TInt.ring_1_class.of_int_power,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ (cInt.ring_1_class.of_int @ V0)) @ V1)))))))
(TInt.ring_char_0.of_int_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V7))) @ ((cHOL.eq @ V6) @ V7))))))))))))))))))))
(TLattices.class.lattice.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ (((cLattices.class.semilattice_sup @ V3) @ V1) @ V2)))))))))))
(TLattices.class.lattice.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)))))))))))
(TLattices.inf_fun_inst.inf_fun,((c== @ cLattices.inf_fun_inst.inf_fun) @ cLattices.inf_fun_inst.inf_fun))
(TLattices.lattice.distrib_imp1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((cHOL.eq @ ((V0 @ V7) @ ((V3 @ V8) @ V9))) @ ((V3 @ ((V0 @ V7) @ V8)) @ ((V0 @ V7) @ V9)))))))))) @ ((cHOL.eq @ ((V3 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V3 @ V4) @ V5)) @ ((V3 @ V4) @ V6))))))))))))))))))))
(TLattices.lattice.distrib_imp2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((cHOL.eq @ ((V3 @ V7) @ ((V0 @ V8) @ V9))) @ ((V0 @ ((V3 @ V7) @ V8)) @ ((V3 @ V7) @ V9)))))))))) @ ((cHOL.eq @ ((V0 @ V4) @ ((V3 @ V5) @ V6))) @ ((V3 @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TLattices.lattice.dual_lattice,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((((cLattices.class.lattice @ V3) @ (^[V4]: (^[V5]: ((V1 @ V5) @ V4)))) @ (^[V4]: (^[V5]: ((V2 @ V5) @ V4)))) @ V0)))))))))))
(TLattices.sup_fun_inst.sup_fun,((c== @ cLattices.sup_fun_inst.sup_fun) @ cLattices.sup_fun_inst.sup_fun))
(TLazy_Sequence.small_lazy'_def,((c== @ cLazy_Sequence.small_lazy') @ (^[V0]: (^[V1]: (cLazy_Sequence.small_lazy'_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TLifting.Quotient_right_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ (cTransfer.right_unique @ V3)))))))))))
(TLifting.bi_unique_left_unique,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ (cLifting.left_unique @ V0)))))
(TLifting.left_unique_conversep,(call @ (^[V0]: ((cHOL.eq @ (cLifting.left_unique @ (cRelation.conversep @ V0))) @ (cTransfer.right_unique @ V0)))))
(TLifting.right_total_conversep,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.right_total @ (cRelation.conversep @ V0))) @ (cLifting.left_total @ V0)))))
(TLifting_Option.Domainp_option,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((cHOL.eq @ (cRelation.Domainp @ (cLifting_Option.option_rel @ V0))) @ ((cOption.option.option_case @ cHOL.True) @ V1))))))))
(TLifting_Option.option_rel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLifting_Option.option_rel @ V0) @ V1) @ V2)) @ ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (((cOption.option.option_case @ (((cOption.option.option_case @ cHOL.True) @ (^[V5]: cHOL.False)) @ V4)) @ (^[V5]: (((cOption.option.option_case @ cHOL.False) @ (^[V6]: ((V0 @ V5) @ V6))) @ V4))) @ V3)))) @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TLifting_Product.Pair_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ ((cLifting_Product.prod_rel @ V0) @ V1))) @ cProduct_Type.Pair) @ cProduct_Type.Pair))))))
(TLifting_Product.Quotient_prod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cLifting.Quotient @ V4) @ V5) @ V6) @ V7)) @ ((((cLifting.Quotient @ ((cLifting_Product.prod_rel @ V0) @ V4)) @ ((cProduct_Type.map_pair @ V1) @ V5)) @ ((cProduct_Type.map_pair @ V2) @ V6)) @ ((cLifting_Product.prod_rel @ V3) @ V7)))))))))))))))))))))
(TLifting_Product.prod_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLifting_Product.prod_pred @ V0) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V3)))))))))))
(TLifting_Product.prod_rel_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLifting_Product.prod_rel @ V0) @ V2)) @ ((cLifting_Product.prod_rel @ V1) @ V3)))))))))))))
(TLifting_Set.bi_unique_set_rel,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ (cTransfer.bi_unique @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Set.set_rel_conversep,(call @ (^[V0]: ((cHOL.eq @ (cLifting_Set.set_rel @ (cRelation.conversep @ V0))) @ (cRelation.conversep @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Set.setsum_parametric,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ cHOL.eq)) @ cBig_Operators.comm_monoid_add_class.setsum) @ cBig_Operators.comm_monoid_add_class.setsum)))))
(TLifting_Set.vimage_parametric,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((c==> @ (cTransfer.bi_unique @ V1)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V1)) @ (cLifting_Set.set_rel @ V0))) @ cSet.vimage) @ cSet.vimage))))))))
(TLifting_Sum.bi_unique_sum_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.bi_unique @ V1)) @ (cTransfer.bi_unique @ ((cLifting_Sum.sum_rel @ V0) @ V1)))))))))
(TLifting_Sum.sum_case_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V2) @ V1)) @ ((cTransfer.fun_rel @ ((cLifting_Sum.sum_rel @ V0) @ V2)) @ V1))) @ cSum_Type.sum.sum_case) @ cSum_Type.sum.sum_case))))))))
(TLimited_Sequence.map_seq_code,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cLimited_Sequence.map_seq @ V0) @ V1) @ V2) @ V3)) @ (((cOption.option.option_case @ (cOption.option.Some @ cLazy_Sequence.empty)) @ (^[V4]: ((cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (((cOption.option.option_case @ cOption.option.None) @ (^[V7]: (((cOption.option.option_case @ cOption.option.None) @ (^[V8]: (cOption.option.Some @ ((cLazy_Sequence.append @ V7) @ V8)))) @ ((((cLimited_Sequence.map_seq @ V0) @ V6) @ V2) @ V3)))) @ (((cLimited_Sequence.eval @ (V0 @ V5)) @ V2) @ V3))))) @ V4))) @ (cLazy_Sequence.yield @ V1))))))))))))
(TLimited_Sequence.neg_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.neg_bind @ V0) @ V1)) @ (^[V2]: ((cLazy_Sequence.hb_bind @ (V0 @ V2)) @ (^[V3]: ((V1 @ V3) @ V2))))))))))
(TLimited_Sequence.pos_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.pos_bind @ V0) @ V1)) @ (^[V2]: ((cLazy_Sequence.bind @ (V0 @ V2)) @ (^[V3]: ((V1 @ V3) @ V2))))))))))
(TList.append_eq_append_conv_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ ((cList.append @ V2) @ V3))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.take @ (cNat.size_class.size @ V0)) @ V2))) @ ((cHOL.eq @ V1) @ ((cList.append @ ((cList.drop @ (cNat.size_class.size @ V0)) @ V2)) @ V3)))) @ ((cHOL.conj @ ((cHOL.eq @ ((cList.take @ (cNat.size_class.size @ V2)) @ V0)) @ V2)) @ ((cHOL.eq @ ((cList.append @ ((cList.drop @ (cNat.size_class.size @ V2)) @ V0)) @ V1)) @ V3)))))))))))))
(TList.append_replicate_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.append @ ((cList.replicate @ V0) @ V1)) @ ((cList.replicate @ V2) @ V1))) @ ((cList.append @ ((cList.replicate @ V2) @ V1)) @ ((cList.replicate @ V0) @ V1))))))))))
(TList.comm_append_is_replicate,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ ((cList.append @ V1) @ V0))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.one_nat_inst.one_nat) @ V2)) @ ((cHOL.eq @ (cList.concat @ ((cList.replicate @ V2) @ V3))) @ ((cList.append @ V0) @ V1)))))))))))))))
(TList.concat_replicate_trivial,(call @ (^[V0]: ((cHOL.eq @ (cList.concat @ ((cList.replicate @ V0) @ cList.list.Nil))) @ cList.list.Nil))))
(TList.greaterThanLessThan_upto,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ (cList.set @ ((cList.upto @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int)))))))))
(TList.in_set_conv_decomp_first,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cList.set @ V1))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.append @ V2) @ ((cList.list.Cons @ V0) @ V3)))) @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V2))))))))))))))
(TList.length_remdups_card_conv,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.remdups @ V0))) @ (cFinite_Set.card @ (cList.set @ V0))))))
(TList.linorder.distinct_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cList.distinct @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V3) @ (cList.set @ V4)))) @ (cList.distinct @ V4)))))))))))))))
(TList.linorder.sorted_map_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ ((cList.filter @ (^[V5]: ((cHOL.eq @ (V2 @ V5)) @ (V3 @ V4)))) @ V4)))))))))))))))
(TList.linorder.sorted_nth_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V4)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V4) @ (cNat.size_class.size @ V2))) @ ((V0 @ ((cList.nth @ V2) @ V3)) @ ((cList.nth @ V2) @ V4)))))))))))))))))
(TList.linorder.sorted_sort_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ (((cList.linorder.sort_key @ V0) @ V2) @ V3)))))))))))))
(TList.linorder_class.sorted_tl,(call @ (^[V0]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ (cList.tl @ V0))))))
(TList.list.list_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TList.list.list_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cList.list.list_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((((cList.list.list_rec_set @ V0) @ V1) @ ((cList.list.Cons @ V4) @ V2)) @ (((V1 @ V4) @ V2) @ V3))))))))))))))
(TList.list.list_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cList.list.list_rec_set @ V0) @ V1) @ cList.list.Nil) @ V0))))))
(TList.list.list_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.list.list_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cList.list.list_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V3)) @ V2)))))))))) @ (V1 @ V0)))))))))
(TList.list.list_rep_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.list.list_rep_set @ V0)) @ (cList.list.list_rep_set @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V1)) @ V0)))))))))
(TList.list.list_rep_set.intros_1,(cList.list.list_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TList.listsum_eq_0_nat_iff_nat,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ V0)) @ cNat.zero_nat_inst.zero_nat)) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V1]: ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat)))))))
(TList.map_tailrec_rev_sumC_def,((c== @ cList.map_tailrec_rev_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cList.map_tailrec_rev_graph @ V0) @ V1))))))
(TList.monoid_add.length_concat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (cNat.size_class.size @ (cList.concat @ V2))) @ (cList.monoid_add_class.listsum @ ((cList.map @ cNat.size_class.size) @ V2)))))))))))
(TList.monoid_add.listsum_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ ((V0 @ V2) @ (((cList.monoid_add.listsum @ V0) @ V1) @ V3)))))))))))))
(TList.monoid_add.listsum_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ cList.list.Nil)) @ V1)))))))
(TList.not_distinct_conv_prefix,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ (cList.distinct @ V0))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V2) @ (cList.set @ V1))) @ ((cHOL.conj @ (cList.distinct @ V1)) @ ((cHOL.eq @ V0) @ ((cList.append @ V1) @ ((cList.list.Cons @ V2) @ V3)))))))))))))))
(TList.nth_nth_transpose_sorted,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ ((cList.map @ cNat.size_class.size) @ V0)))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ (cList.transpose @ V0)))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ ((cList.filter @ (^[V3]: ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V3)))) @ V0)))) @ ((cHOL.eq @ ((cList.nth @ ((cList.nth @ (cList.transpose @ V0)) @ V1)) @ V2)) @ ((cList.nth @ ((cList.nth @ V0) @ V2)) @ V1))))))))))))
(TList.remdups_adj_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.remdups_adj_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ cList.list.Nil) @ cList.list.Nil)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cList.list.Cons @ V4) @ cList.list.Nil)) @ ((cList.list.Cons @ V4) @ cList.list.Nil))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ V5)) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V4) @ V6)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ V5)) @ ((V2 @ ((cList.list.Cons @ V4) @ V6)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V5) @ V6)) @ (V3 @ ((cList.list.Cons @ V5) @ V6))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((V2 @ ((cList.list.Cons @ V5) @ V6)) @ (V3 @ ((cList.list.Cons @ V5) @ V6))))) @ ((V2 @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ (((cHOL.If @ ((cHOL.eq @ V4) @ V5)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))) @ ((cList.list.Cons @ V4) @ (V3 @ ((cList.list.Cons @ V5) @ V6)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))))
(TList.remdups_adj_graph.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V0) @ V2)) @ (V3 @ ((cList.list.Cons @ V0) @ V2))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V1) @ V2)) @ (V3 @ ((cList.list.Cons @ V1) @ V2))))) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ V1)) @ (V3 @ ((cList.list.Cons @ V0) @ V2))) @ ((cList.list.Cons @ V0) @ (V3 @ ((cList.list.Cons @ V1) @ V2))))))))))))))))
(TList.remdups_adj_graph.intros_2,(call @ (^[V0]: ((cList.remdups_adj_graph @ ((cList.list.Cons @ V0) @ cList.list.Nil)) @ ((cList.list.Cons @ V0) @ cList.list.Nil)))))
(TList.remdups_adj_graph.intros_1,((cList.remdups_adj_graph @ cList.list.Nil) @ cList.list.Nil))
(TList.remdups_eq_nil_right_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cList.list.Nil) @ (cList.remdups @ V0))) @ ((cHOL.eq @ V0) @ cList.list.Nil)))))
(TList.set_drop_subset_set_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.set @ ((cList.drop @ V1) @ V2))) @ (cList.set @ ((cList.drop @ V0) @ V2)))))))))))
(TList.set_take_subset_set_take,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cList.set @ ((cList.take @ V0) @ V2))) @ (cList.set @ ((cList.take @ V1) @ V2)))))))))))
(TList.set_update_subset_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ (cList.set @ (((cList.list_update @ V0) @ V1) @ V2))) @ ((cSet.insert @ V2) @ (cList.set @ V0))))))))))
(TList.sorted_list_of_set_range,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cList.upt @ V0) @ V1)))))))
(TList.split_list_last_prop_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ ((cHOL.conj @ (V1 @ V3)) @ ((cSet.Ball @ (cList.set @ V4)) @ (^[V5]: (cHOL.Not @ (V1 @ V5))))))))))))))))))
(TMain.sumbool.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cMain.random_aux_sumbool @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cExtraction.sumbool.Left) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cExtraction.sumbool.Right) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))) @ V2)))))))))
(TMap.dom_map_of_conv_image_fst,(call @ (^[V0]: ((cHOL.eq @ (cMap.dom @ (cMap.map_of @ V0))) @ ((cSet.image @ cProduct_Type.fst) @ (cList.set @ V0))))))
(TMap.finite_set_of_finite_maps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (cMap.dom @ V2)) @ V0)) @ ((cOrderings.ord_class.less_eq @ (cMap.ran @ V2)) @ V1))))))))))))
(TNat.arity_distrib_lattice_nat,(cLattices.distrib_lattice_class @ cTYPE))
(TNat.class.semiring_char_0_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cNat.class.semiring_char_0_axioms @ V0) @ V2) @ V3))))))))))))
(TNat.dvd.order.ordering_axioms,((cOrderings.ordering @ cRings.dvd_class.dvd) @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))
(TNat.infinite_descent0_measure,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (V0 @ V3)) @ cNat.zero_nat_inst.zero_nat)) @ (V1 @ V3))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (V0 @ V3))) @ ((c==> @ (cHOL.Not @ (V1 @ V3))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ (V0 @ V4)) @ (V0 @ V3))) @ (cHOL.Not @ (V1 @ V4)))))))))) @ (V1 @ V2))))))))))
(TNat.semiring_1.of_nat_aux_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c== @ cNat.semiring_1.of_nat_aux) @ (^[V4]: (^[V5]: ((((cNat.nat.nat_rec @ (^[V6]: (^[V7]: V7))) @ (^[V6]: (^[V7]: (^[V8]: (^[V9]: ((V7 @ V8) @ (V8 @ V9))))))) @ V5) @ V4))))))))))))))
(TNat.semiring_1.of_nat_in_Nats,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cSet.member @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ (((cNat.semiring_1.Nats @ V0) @ V2) @ V3))))))))))))))
(TNat.semiring_1_class.Nats_add,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cNat.semiring_1_class.Nats)) @ ((c==> @ ((cSet.member @ V1) @ cNat.semiring_1_class.Nats)) @ ((cSet.member @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cNat.semiring_1_class.Nats))))))))
(TNat.semiring_1_class.Nats_def,((cHOL.eq @ cNat.semiring_1_class.Nats) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ cOrderings.top_class.top)))
(TNat.semiring_1_class.of_nat_0,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ cNat.zero_nat_inst.zero_nat)) @ cGroups.zero_class.zero))
(TNat.semiring_1_class.of_nat_1,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ cNat.one_nat_inst.one_nat)) @ cGroups.one_class.one))
(TNat.semiring_char_0_class_def,((c== @ (cNat.semiring_char_0_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.semiring_1_class @ cTYPE)) @ (((cNat.class.semiring_char_0_axioms @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))))
(TNitpick.arity_random_pair_box,(cQuickcheck_Random.random_class @ cTYPE))
(TNitpick.arity_term_of_fun_box,(cCode_Evaluation.term_of_class @ cTYPE))
(TNitpick.arity_type_signed_bit,(cHOL.type_class @ cTYPE))
(TNitpick.arity_typerep_fun_box,(cTyperep.typerep_class @ cTYPE))
(TNitpick.nat_gcd_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.nat_gcd_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat))) @ ((cNitpick.nat_gcd_graph @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat))) @ ((V2 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cNat.zero_nat_inst.zero_nat)) @ V4) @ (V3 @ ((cProduct_Type.Pair @ V5) @ ((cDivides.div_nat_inst.mod_nat @ V4) @ V5)))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.norm_frac.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V1)) @ (cInt.uminus_int_inst.uminus_int @ V2))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cNitpick.norm_frac_rel) @ V1))))))))
(TNitpick.norm_frac_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.norm_frac_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V4) @ V5)) @ (^[V6]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V4) @ V6)) @ ((cDivides.div_int_inst.div_int @ V5) @ V6)))))))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac_graph @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))))) @ V2)))))))))) @ V2)))))))))
(TNitpick.norm_frac_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNitpick.norm_frac_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ (V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4)))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V3) @ V4)) @ (^[V5]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V3) @ V5)) @ ((cDivides.div_int_inst.div_int @ V4) @ V5)))))))) @ ((cHOL.implies @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac_graph @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4))) @ (V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4)))))))))))))))))))
(TNitpick.norm_frac_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.norm_frac_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V3)) @ (cInt.uminus_int_inst.uminus_int @ V4))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.pair_box.Rep_pair_box,(call @ (^[V0]: ((cSet.member @ (cNitpick.Rep_pair_box @ V0)) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set)))))
(TNitpick.term_of_pair_box_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TNitpick.word.Abs_word_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.word.word_rep_set))) @ ((cHOL.eq @ (cNitpick.Rep_word @ (cNitpick.Abs_word @ V0))) @ V0)))))
(TNitpick.word.Rep_word_inverse,(call @ (^[V0]: ((cHOL.eq @ (cNitpick.Abs_word @ (cNitpick.Rep_word @ V0))) @ V0))))
(TNitpick.word.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNitpick.random_aux_word @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.word.Word) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))))))))
(TNitpick.word.word_rec_set_def,((c== @ cNitpick.word.word_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cNitpick.word.Word @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4))))))))))))
(TNitpick.word.word_rep_set_def,((c== @ cNitpick.word.word_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.Leaf @ V2)))))))))
(TNum.neg_numeral.dbl_dec_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNum.neg_numeral.dbl_dec @ V0) @ V1) @ V4) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))) @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.BitM @ V5)))))))))))))))))
(TNum.neg_numeral.dbl_dec_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNum.neg_numeral.dbl_dec @ V0) @ V1) @ V4) @ V4)) @ V4)))))))))))))
(TNum.neg_numeral.dbl_dec_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNum.neg_numeral.dbl_dec @ V0) @ V1) @ V4) @ V2)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ cNum.num.One))))))))))))))
(TNum.neg_numeral.dbl_dec_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNum.neg_numeral.dbl_dec @ V0) @ V1) @ V4) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ (cNum.num.Bit1 @ V5)))))))))))))))))
(TNum.neg_numeral.dbl_inc_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNum.neg_numeral.dbl_inc @ V1) @ V4) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))) @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.num.Bit1 @ V5)))))))))))))))))
(TNum.neg_numeral.dbl_inc_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNum.neg_numeral.dbl_inc @ V1) @ V4) @ V4)) @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))))
(TNum.neg_numeral.dbl_inc_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNum.neg_numeral.dbl_inc @ V1) @ V4) @ V2)) @ V4)))))))))))))
(TNum.neg_numeral.dbl_inc_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNum.neg_numeral.dbl_inc @ V1) @ V4) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ (cNum.BitM @ V5)))))))))))))))))
(TNum.neg_numeral.is_num.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ (V6 @ V4)) @ ((c==> @ (call @ (^[V7]: ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V7)) @ ((c==> @ (V6 @ V7)) @ (V6 @ (V3 @ V7))))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V7)) @ ((c==> @ (V6 @ V7)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V8)) @ ((c==> @ (V6 @ V8)) @ (V6 @ ((V1 @ V7) @ V8))))))))))) @ (V6 @ V5)))))))))))))))))))))
(TNum.neg_numeral.is_num.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ ((V1 @ V5) @ V6))))))))))))))))))))
(TNum.neg_numeral.is_num.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ (V3 @ V5)))))))))))))))))
(TNum.neg_numeral.is_num.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V4)))))))))))))
(TNum.neg_numeral.minus_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))))))))))))))))
(TNum.neg_numeral.sub_num_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ (cNum.num.Bit1 @ V5)) @ (cNum.num.Bit1 @ V6))) @ ((cNum.neg_numeral.dbl @ V1) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral.sub_num_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ (cNum.num.Bit1 @ V5)) @ (cNum.num.Bit0 @ V6))) @ (((cNum.neg_numeral.dbl_inc @ V1) @ V4) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral.sub_num_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ (cNum.num.Bit0 @ V5)) @ (cNum.num.Bit1 @ V6))) @ ((((cNum.neg_numeral.dbl_dec @ V0) @ V1) @ V4) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral.sub_num_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ (cNum.num.Bit0 @ V5)) @ (cNum.num.Bit0 @ V6))) @ ((cNum.neg_numeral.dbl @ V1) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral.sub_num_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ (cNum.num.Bit1 @ V5)) @ cNum.num.One)) @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.num.Bit0 @ V5)))))))))))))))))
(TNum.neg_numeral.sub_num_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ (cNum.num.Bit0 @ V5)) @ cNum.num.One)) @ (((cNum.numeral.numeral @ V4) @ V1) @ (cNum.BitM @ V5)))))))))))))))))
(TNum.neg_numeral.sub_num_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ cNum.num.One) @ (cNum.num.Bit1 @ V5))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ (cNum.num.Bit0 @ V5)))))))))))))))))
(TNum.neg_numeral.sub_num_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ cNum.num.One) @ (cNum.num.Bit0 @ V5))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ (cNum.BitM @ V5)))))))))))))))))
(TNum.neg_numeral.sub_num_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ cNum.num.One) @ cNum.num.One)) @ V2)))))))))))))
(TNum.neg_numeral_class.dbl_def,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl @ V0)) @ ((cGroups.plus_class.plus @ V0) @ V0)))))
(TNum.neg_numeral_class.sub_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ V0) @ V1)) @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TNum.numeral_class.numeral_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TNum.numeral_class.numeral_def,((c== @ cNum.numeral_class.numeral) @ (^[V0]: ((((cNum.num.num_rec @ cGroups.one_class.one) @ (^[V1]: (^[V2]: ((cGroups.plus_class.plus @ V2) @ V2)))) @ (^[V1]: (^[V2]: ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V2) @ V2)) @ cGroups.one_class.one)))) @ V0))))
(TNum.numeral_class.numeral_inc,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.inc @ V0))) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.numeral_class.one_add_one,((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNum.ring_1.eq_iff_iszero_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V6) @ V7)) @ ((cNum.ring_1.iszero @ V3) @ ((V4 @ V6) @ V7)))))))))))))))))))))
(TNum.ring_1.iszero_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cNum.ring_1.iszero @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6))) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)))))))))))))))))))
(TNum.ring_1_class.not_iszero_1,(cHOL.Not @ (cNum.ring_1_class.iszero @ cGroups.one_class.one)))
(TNum.semiring_1.of_nat_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ (cNum.numeral_class.numeral @ V4))) @ (((cNum.numeral.numeral @ V0) @ V2) @ V4))))))))))))))
(TOption.option.option_case_def,((c== @ cOption.option.option_case) @ (^[V0]: (^[V1]: ((cOption.option.option_rec @ V0) @ (^[V2]: (V1 @ V2)))))))
(TOption.option.option_size_def,(call @ (^[V0]: ((c== @ (cOption.option.option_size @ V0)) @ ((cOption.option.option_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V1]: ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TOption.type_definition_option,(((cTypedef.type_definition @ cOption.Rep_option) @ cOption.Abs_option) @ (cSet.Collect @ cOption.option.option_rep_set)))
(TOrderings.arity_linorder_bool,(cOrderings.linorder_class @ cTYPE))
(TOrderings.arity_order_bot_fun,(cOrderings.order_bot_class @ cTYPE))
(TOrderings.arity_order_top_fun,(cOrderings.order_top_class @ cTYPE))
(TOrderings.class.no_bot.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cOrderings.class.no_bot_axioms @ V1)))))))
(TOrderings.class.no_bot.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ ((cOrderings.class.order @ V0) @ V1)))))))
(TOrderings.class.no_top.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cOrderings.class.no_top_axioms @ V1)))))))
(TOrderings.class.no_top.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ ((cOrderings.class.order @ V0) @ V1)))))))
(TOrderings.class.order_bot_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cOrderings.class.order @ V1) @ V2)) @ ((cOrderings.class.order_bot_axioms @ V0) @ V1))))))))))
(TOrderings.class.order_top_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cOrderings.class.order @ V0) @ V1)) @ ((cOrderings.class.order_top_axioms @ V0) @ V2))))))))))
(TOrderings.class.wellorder_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.linorder @ V0) @ V1)) @ (cOrderings.class.wellorder_axioms @ V1))))))))
(TOrderings.linorder_class.neqE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)) @ V2))))))))))
(TOrderings.no_bot_class.axioms,(cOrderings.class.no_bot_axioms @ cOrderings.ord_class.less))
(TOrderings.no_top_class.axioms,(cOrderings.class.no_top_axioms @ cOrderings.ord_class.less))
(TOrderings.ord.ord_eq_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((V2 @ V1) @ V3)) @ ((V2 @ V0) @ V3))))))))))))
(TOrderings.ord.ord_le_eq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((V0 @ V1) @ V3))))))))))))
(TOrderings.ord_class.Least_def,(call @ (^[V0]: ((cHOL.eq @ (cOrderings.ord_class.Least @ V0)) @ (cHOL.The @ (^[V1]: ((cHOL.conj @ (V0 @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2)))))))))))
(TOrderings.order.LeastI2_order,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V2 @ V5)) @ ((V0 @ V3) @ V5))))) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V2 @ V5)) @ ((c==> @ (cHOL.All @ (^[V6]: ((cHOL.implies @ (V2 @ V6)) @ ((V0 @ V5) @ V6))))) @ (V4 @ V5)))))) @ (V4 @ ((cOrderings.ord.Least @ V0) @ V2)))))))))))))))))
(TOrderings.order_bot.bot_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((V1 @ V0) @ V3)))))))))))
(TOrderings.order_bot_class_def,((c== @ (cOrderings.order_bot_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.bot_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ ((cOrderings.class.order_bot_axioms @ cOrderings.bot_class.bot) @ cOrderings.ord_class.less_eq)))))
(TOrderings.order_class.antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_class.le_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_class.less_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TOrderings.order_le_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_less_imp_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)) @ cHOL.True)))))))))
(TOrderings.order_less_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_top_class_def,((c== @ (cOrderings.order_top_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.top_class @ cTYPE)) @ ((cOrderings.class.order_top_axioms @ cOrderings.ord_class.less_eq) @ cOrderings.top_class.top)))))
(TOrderings.ordering_top.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ ((cOrderings.ordering_top_axioms @ V0) @ V2)))))))))
(TOrderings.ordering_top.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ ((cOrderings.ordering @ V0) @ V1)))))))))
(TOrderings.preorder.less_asym',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V2)) @ V4))))))))))))))
(TOrderings.preorder.less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.preorder.order_refl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((V0 @ V2) @ V2)))))))))
(TOrderings.wellorder.LeastI_ex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (cHOL.Ex @ (^[V3]: (V2 @ V3)))) @ (V2 @ ((cOrderings.ord.Least @ V0) @ V2)))))))))))
(TOrderings.wellorder_class_def,((c== @ (cOrderings.wellorder_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.linorder_class @ cTYPE)) @ (cOrderings.class.wellorder_axioms @ cOrderings.ord_class.less))))
(TPartial_Function.flat_lub_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPartial_Function.flat_lub @ V0) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0) @ (cHOL.The @ (^[V2]: ((cSet.member @ V2) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))))))))
(TPartial_Function.flat_ord_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cPartial_Function.flat_ord @ V0) @ V1) @ V2)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TPartial_Function.tailrec.ccpo,(((cComplete_Partial_Order.class.ccpo @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cHOL.undefined))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ (cPartial_Function.mk_less @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined)))))
(TPower.nat_power_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TPower.nat_zero_less_power_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cPower.power_class.power @ V0) @ V1))) @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TPower.power_class.power.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPower.power_class.power.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cGroups.one_class.one))))
(TPower.ring_1.power_minus1_odd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ cNum.num.One)) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V6)))) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ cNum.num.One))))))))))))))))))
(TPower.ring_1.power_minus_Bit0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ (V5 @ V6)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V7)))) @ ((((cPower.power.power @ V0) @ V1) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V7))))))))))))))))))))))
(TPower.ring_1.power_minus_Bit1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ (V5 @ V6)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V7)))) @ (V5 @ ((((cPower.power.power @ V0) @ V1) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V7)))))))))))))))))))))))
(TPower.ring_1.power_minus_even,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ (V5 @ V6)) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V7))) @ ((((cPower.power.power @ V0) @ V1) @ V6) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V7)))))))))))))))))))))
(TPower.semiring_1.of_nat_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ ((cPower.power_class.power @ V4) @ V5))) @ ((((cPower.power.power @ V0) @ V1) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ V5))))))))))))))))
(TPredicate.iterate_upto.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ (((V0 @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TPredicate.iterate_upto.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cPredicate.iterate_upto @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cPredicate.iterate_upto_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (cPredicate.Seq @ (^[V8]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V7) @ V6)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V5 @ V6)) @ (((cPredicate.iterate_upto @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7))))))) @ ((c==> @ ((cWellfounded.accp @ cPredicate.iterate_upto_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TPredicate.iterate_upto.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cPredicate.iterate_upto_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cPredicate.iterate_upto @ V0) @ V1) @ V2)) @ (cPredicate.Seq @ (^[V3]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ V1)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V0 @ V1)) @ (((cPredicate.iterate_upto @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2))))))))))))))
(TPredicate.not_is_empty_single,(call @ (^[V0]: (cHOL.Not @ (cPredicate.is_empty @ (cPredicate.single @ V0))))))
(TPredicate.pred.Abs_pred_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cPredicate.Abs_pred @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cPredicate.pred.pred_rep_set))) @ V1))))) @ V1))))))
(TPredicate.pred.Rep_pred_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.pred.pred_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cPredicate.Rep_pred @ V2))) @ V1)))) @ V1)))))))
(TPredicate.pred.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cPredicate.pred.pred_case @ V2) @ V0)) @ ((cPredicate.pred.pred_case @ V2) @ V1))))))))))
(TPredicate.seq.Abs_seq_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.seq.seq_rep_set))) @ ((cHOL.eq @ (cPredicate.Rep_seq @ (cPredicate.Abs_seq @ V0))) @ V0)))))
(TPredicate.seq.Rep_seq_inverse,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.Abs_seq @ (cPredicate.Rep_seq @ V0))) @ V0))))
(TPredicate.seq.seq_rec_set_def,((c== @ cPredicate.seq.seq_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (cInductive.complete_lattice_class.lfp @ (^[V3]: (^[V4]: (^[V5]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cPredicate.seq.Empty)) @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Insert @ V6) @ V7))) @ ((cHOL.eq @ V5) @ ((V1 @ V6) @ V7)))))))) @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cPredicate.seq.Join @ V8) @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ (((V2 @ V8) @ V6) @ V7))) @ ((V3 @ V6) @ V7))))))))))))))))))))
(TPredicate.seq.seq_rep_set_def,((c== @ cPredicate.seq.seq_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))) @ V2))))) @ (V0 @ V2)))))))))))))
(TPredicate.single_less_eq_eval,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cPredicate.single @ V0)) @ V1)) @ ((cPredicate.eval @ V1) @ V0)))))))
(TPredicate.type_definition_seq,(((cTypedef.type_definition @ cPredicate.Rep_seq) @ cPredicate.Abs_seq) @ (cSet.Collect @ cPredicate.seq.seq_rep_set)))
(TPresburger.periodic_finite_ex,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ (V1 @ V2)) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V2) @ ((cInt.times_int_inst.times_int @ V3) @ V0))))))))) @ ((cHOL.eq @ (cHOL.Ex @ (^[V2]: (V1 @ V2)))) @ ((cSet.Bex @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.one_int_inst.one_int) @ V0)) @ (^[V2]: (V1 @ V2)))))))))))
(TProduct_Type.Times_eq_cancel2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cProduct_Type.Sigma @ V2) @ (^[V4]: V1))) @ ((cProduct_Type.Sigma @ V3) @ (^[V4]: V1)))) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TProduct_Type.UN_Times_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cProduct_Type.Sigma @ V0) @ (^[V4]: V1))) @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cProduct_Type.Sigma @ (V2 @ V4)) @ (^[V6]: (V3 @ V5)))))))) @ ((cProduct_Type.Sigma @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V2)) @ (^[V4]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V3)))))))))))))
(TProduct_Type.arity_equal_bool,(cHOL.equal_class @ cTYPE))
(TProduct_Type.arity_equal_prod,(cHOL.equal_class @ cTYPE))
(TProduct_Type.arity_equal_unit,(cHOL.equal_class @ cTYPE))
(TProduct_Type.default_unit_def,((cHOL.eq @ cProduct_Type.default_unit_inst.default_unit) @ cProduct_Type.Unity))
(TProduct_Type.map_pair_compose,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cProduct_Type.map_pair @ ((cFun.comp @ V0) @ V1)) @ ((cFun.comp @ V2) @ V3))) @ ((cFun.comp @ ((cProduct_Type.map_pair @ V0) @ V2)) @ ((cProduct_Type.map_pair @ V1) @ V3))))))))))))
(TProduct_Type.map_pair_surj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((c==> @ ((cHOL.eq @ ((cSet.image @ V3) @ V4)) @ V5)) @ ((cHOL.eq @ ((cSet.image @ ((cProduct_Type.map_pair @ V0) @ V3)) @ ((cProduct_Type.Sigma @ V1) @ (^[V6]: V4)))) @ ((cProduct_Type.Sigma @ V2) @ (^[V6]: V5))))))))))))))))))
(TProduct_Type.prod_case_unfold,((cHOL.eq @ cProduct_Type.prod.prod_case) @ (^[V0]: (^[V1]: ((V0 @ (cProduct_Type.fst @ V1)) @ (cProduct_Type.snd @ V1))))))
(TProduct_Type.split_paired_All,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TProduct_Type.split_paired_The,(call @ (^[V0]: ((cHOL.eq @ (cHOL.The @ (^[V1]: (V0 @ V1)))) @ (cHOL.The @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TProduct_Type.split_paired_all,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (call @ (^[V1]: (call @ (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TProduct_Type.split_tupled_all_2,(call @ (^[V0]: ((c== @ (call @ (^[V1]: V0))) @ V0))))
(TProduct_Type.split_tupled_all_1,(call @ (^[V0]: ((c== @ (call @ (^[V1]: (V0 @ V1)))) @ (call @ (^[V1]: (call @ (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(TQuickcheck_Narrowing.cons_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.cons @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ ((cList.list.Cons @ cList.list.Nil) @ cList.list.Nil))) @ ((cList.list.Cons @ (^[V2]: V0)) @ cList.list.Nil))))))))
(TQuickcheck_Narrowing.conv_def,((c== @ cQuickcheck_Narrowing.conv) @ (^[V0]: (^[V1]: (cQuickcheck_Narrowing.conv_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TQuickcheck_Random.beyond_zero,(call @ (^[V0]: ((cHOL.eq @ ((cQuickcheck_Random.beyond @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cCode_Numeral.zero_natural_inst.zero_natural))))
(TQuotient.quot_type.rep_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ (V2 @ V3)) @ (V2 @ V4))) @ ((cHOL.eq @ V3) @ V4))))))))))))))
(TRandom_Pred.if_randompred_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Pred.if_randompred @ V0)) @ (((cHOL.If @ V0) @ (cRandom_Pred.single @ cProduct_Type.Unity)) @ cRandom_Pred.empty)))))
(TRandom_Pred.iter'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V5) @ ((cQuickcheck_Random.random_class.random @ V3) @ V4))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V6) @ V7)) @ V5)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V6)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V3) @ V10)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))))) @ V0)))))))))))))))))))))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cRandom_Pred.iter'_rel) @ V1))))))))
(TRandom_Pred.iter'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Pred.iter'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7))))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V6) @ V7)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cPredicate.Seq @ (^[V11]: ((cPredicate.seq.Insert @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V10)))))))))))))))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ ((cQuickcheck_Random.random_class.random @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((cRandom_Pred.iter'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))))))))))))))))))))))) @ V2)))))))))))))) @ V2)))))))))
(TRandom_Pred.iter'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Pred.iter'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V5) @ V6)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (^[V9]: (cPredicate.Seq @ (^[V10]: ((cPredicate.seq.Insert @ V7) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V9)))))))))))))))) @ (cHOL.All @ (^[V7]: (cHOL.All @ (^[V8]: (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: (cHOL.All @ (^[V11]: (cHOL.All @ (^[V12]: (cHOL.All @ (^[V13]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.implies @ ((cHOL.eq @ V7) @ ((cQuickcheck_Random.random_class.random @ V5) @ V6))) @ ((cHOL.implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((cHOL.implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ ((cRandom_Pred.iter'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V12)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V12)))))))))))))))))))))))))))))))))))))))))
(TRandom_Pred.iter'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Pred.iter'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V7) @ ((cQuickcheck_Random.random_class.random @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V5) @ V12)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))))))))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.Random.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TRandom_Sequence.Random.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cRandom_Sequence.Random @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.Random_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V4 @ V6)) @ (^[V7]: ((cProduct_Type.scomp @ (((cRandom_Sequence.Random @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)) @ (^[V8]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V7))) @ V8)))))))))) @ ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.Random_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TRandom_Sequence.Random.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.Random_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cRandom_Sequence.Random @ V0) @ V1)) @ (^[V2]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V0 @ V2)) @ (^[V3]: ((cProduct_Type.scomp @ (((cRandom_Sequence.Random @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)) @ (^[V4]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V3))) @ V4)))))))))))))))
(TRandom_Sequence.iter_sumC_def,((c== @ cRandom_Sequence.iter_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cRandom_Sequence.iter_graph @ V0) @ V1))))))
(TRandom_Sequence.neg_empty_def,((cHOL.eq @ cRandom_Sequence.neg_empty) @ (^[V0]: (^[V1]: (^[V2]: cLimited_Sequence.neg_empty)))))
(TRandom_Sequence.neg_union_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.neg_union @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cLimited_Sequence.neg_union @ (((V0 @ V2) @ V3) @ V4)) @ (((V1 @ V2) @ V3) @ V4)))))))))))
(TRandom_Sequence.pos_empty_def,((cHOL.eq @ cRandom_Sequence.pos_empty) @ (^[V0]: (^[V1]: (^[V2]: cLimited_Sequence.pos_empty)))))
(TRandom_Sequence.pos_union_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.pos_union @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cLimited_Sequence.pos_union @ (((V0 @ V2) @ V3) @ V4)) @ (((V1 @ V2) @ V3) @ V4)))))))))))
(TRecord.isomorphic_tuple.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((cHOL.eq @ ((cRecord.abst @ V0) @ ((cRecord.repr @ V0) @ V1))) @ V1)))) @ ((c==> @ (call @ (^[V1]: ((cHOL.eq @ ((cRecord.repr @ V0) @ ((cRecord.abst @ V0) @ V1))) @ V1)))) @ (cRecord.isomorphic_tuple @ V0))))))
(TRecord.isomorphic_tuple.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cRecord.abst @ V0) @ V1)) @ ((cRecord.abst @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TRecord.isomorphic_tuple.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cRecord.repr @ V0) @ V1)) @ ((cRecord.repr @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TRecord.isomorphic_tuple.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cRecord.repr @ V0) @ ((cRecord.abst @ V0) @ V1))) @ V1)))))))
(TRecord.isomorphic_tuple.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cRecord.abst @ V0) @ ((cRecord.repr @ V0) @ V1))) @ V1)))))))
(TRecord.isomorphic_tuple.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c== @ ((cHOL.Let @ V1) @ V2)) @ (V2 @ V1))))))))))
(TRecord.isomorphic_tuple_intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cHOL.eq @ (V0 @ V3)) @ (V0 @ V4))) @ ((cHOL.eq @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V0 @ (V1 @ V3))) @ V3)))) @ ((c==> @ ((c== @ V2) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1))) @ (cRecord.isomorphic_tuple @ V2)))))))))))
(TRecord.tuple_isomorphism.recs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRecord.tuple_isomorphism.tuple_isomorphism_rec @ V0) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TRecord.tuple_isomorphism.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TRecord.tuple_isomorphism.size_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((cRecord.tuple_isomorphism.tuple_isomorphism_size @ V0) @ V1) @ V2) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V3) @ V4))) @ cNat.zero_nat_inst.zero_nat))))))))))))
(TRelation.Domain_Collect_split,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2))))))) @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TRelation.converse_subset_swap,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cRelation.converse @ V1))) @ ((cOrderings.ord_class.less_eq @ (cRelation.converse @ V0)) @ V1)))))))
(TRelation.relcomp_subset_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V5]: V2)))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ ((cProduct_Type.Sigma @ V2) @ (^[V5]: V4)))) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ V0) @ V3)) @ ((cProduct_Type.Sigma @ V1) @ (^[V5]: V4))))))))))))))))
(TRelation.single_valued_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cRelation.single_valued @ V1)) @ (cRelation.single_valued @ V0))))))))
(TRelation.sym_conv_converse_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.sym @ V0)) @ ((cHOL.eq @ (cRelation.converse @ V0)) @ V0)))))
(TRings.class.comm_ring_1.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((c==> @ (((((cRings.class.comm_ring @ V2) @ V3) @ V4) @ V5) @ V0)) @ ((c==> @ ((cRings.class.zero_neq_one @ V1) @ V3)) @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))))
(TRings.class.comm_semiring_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.class.comm_semiring @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.conj @ (cGroups.class.ab_semigroup_mult @ V1)) @ ((cRings.class.comm_semiring_axioms @ V0) @ V1)))))))))
(TRings.class.semiring_0.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.semiring_0 @ V0) @ V1) @ V2)) @ ((cRings.class.semiring @ V0) @ V2)))))))))
(TRings.class.semiring_0.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.semiring_0 @ V0) @ V1) @ V2)) @ ((cRings.class.mult_zero @ V2) @ V1)))))))))
(TRings.class.semiring_0.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.semiring_0 @ V0) @ V1) @ V2)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))))
(TRings.class.semiring_1.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.zero_neq_one @ V0) @ V3)))))))))))
(TRings.class.semiring_1.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cRings.class.semiring_0 @ V2) @ V3) @ V1)))))))))))
(TRings.class.semiring_1.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.monoid_mult @ V0) @ V1)))))))))))
(TRings.classrel_comm_ring_ring,(cRings.ring_class @ cTYPE))
(TRings.comm_ring_1_class.intro,((c==> @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ ((c==> @ (cRings.comm_ring_class @ cTYPE)) @ ((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cRings.comm_ring_1_class @ cTYPE)))))
(TRings.comm_ring_1_class.super_3,((c==> @ (cRings.comm_ring_1_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))
(TRings.comm_ring_1_class.super_2,((c==> @ (cRings.comm_ring_1_class @ cTYPE)) @ (cRings.comm_ring_class @ cTYPE)))
(TRings.comm_ring_1_class.super_1,((c==> @ (cRings.comm_ring_1_class @ cTYPE)) @ (cGroups.comm_monoid_mult_class @ cTYPE)))
(TRings.comm_semiring_1.dvd_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V6)) @ (((cRings.dvd.dvd @ V0) @ V4) @ ((V2 @ V5) @ V6))))))))))))))))))))
(TRings.comm_semiring_1.one_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cRings.dvd.dvd @ V0) @ V1) @ V4)))))))))))))
(TRings.comm_semiring_class_def,((c== @ (cRings.comm_semiring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_semigroup_mult_class @ cTYPE)) @ ((cRings.class.comm_semiring_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times)))))
(TRings.linordered_idom.abs_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ V7)) @ V7)))))))))))))))))))))))
(TRings.linordered_idom.abs_sgn,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ V10)) @ ((V9 @ V10) @ (V8 @ V10)))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_0_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((cHOL.eq @ (V8 @ V10)) @ V3)) @ ((cHOL.eq @ V10) @ V3))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V5 @ V10) @ V3)) @ ((cHOL.eq @ (V8 @ V10)) @ (V2 @ V7)))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V5 @ V3) @ V10)) @ ((cHOL.eq @ (V8 @ V10)) @ V7))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_sgn,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V8 @ (V8 @ V10))) @ (V8 @ V10))))))))))))))))))))))))))
(TRings.ring.minus_mult_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ (V3 @ V5)) @ V6)) @ ((V4 @ V5) @ (V3 @ V6)))))))))))))))))))
(TRings.ring.right_diff_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V4 @ V5) @ ((V2 @ V6) @ V7))) @ ((V2 @ ((V4 @ V5) @ V6)) @ ((V4 @ V5) @ V7)))))))))))))))))))))
(TSMT.pattern.Abs_pattern_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSMT.Abs_pattern @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set))) @ V1))))) @ V1))))))
(TSMT.pattern.Rep_pattern_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cSMT.Rep_pattern @ V2))) @ V1)))) @ V1)))))))
(TSet.arity_boolean_algebra_set,(cLattices.boolean_algebra_class @ cTYPE))
(TSet_Interval.UN_finite_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V2)) @ (^[V3]: (V0 @ V3)))) @ V1)))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(TSet_Interval.UN_lessThan_UNIV,((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V0]: (cSet_Interval.ord_class.lessThan @ V0)))) @ cOrderings.top_class.top))
(TSet_Interval.arith_series_int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cInt.plus_int_inst.plus_int @ V0) @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ V3)) @ V1)))) @ (cSet_Interval.ord_class.lessThan @ V2)))) @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ V2)) @ ((cInt.plus_int_inst.plus_int @ V0) @ ((cInt.plus_int_inst.plus_int @ V0) @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ ((cNat.minus_nat_inst.minus_nat @ V2) @ cNat.one_nat_inst.one_nat))) @ V1))))))))))))
(TSet_Interval.arith_series_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ V3) @ V1)))) @ (cSet_Interval.ord_class.lessThan @ V2)))) @ ((cNat.times_nat_inst.times_nat @ V2) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V2) @ cNat.one_nat_inst.one_nat)) @ V1))))))))))))
(TSet_Interval.atLeast0LessThan,(call @ (^[V0]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V0)) @ (cSet_Interval.ord_class.lessThan @ V0)))))
(TSet_Interval.atLeastLessThan0,(call @ (^[V0]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cOrderings.bot_class.bot))))
(TSet_Interval.dvd.lessThan_def,(call @ (^[V0]: ((c== @ ((cSet_Interval.ord.lessThan @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))))) @ V0)) @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))))
(TSet_Interval.dvd.lessThan_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.lessThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))))
(TSet_Interval.ivl_disj_int_one_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_one_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_one_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_one_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_one_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_one_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_one_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_one_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ cOrderings.bot_class.bot))))))
(TSet_Interval.ivl_disj_int_two_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_two_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_two_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_two_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_two_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_two_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_two_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ivl_disj_int_two_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.ord.lessThan_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord.lessThan @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TSet_Interval.ord.lessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.lessThan @ V1) @ V2))) @ ((V1 @ V0) @ V2)))))))))
(TSet_Interval.order.Icc_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V4) @ V5))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.eq @ V3) @ V5))) @ ((cHOL.conj @ (cHOL.Not @ ((V0 @ V2) @ V3))) @ (cHOL.Not @ ((V0 @ V4) @ V5)))))))))))))))))))
(TSet_Interval.setsum_image_gen,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ (cSet.Collect @ (^[V4]: ((cHOL.conj @ ((cSet.member @ V4) @ V0)) @ ((cHOL.eq @ (V2 @ V4)) @ V3))))))) @ ((cSet.image @ V2) @ V0)))))))))))
(TSet_Interval.sum_diff_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: ((cNat.ord_nat_inst.less_eq_nat @ (V0 @ V3)) @ (V1 @ V3))))) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V1 @ V3))) @ (cSet_Interval.ord_class.lessThan @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V0 @ V3))) @ (cSet_Interval.ord_class.lessThan @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cNat.minus_nat_inst.minus_nat @ (V1 @ V3)) @ (V0 @ V3)))) @ (cSet_Interval.ord_class.lessThan @ V2)))))))))))
(TString.literal.explode_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cString.explode @ V2))))) @ (V1 @ V0))))))))
(TString.literal.explode_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cString.explode @ V0)) @ (cString.explode @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.nibble.nibble_case_def,((c== @ cString.nibble.nibble_case) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (^[V6]: (^[V7]: (^[V8]: (^[V9]: (^[V10]: (^[V11]: (^[V12]: (^[V13]: (^[V14]: (^[V15]: ((((((((((((((((cString.nibble.nibble_rec @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15)))))))))))))))))))
(TString.nibble.nibble_size_def,((c== @ cString.nibble.nibble_size) @ ((((((((((((((((cString.nibble.nibble_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TString.type_definition_nibble,(((cTypedef.type_definition @ cString.Rep_nibble) @ cString.Abs_nibble) @ (cSet.Collect @ cString.nibble.nibble_rep_set)))
(TTransfer.right_unique_alt_def,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.right_unique @ V0)) @ ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V0) @ cHOL.implies)) @ cHOL.eq) @ cHOL.eq)))))
(TTransfer.transfer_bforall_def,((c== @ cTransfer.transfer_bforall) @ (^[V0]: (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (V1 @ V2))))))))
(TTransfer.transfer_implies_def,((c== @ cHOL.implies) @ cHOL.implies))
(TTransitive_Closure.relpow_0_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V2))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V3)) @ V3)))))))))))
(TTransitive_Closure.relpow_0_I,(call @ (^[V0]: (call @ (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V0)) @ ((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V1)))))))
(TTransitive_Closure.relpow_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.compow @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cRelation.relcomp @ ((cNat.compow @ V0) @ V2)) @ ((cNat.compow @ V1) @ V2))))))))))
(TTransitive_Closure.relpow_def,((c== @ cNat.compow) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: cRelation.Id)) @ (^[V1]: (^[V2]: (^[V3]: ((cRelation.relcomp @ (V2 @ V3)) @ V3))))) @ V0))))
(TTransitive_Closure.relpowp_E2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.compow @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.Suc @ V6))) @ ((c==> @ ((V1 @ V2) @ V5)) @ ((c==> @ ((((cNat.compow @ V6) @ V1) @ V5) @ V3)) @ V4)))))))) @ V4))))))))))))))
(TTransitive_Closure.sym_trancl,(call @ (^[V0]: ((c==> @ (cRelation.sym @ V0)) @ (cRelation.sym @ (cTransitive_Closure.trancl @ V0))))))
(TTransitive_Closure.trancl_def,((c== @ cTransitive_Closure.trancl) @ (^[V0]: (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (((cTransitive_Closure.tranclp @ (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)))) @ V1) @ V2))))))))
(TTypedef.type_definition.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cSet.member @ (V0 @ V3)) @ V1)))) @ ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V2 @ (V0 @ V3))) @ V3)))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cHOL.eq @ (V0 @ (V2 @ V3))) @ V3))))) @ (((cTypedef.type_definition @ V0) @ V2) @ V1)))))))))))
(TTyperep.arity_typerep_integer,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_literal,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_natural,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_typerep,(cTyperep.typerep_class @ cTYPE))
(TWellfounded.acc_downwards_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cHOL.implies @ ((cSet.member @ V1) @ (cWellfounded.acc @ V2))) @ ((cSet.member @ V0) @ (cWellfounded.acc @ V2)))))))))))
(TWellfounded.acc_subset_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (cWellfounded.acc @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V4)) @ V1)) @ ((cSet.member @ V5) @ V0)))))))) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V4)) @ V1)) @ (V3 @ V5))))) @ (V3 @ V4)))))) @ (V3 @ V2))))))))))))))
(TWellfounded.finite_acyclic_wf,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cTransitive_Closure.acyclic @ V0)) @ (cWellfounded.wf @ V0))))))
(TWellfounded.in_finite_psubset,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ cWellfounded.finite_psubset)) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cFinite_Set.finite @ V1))))))))
(TWellfounded.max_extp.max_extI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ (cSet.Collect @ (^[V3]: (cOrderings.bot_class.bot @ V3)))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cSet.Bex @ V1) @ (V2 @ V3)))))) @ (((cWellfounded.max_extp @ V2) @ V0) @ V1))))))))))))
(TWellfounded.wf_finite_psubset,(cWellfounded.wf @ cWellfounded.finite_psubset))
(TWellfounded.wf_map_pair_image,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ ((cFun.inj_on @ V1) @ cOrderings.top_class.top)) @ (cWellfounded.wf @ ((cSet.image @ ((cProduct_Type.map_pair @ V1) @ V1)) @ V0)))))))))
(TBig_Operators.card_UN_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ (V1 @ V2))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V1 @ V2)) @ (V1 @ V3))) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ (cFinite_Set.card @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cFinite_Set.card @ (V1 @ V2)))) @ V0))))))))))
(TBig_Operators.linorder.Max_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cBig_Operators.linorder.Max @ V0)) @ (cBig_Operators.semilattice_set.F @ (cOrderings.ord.max @ V0)))))))))
(TBig_Operators.linorder.Max_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((V0 @ V4) @ V3))))) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((cHOL.eq @ ((cBig_Operators.linorder.Max @ V0) @ V2)) @ V3))))))))))))))
(TBig_Operators.linorder.Min_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cBig_Operators.linorder.Min @ V0)) @ (cBig_Operators.semilattice_set.F @ (cOrderings.ord.min @ V0)))))))))
(TBig_Operators.linorder.Min_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((V0 @ V3) @ V4))))) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((cHOL.eq @ ((cBig_Operators.linorder.Min @ V0) @ V2)) @ V3))))))))))))))
(TBig_Operators.setprod_constant,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: V1)) @ V0)) @ ((cPower.power_class.power @ V1) @ (cFinite_Set.card @ V0)))))))))
(TBig_Operators.setprod_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ cNat.one_nat_inst.one_nat)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cNat.one_nat_inst.one_nat))))))))))
(TBig_Operators.setprod_infinite,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ cGroups.one_class.one)))))))
(TBig_Operators.setprod_inversef,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ ((cFun.comp @ cFields.inverse_class.inverse) @ V1)) @ V0)) @ (cFields.inverse_class.inverse @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)))))))))
(TBig_Operators.setprod_zero_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ cGroups.zero_class.zero)) @ ((cSet.Bex @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cGroups.zero_class.zero))))))))))
(TBig_Operators.setsum_diff1_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ (((cHOL.If @ ((cSet.member @ V2) @ V1)) @ ((cNat.minus_nat_inst.minus_nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ (V0 @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1))))))))))
(TBig_Operators.setsum_subtractf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cGroups.minus_class.minus @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((cGroups.minus_class.minus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V2))))))))))
(TCode_Evaluation.equal_term_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TCode_Evaluation.term.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cCode_Evaluation.term.dummy_term)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cCode_Evaluation.term.term_case @ V2) @ V0)) @ ((cCode_Evaluation.term.term_case @ V3) @ V1)))))))))))))
(TCode_Evaluation.term.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cCode_Evaluation.term.term_case @ V1) @ V2))) @ (cHOL.Not @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cCode_Evaluation.term.dummy_term)) @ (cHOL.Not @ (V0 @ V1))))))))))))
(TCode_Numeral.equal_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TCode_Numeral.equal_integer_def,((c== @ cHOL.equal_class.equal) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cFun.id)) @ cHOL.equal_class.equal)))
(TCode_Numeral.equal_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TCode_Numeral.equal_natural_def,((c== @ cHOL.equal_class.equal) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cFun.id)) @ cHOL.equal_class.equal)))
(TCode_Numeral.integer.bi_unique,(cTransfer.bi_unique @ cCode_Numeral.pcr_integer))
(TCode_Numeral.integer.pcr_cr_eq,((cHOL.eq @ cCode_Numeral.pcr_integer) @ cCode_Numeral.cr_integer))
(TCode_Numeral.less_integer_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Neg @ V1))) @ ((cNum.ord_num_inst.less_num @ V1) @ V0)))))))
(TCode_Numeral.less_integer_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Pos @ V1))) @ cHOL.True))))))
(TCode_Numeral.less_integer_code_7,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ (cCode_Numeral.Neg @ V0)) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.True))))
(TCode_Numeral.less_integer_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Neg @ V1))) @ cHOL.False))))))
(TCode_Numeral.less_integer_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Pos @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TCode_Numeral.less_integer_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ (cCode_Numeral.Pos @ V0)) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.False))))
(TCode_Numeral.less_integer_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.Neg @ V0))) @ cHOL.False))))
(TCode_Numeral.less_integer_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.Pos @ V0))) @ cHOL.True))))
(TCode_Numeral.less_integer_code_1,((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.False))
(TCode_Numeral.minus_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cInt.minus_int_inst.minus_int) @ cInt.minus_int_inst.minus_int))
(TCode_Numeral.minus_integer_def,((c== @ cCode_Numeral.minus_integer_inst.minus_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int)) @ cInt.minus_int_inst.minus_int)))
(TCode_Numeral.minus_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cNat.minus_nat_inst.minus_nat) @ cNat.minus_nat_inst.minus_nat))
(TCode_Numeral.minus_natural_def,((c== @ cCode_Numeral.minus_natural_inst.minus_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.natural_of_nat)) @ cNat.minus_nat_inst.minus_nat)))
(TCode_Numeral.natural.bi_unique,(cTransfer.bi_unique @ cCode_Numeral.pcr_natural))
(TCode_Numeral.natural.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ (cCode_Numeral.Suc @ V6))) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ (((cCode_Numeral.natural.natural_case @ V2) @ V4) @ V0)) @ (((cCode_Numeral.natural.natural_case @ V3) @ V5) @ V1))))))))))))))))))
(TCode_Numeral.natural.pcr_cr_eq,((cHOL.eq @ cCode_Numeral.pcr_natural) @ cCode_Numeral.cr_natural))
(TCode_Numeral.natural.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cCode_Numeral.natural.natural_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cCode_Numeral.Suc @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TCode_Numeral.of_int_integer_of,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cCode_Numeral.int_of_integer @ V0))) @ V0))))
(TCode_Numeral.of_nat_of_integer,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_integer @ V0))) @ ((cOrderings.ord_class.max @ cCode_Numeral.zero_integer_inst.zero_integer) @ V0)))))
(TCode_Numeral.of_nat_of_natural,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_natural @ V0))) @ V0))))
(TCode_Numeral.plus_integer_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.plus_integer_inst.plus_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Neg @ V1))) @ (cCode_Numeral.Neg @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TCode_Numeral.plus_integer_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.plus_integer_inst.plus_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Pos @ V1))) @ ((cCode_Numeral.sub @ V1) @ V0)))))))
(TCode_Numeral.plus_integer_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.plus_integer_inst.plus_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Neg @ V1))) @ ((cCode_Numeral.sub @ V0) @ V1)))))))
(TCode_Numeral.plus_integer_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.plus_integer_inst.plus_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Pos @ V1))) @ (cCode_Numeral.Pos @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TCode_Numeral.plus_integer_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.plus_integer_inst.plus_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ V0)) @ V0))))
(TCode_Numeral.plus_integer_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ V0))))
(TCode_Numeral.times_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cInt.times_int_inst.times_int) @ cInt.times_int_inst.times_int))
(TCode_Numeral.times_integer_def,((c== @ cCode_Numeral.times_integer_inst.times_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int)) @ cInt.times_int_inst.times_int)))
(TCode_Numeral.times_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cNat.times_nat_inst.times_nat) @ cNat.times_nat_inst.times_nat))
(TCode_Numeral.times_natural_def,((c== @ cCode_Numeral.times_natural_inst.times_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.natural_of_nat)) @ cNat.times_nat_inst.times_nat)))
(TComplete_Lattices.INT_constant,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: V1))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top) @ V1)))))))
(TComplete_Lattices.INT_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ (V2 @ V3)))))) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.Inf_bool_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_bool_inst.Inf_bool @ V0)) @ (cHOL.Not @ ((cSet.member @ cHOL.False) @ V0))))))
(TComplete_Lattices.Inter_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cSet.insert @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))))))))
(TComplete_Lattices.Inter_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1))))))))
(TComplete_Lattices.Sup_bool_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_bool_inst.Sup_bool @ V0)) @ ((cSet.member @ cHOL.True) @ V0)))))
(TComplete_Lattices.UN_singleton,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ V0))))
(TComplete_Lattices.Union_Pow_eq,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ (cSet.Pow @ V0))) @ V0))))
(TComplete_Lattices.Union_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.insert @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.vimage_Union,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.vimage @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: ((cSet.vimage @ V0) @ V2)))))))))
(TComplete_Lattices.vimage_eq_UN,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.vimage @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: ((cSet.vimage @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))))))))
(TDatatype.node.Abs_Node_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cDatatype.Node)) @ ((cHOL.eq @ (cDatatype.Rep_Node @ (cDatatype.Abs_Node @ V0))) @ V0)))))
(TDatatype.node.Rep_Node_inverse,(call @ (^[V0]: ((cHOL.eq @ (cDatatype.Abs_Node @ (cDatatype.Rep_Node @ V0))) @ V0))))
(TDivides.arity_semiring_div_nat,(cDivides.semiring_div_class @ cTYPE))
(TDivides.class.semiring_div_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((cRings.class.comm_semiring_1_cancel @ V3) @ V4) @ V0) @ V5)) @ ((cHOL.conj @ ((cRings.class.no_zero_divisors @ V0) @ V4)) @ (((((cDivides.class.semiring_div_axioms @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))))
(TDivides.divmod_int_rel_div_mod,(call @ (^[V0]: (call @ (^[V1]: (((cDivides.divmod_int_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V0) @ V1)) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))))))))
(TDivides.divmod_nat_rel_add1_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((c==> @ (((cDivides.divmod_nat_rel @ V4) @ V1) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cDivides.divmod_nat_rel @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V4)) @ V1) @ ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V5)) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V6)) @ V1))) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V6)) @ V1))))))))))))))))))))
(TDivides.negDivAlg_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.negDivAlg_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.negDivAlg_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.negDivAlg_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.negDivAlg_graph @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))))) @ ((cDivides.negDivAlg_graph @ ((cProduct_Type.Pair @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))) @ ((cDivides.adjust @ V1) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))))))))))))))
(TDivides.posDivAlg_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.posDivAlg_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.posDivAlg_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.posDivAlg_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.posDivAlg_graph @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))))) @ ((cDivides.posDivAlg_graph @ ((cProduct_Type.Pair @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cDivides.adjust @ V1) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))))))))))))))
(TDivides.ring_div.mod_diff_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ ((V2 @ V8) @ V9)) @ ((V2 @ V10) @ V9))) @ ((c==> @ ((cHOL.eq @ ((V2 @ V11) @ V9)) @ ((V2 @ V12) @ V9))) @ ((cHOL.eq @ ((V2 @ ((V6 @ V8) @ V11)) @ V9)) @ ((V2 @ ((V6 @ V10) @ V12)) @ V9))))))))))))))))))))))))))))))))
(TDivides.semiring_div.div_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((((cPower.power.power @ V5) @ V0) @ ((V1 @ V7) @ V6)) @ V8)) @ ((V1 @ ((((cPower.power.power @ V5) @ V0) @ V7) @ V8)) @ ((((cPower.power.power @ V5) @ V0) @ V6) @ V8))))))))))))))))))))))))
(TDivides.semiring_div.power_mod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((((cPower.power.power @ V5) @ V0) @ ((V2 @ V6) @ V7)) @ V8)) @ V7)) @ ((V2 @ ((((cPower.power.power @ V5) @ V0) @ V6) @ V8)) @ V7))))))))))))))))))))))
(TDivides.semiring_div_class_def,((c== @ (cDivides.semiring_div_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cDivides.div_class @ cTYPE)) @ (cRings.comm_semiring_1_cancel_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.no_zero_divisors_class @ cTYPE)) @ (((((cDivides.class.semiring_div_axioms @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))))
(TEnum.enum_fun_inst.enum_ex_fun,((c== @ cEnum.enum_fun_inst.enum_ex_fun) @ cEnum.enum_fun_inst.enum_ex_fun))
(TEnum.enum_set_inst.enum_ex_set,((c== @ cEnum.enum_set_inst.enum_ex_set) @ cEnum.enum_set_inst.enum_ex_set))
(TEnum.enum_sum_inst.enum_ex_sum,((c== @ cEnum.enum_sum_inst.enum_ex_sum) @ cEnum.enum_sum_inst.enum_ex_sum))
(TEnum.finite_1.finite_1_rec_def,((c== @ cEnum.finite_1.finite_1_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cEnum.finite_1.finite_1_rec_set @ V0) @ V1) @ V2)))))))
(TEnum.finite_2.finite_2_rec_def,((c== @ cEnum.finite_2.finite_2_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cEnum.finite_2.finite_2_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TEnum.finite_3.finite_3_rec_def,((c== @ cEnum.finite_3.finite_3_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cHOL.The @ (^[V4]: (((((cEnum.finite_3.finite_3_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)))))))))
(TEnum.finite_4.finite_4_rec_def,((c== @ cEnum.finite_4.finite_4_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (cHOL.The @ (^[V5]: ((((((cEnum.finite_4.finite_4_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))
(TEnum.finite_5.finite_5_rec_def,((c== @ cEnum.finite_5.finite_5_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (cHOL.The @ (^[V6]: (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)))))))))))
(TEquiv_Relations.UN_constant_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ V3)))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V2 @ V4)))) @ V3))))))))))))
(TEquiv_Relations.UN_equiv_class,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cEquiv_Relations.congruent @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cRelation.Image @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))) @ (^[V4]: (V2 @ V4)))) @ (V2 @ V3))))))))))))))
(TEquiv_Relations.Union_quotient,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ V0)))))))
(TEquiv_Relations.congruent2_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cEquiv_Relations.congruent2 @ V0) @ V1) @ V2)) @ ((cSet.Ball @ V0) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cSet.Ball @ V1) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cHOL.eq @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V6))))))))))))))))))
(TEquiv_Relations.eq_equiv_class,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cRelation.Image @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))) @ ((c==> @ ((cEquiv_Relations.equiv @ V3) @ V0)) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)))))))))))))
(TEquiv_Relations.equiv_class_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)) @ ((cHOL.eq @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))))))))))))))
(TEquiv_Relations.quotient_diff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ (^[V3]: ((cEquiv_Relations.quotient @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)) @ V0))) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ ((cEquiv_Relations.quotient @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ V0)) @ ((cGroups.minus_class.minus @ ((cEquiv_Relations.quotient @ V1) @ V0)) @ ((cEquiv_Relations.quotient @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)) @ V0))))))))))))
(TEquiv_Relations.quotient_empty,(call @ (^[V0]: ((cHOL.eq @ ((cEquiv_Relations.quotient @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TExtraction.arity_equal_sumbool,(cHOL.equal_class @ cTYPE))
(TExtraction.sumbool.Rep_sumbool,(call @ (^[V0]: ((cSet.member @ (cExtraction.Rep_sumbool @ V0)) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set)))))
(TFields.class.division_ring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((cRings.class.ring_1 @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cFields.class.division_ring_axioms @ V0) @ V1) @ V2) @ V3) @ V5))))))))))))))))))))
(TFields.division_ring.inverse_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ V2)) @ V2)))))))))))))))))))
(TFields.division_ring_class_def,((c== @ (cFields.division_ring_class @ cTYPE)) @ ((cPure.conjunction @ (cFields.inverse_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.ring_1_class @ cTYPE)) @ (((((cFields.class.division_ring_axioms @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.zero_class.zero)))))
(TFields.field.add_divide_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V4 @ V9) @ ((V1 @ V10) @ V8))) @ ((V1 @ ((V4 @ ((V2 @ V8) @ V9)) @ V10)) @ V8)))))))))))))))))))))))))))
(TFields.field.divide_add_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V4 @ ((V1 @ V9) @ V8)) @ V10)) @ ((V1 @ ((V4 @ V9) @ ((V2 @ V8) @ V10))) @ V8)))))))))))))))))))))))))))
(TFields.field_class.add_frac_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cFields.inverse_class.divide @ V2) @ V0)) @ ((cFields.inverse_class.divide @ V3) @ V1))) @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V3) @ V0))) @ ((cGroups.times_class.times @ V0) @ V1))))))))))))))
(TFields.field_class.inverse_add,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ (cFields.inverse_class.inverse @ V0))) @ (cFields.inverse_class.inverse @ V1))))))))))
(TFinite_Set.arity_finite_option,(cFinite_Set.finite_class @ cTYPE))
(TFinite_Set.card.folding_axioms,(cFinite_Set.folding @ (^[V0]: cNat.Suc)))
(TFinite_Set.card_Collect_le_nat,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V0))))) @ (cNat.Suc @ V0)))))
(TFinite_Set.card_Diff_singleton,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V0)) @ cNat.one_nat_inst.one_nat)))))))))
(TFinite_Set.comp_fun_idem.intro,(call @ (^[V0]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.comp_fun_idem_axioms @ V0)) @ (cFinite_Set.comp_fun_idem @ V0))))))
(TFinite_Set.finite_class.axioms,(cFinite_Set.class.finite @ cTYPE))
(TFinite_Set.finite_class.finite,(call @ (^[V0]: (cFinite_Set.finite @ V0))))
(TFinite_Set.finite_empty_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (V1 @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cGroups.minus_class.minus @ V3) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))))))))) @ (V1 @ cOrderings.bot_class.bot)))))))))
(TFinite_Set.finite_range_imageI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cSet.image @ V0) @ cOrderings.top_class.top))) @ (cFinite_Set.finite @ ((cSet.image @ (^[V2]: (V1 @ (V0 @ V2)))) @ cOrderings.top_class.top))))))))
(TFinite_Set.finite_subset_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.image @ V1) @ V2))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((cHOL.conj @ (cFinite_Set.finite @ V3)) @ ((cHOL.eq @ V0) @ ((cSet.image @ V1) @ V3)))))))))))))))
(TFinite_Set.folding_idem.axioms_2,(call @ (^[V0]: ((c==> @ (cFinite_Set.folding_idem @ V0)) @ (cFinite_Set.folding_idem_axioms @ V0)))))
(TFinite_Set.folding_idem.axioms_1,(call @ (^[V0]: ((c==> @ (cFinite_Set.folding_idem @ V0)) @ (cFinite_Set.folding @ V0)))))
(TFinite_Set.pigeonhole_infinite,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((c==> @ (cFinite_Set.finite @ ((cSet.image @ V1) @ V0))) @ ((cSet.Bex @ V0) @ (^[V2]: (cHOL.Not @ (cFinite_Set.finite @ (cSet.Collect @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V2))))))))))))))))
(TFunDef.termination_basic_simps_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TFunDef.termination_basic_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TFunDef.termination_basic_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TFunDef.termination_basic_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V1))))))))))
(TFunDef.termination_basic_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TGroups.ab_semigroup_add.add_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ V2) @ ((V0 @ V1) @ V3)))))))))))))
(TGroups.ab_semigroup_add.add_ac_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.ab_semigroup_add.add_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TGroups.class.monoid_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cGroups.class.monoid_add_axioms @ V0) @ V1)))))))
(TGroups.class.monoid_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ (cGroups.class.semigroup_add @ V0)))))))
(TGroups.class.monoid_mult.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.class.semigroup_mult @ V0)) @ ((c==> @ ((cGroups.class.monoid_mult_axioms @ V1) @ V0)) @ ((cGroups.class.monoid_mult @ V1) @ V0))))))))
(TGroups.class.semigroup_add_def,(call @ (^[V0]: ((c== @ (cGroups.class.semigroup_add @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TGroups.comm_monoid_mult.mult_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))))))))
(TGroups.group_add.diff_diff_eq2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V1 @ V4) @ V6)) @ V5))))))))))))))))))
(TGroups.group_add.equals_zero_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ ((V1 @ V4) @ V5)) @ V2)) @ ((cHOL.eq @ (V3 @ V4)) @ V5))))))))))))))))
(TGroups.group_add.minus_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ ((V0 @ V4) @ V5))) @ ((V0 @ V5) @ V4))))))))))))))))
(TGroups.monoid_add_class.axioms,((cGroups.class.monoid_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.monoid_mult.mult_1_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V0) @ V2)) @ V2)))))))))
(TGroups.monoid_mult_class.intro,((c==> @ (cGroups.one_class @ cTYPE)) @ ((c==> @ (cGroups.semigroup_mult_class @ cTYPE)) @ ((c==> @ ((cGroups.class.monoid_mult_axioms @ cGroups.one_class.one) @ cGroups.times_class.times)) @ (cGroups.monoid_mult_class @ cTYPE)))))
(TGroups.monoid_mult_class.super_2,((c==> @ (cGroups.monoid_mult_class @ cTYPE)) @ (cGroups.semigroup_mult_class @ cTYPE)))
(TGroups.monoid_mult_class.super_1,((c==> @ (cGroups.monoid_mult_class @ cTYPE)) @ (cGroups.one_class @ cTYPE)))
(TGroups.semigroup_add.add_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.semigroup_add @ V0)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TGroups.semigroup_add_class_def,((c== @ (cGroups.semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.plus_class @ cTYPE)) @ (cGroups.class.semigroup_add @ cGroups.plus_class.plus))))
(THilbert_Choice.LeastM_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ (V2 @ V3)))))) @ ((cHOL.eq @ (V2 @ ((cHilbert_Choice.LeastM @ V2) @ (^[V3]: (V0 @ V3))))) @ (V2 @ V1)))))))))))
(THilbert_Choice.bij_imp_bij_inv,(call @ (^[V0]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ (((cFun.bij_betw @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ cOrderings.top_class.top) @ cOrderings.top_class.top)))))
(THilbert_Choice.inj_on_iff_surj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cFun.inj_on @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V2) @ V0)) @ V1))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ ((cSet.image @ V2) @ V1)) @ V0))))))))))
(THilbert_Choice.inj_on_inv_into,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet.image @ V1) @ V2))) @ ((cFun.inj_on @ ((cHilbert_Choice.inv_into @ V2) @ V1)) @ V0)))))))))
(THilbert_Choice.some_eq_trivial,(call @ (^[V0]: ((cHOL.eq @ (cHilbert_Choice.Eps @ (^[V1]: ((cHOL.eq @ V1) @ V0)))) @ V0))))
(THilbert_Choice.surj_imp_inv_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((c==> @ (cHOL.All @ (^[V2]: ((cHOL.eq @ (V1 @ (V0 @ V2))) @ V2)))) @ ((cHOL.eq @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ V1))))))))
(TInductive.coinduct3_mono_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ (cOrderings.order_class.mono @ (^[V3]: ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ (V0 @ V3)) @ V1)) @ V2)))))))))))
(TInductive.def_Collect_coinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c== @ V0) @ (cInductive.complete_lattice_class.gfp @ (^[V4]: (cSet.Collect @ (V1 @ V4)))))) @ ((c==> @ (cOrderings.order_class.mono @ (^[V4]: (cSet.Collect @ (V1 @ V4))))) @ ((c==> @ ((cSet.member @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V3)) @ ((V1 @ ((cLattices.sup_class.sup @ V3) @ V0)) @ V4))))) @ ((cSet.member @ V2) @ V0))))))))))))))
(TInt.equation_minus_iff_numeral_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cHOL.eq @ V1) @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V0)))))))))
(TInt.equation_minus_iff_numeral_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cHOL.eq @ V1) @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0)))))))))
(TInt.minus_equation_iff_numeral_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ V0)))))))
(TInt.minus_equation_iff_numeral_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V1))) @ V0)))))))
(TInt.right_diff_distrib_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))))))))))
(TInt.ring_1_class.of_int.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cInt.Abs_Integ @ V0))) @ ((cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cGroups.minus_class.minus @ (cNat.semiring_1_class.of_nat @ V1)) @ (cNat.semiring_1_class.of_nat @ V2))))) @ V0)))))
(TInt.ring_1_class.of_int.rep_eq,(call @ (^[V0]: ((c== @ (cInt.ring_1_class.of_int @ V0)) @ ((cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cGroups.minus_class.minus @ (cNat.semiring_1_class.of_nat @ V1)) @ (cNat.semiring_1_class.of_nat @ V2))))) @ (cInt.Rep_Integ @ V0))))))
(TInt.ring_1_class.of_int_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ (cGroups.uminus_class.uminus @ (cNat.semiring_1_class.of_nat @ (cInt.nat @ (cInt.uminus_int_inst.uminus_int @ V0))))) @ (cNat.semiring_1_class.of_nat @ (cInt.nat @ V0)))))))
(TInt.uminus_int_inst.uminus_int,((c== @ cInt.uminus_int_inst.uminus_int) @ cInt.uminus_int_inst.uminus_int))
(TInt.zero_le_divide_iff_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ (cNum.numeral_class.numeral @ V0)) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)))))))))
(TLattices.semilattice.left_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cLattices.semilattice @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V1) @ V2))) @ ((V0 @ V1) @ V2))))))))))
(TLattices.semilattice_neutr_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLattices.semilattice_neutr @ V0) @ V1)) @ ((cHOL.conj @ (cLattices.semilattice @ V0)) @ ((cGroups.comm_monoid @ V0) @ V1))))))))
(TLattices.semilattice_order_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cLattices.semilattice @ V0)) @ (((cLattices.semilattice_order_axioms @ V0) @ V1) @ V2))))))))))
(TLazy_Sequence.iterate_upto_def,((c== @ cLazy_Sequence.iterate_upto) @ (^[V0]: (^[V1]: (^[V2]: (cLazy_Sequence.iterate_upto_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TLifting.Quotient_to_left_total,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cRelation.reflp @ V0)) @ (cLifting.left_total @ V3))))))))))))
(TLifting.UNIV_typedef_to_equivp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ cOrderings.top_class.top)) @ (cEquiv_Relations.equivp @ cHOL.eq)))))))
(TLifting.left_total_composition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_total @ V0)) @ ((c==> @ (cLifting.left_total @ V1)) @ (cLifting.left_total @ ((cRelation.relcompp @ V0) @ V1)))))))))
(TLifting.right_unique_conversep,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.right_unique @ (cRelation.conversep @ V0))) @ (cLifting.left_unique @ V0)))))
(TLifting.typedef_to_part_equivp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ (cEquiv_Relations.part_equivp @ (cLifting.invariant @ (^[V3]: ((cSet.member @ V3) @ V2))))))))))))
(TLifting_Option.Quotient_option,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((((cLifting.Quotient @ (cLifting_Option.option_rel @ V0)) @ (cOption.map @ V1)) @ (cOption.map @ V2)) @ (cLifting_Option.option_rel @ V3))))))))))))
(TLifting_Option.option_rel_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cLifting_Option.option_rel @ V0)) @ (cLifting_Option.option_rel @ V1))))))))
(TLifting_Product.curry_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ ((cLifting_Product.prod_rel @ V0) @ V1)) @ V2)) @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ V2))) @ cProduct_Type.curry) @ cProduct_Type.curry))))))))
(TLifting_Product.prod_rel_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cLifting_Product.prod_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((V0 @ V2) @ V4)) @ ((V1 @ V3) @ V5))))))))))))))))
(TLifting_Product.reflp_prod_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ (cRelation.reflp @ V1)) @ (cRelation.reflp @ ((cLifting_Product.prod_rel @ V0) @ V1)))))))))
(TLifting_Set.left_total_set_rel,(call @ (^[V0]: ((c==> @ (cLifting.left_total @ V0)) @ (cLifting.left_total @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Sum.left_total_sum_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_total @ V0)) @ ((c==> @ (cLifting.left_total @ V1)) @ (cLifting.left_total @ ((cLifting_Sum.sum_rel @ V0) @ V1)))))))))
(TLimited_Sequence.neg_empty_def,((cHOL.eq @ cLimited_Sequence.neg_empty) @ (^[V0]: cLazy_Sequence.empty)))
(TLimited_Sequence.neg_union_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.neg_union @ V0) @ V1)) @ (^[V2]: ((cLazy_Sequence.append @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TLimited_Sequence.pos_empty_def,((cHOL.eq @ cLimited_Sequence.pos_empty) @ (^[V0]: cLazy_Sequence.empty)))
(TLimited_Sequence.pos_union_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.pos_union @ V0) @ V1)) @ (^[V2]: ((cLazy_Sequence.append @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TList.comm_append_are_replicate,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ ((cList.append @ V1) @ V0))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ (cList.concat @ ((cList.replicate @ V2) @ V4))) @ V0)) @ ((cHOL.eq @ (cList.concat @ ((cList.replicate @ V3) @ V4))) @ V1))))))))))))))))
(TList.distinct_length_2_or_more,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.distinct @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.conj @ (cList.distinct @ ((cList.list.Cons @ V0) @ V2))) @ (cList.distinct @ ((cList.list.Cons @ V1) @ V2))))))))))))
(TList.lexord_append_left_rightI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cList.append @ V3) @ ((cList.list.Cons @ V0) @ V4))) @ ((cList.append @ V3) @ ((cList.list.Cons @ V1) @ V5)))) @ (cList.lexord @ V2))))))))))))))))
(TList.linorder.foldr_max_sorted,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ (cList.rev @ V2))) @ ((cHOL.eq @ (((cList.foldr @ (cOrderings.ord.max @ V0)) @ V2) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V2) @ cList.list.Nil)) @ V3) @ (((cOrderings.ord.max @ V0) @ ((cList.nth @ V2) @ cNat.zero_nat_inst.zero_nat)) @ V3))))))))))))))
(TList.linorder.insort_key.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ (((cHOL.If @ ((V0 @ (V2 @ V3)) @ (V2 @ V4))) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ ((cList.list.Cons @ V4) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V5))))))))))))))))))
(TList.linorder.insort_key.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ cList.list.Nil)) @ ((cList.list.Cons @ V3) @ cList.list.Nil))))))))))))
(TList.linorder.insort_left_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ (^[V5]: V5)) @ V2) @ ((((cList.linorder.insort_key @ V0) @ (^[V5]: V5)) @ V3) @ V4))) @ ((((cList.linorder.insort_key @ V0) @ (^[V5]: V5)) @ V3) @ ((((cList.linorder.insort_key @ V0) @ (^[V5]: V5)) @ V2) @ V4)))))))))))))))
(TList.linorder.sorted_dropWhile,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((cList.dropWhile @ V3) @ V2)))))))))))))
(TList.linorder.sorted_nth_monoI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V4)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V4) @ (cNat.size_class.size @ V2))) @ ((V0 @ ((cList.nth @ V2) @ V3)) @ ((cList.nth @ V2) @ V4))))))))) @ ((cList.linorder.sorted @ V0) @ V2))))))))))
(TList.linorder.sorted_takeWhile,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((cList.takeWhile @ V3) @ V2)))))))))))))
(TList.linorder_class.set_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.set @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2))) @ ((cSet.insert @ V1) @ (cList.set @ V2))))))))))
(TList.linorder_class.sorted.Nil,(cList.linorder_class.sorted @ cList.list.Nil))
(TList.linorder_class.sorted_def,((c== @ cList.linorder_class.sorted) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V3) @ V2))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: ((cOrderings.ord_class.less_eq @ V3) @ V4)))) @ (V0 @ V2)))))))))))))
(TList.list.list_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.list.list_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cList.list.list_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V3)) @ V2)))))))))) @ (V1 @ V0)))))))))
(TList.map_tailrec_rev_graph_def,((c== @ cList.map_tailrec_rev_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V5)))) @ ((cHOL.eq @ V2) @ V5))))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V6)) @ V7)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7))))))))))))))))))))))))
(TList.map_tailrec_rev_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.map_tailrec_rev_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V5) @ ((cList.list.Cons @ (V3 @ V4)) @ V6))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ V6)))) @ V2))))))))))) @ V2)))))))))
(TList.map_tailrec_rev_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map_tailrec_rev_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ (V2 @ V3)) @ V5))))) @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V4)) @ V5))))))))))))))))))
(TList.monoid_add.listsum_append,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.append @ V2) @ V3))) @ ((V0 @ (((cList.monoid_add.listsum @ V0) @ V1) @ V2)) @ (((cList.monoid_add.listsum @ V0) @ V1) @ V3)))))))))))))
(TList.remdups_adj_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.remdups_adj_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((V2 @ cList.list.Nil) @ cList.list.Nil)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cList.list.Cons @ V4) @ cList.list.Nil)) @ ((cList.list.Cons @ V4) @ cList.list.Nil))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ V5)) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V4) @ V6)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ V5)) @ ((V2 @ ((cList.list.Cons @ V4) @ V6)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((cList.remdups_adj_graph @ ((cList.list.Cons @ V5) @ V6)) @ (V3 @ ((cList.list.Cons @ V5) @ V6))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((V2 @ ((cList.list.Cons @ V5) @ V6)) @ (V3 @ ((cList.list.Cons @ V5) @ V6))))) @ ((V2 @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ (((cHOL.If @ ((cHOL.eq @ V4) @ V5)) @ (V3 @ ((cList.list.Cons @ V4) @ V6))) @ ((cList.list.Cons @ V4) @ (V3 @ ((cList.list.Cons @ V5) @ V6)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))))
(TList.remdups_adj_map_injective,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (cList.remdups_adj @ ((cList.map @ V0) @ V1))) @ ((cList.map @ V0) @ (cList.remdups_adj @ V1)))))))))
(TList.split_list_first_prop_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ (cList.set @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.append @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ ((cHOL.conj @ (V1 @ V3)) @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V5]: (cHOL.Not @ (V1 @ V5))))))))))))))))))
(TList.transpose_aux_filter_head,(call @ (^[V0]: ((cHOL.eq @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V1]: (^[V2]: ((cList.list.Cons @ V1) @ cList.list.Nil))))) @ V0))) @ ((cList.map @ (^[V1]: (cList.hd @ V1))) @ ((cList.filter @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V1) @ cList.list.Nil)))) @ V0))))))
(TList.transpose_aux_filter_tail,(call @ (^[V0]: ((cHOL.eq @ (cList.concat @ ((cList.map @ ((cList.list.list_case @ cList.list.Nil) @ (^[V1]: (^[V2]: ((cList.list.Cons @ V2) @ cList.list.Nil))))) @ V0))) @ ((cList.map @ (^[V1]: (cList.tl @ V1))) @ ((cList.filter @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ V1) @ cList.list.Nil)))) @ V0))))))
(TMap.map_le_iff_map_add_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMap.map_le @ V0) @ ((cMap.map_add @ V0) @ V1))) @ ((cHOL.eq @ ((cMap.map_add @ V0) @ V1)) @ ((cMap.map_add @ V1) @ V0))))))))
(TMap.map_upds_list_update2_drop,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ (cNat.size_class.size @ V0)) @ V1)) @ ((cHOL.eq @ (((cMap.map_upds @ V2) @ V0) @ (((cList.list_update @ V3) @ V1) @ V4))) @ (((cMap.map_upds @ V2) @ V0) @ V3))))))))))))))
(TNat.arity_comm_monoid_diff_nat,(cGroups.comm_monoid_diff_class @ cTYPE))
(TNat.arity_no_zero_divisors_nat,(cRings.no_zero_divisors_class @ cTYPE))
(TNat.dvd.lift_Suc_mono_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ (V0 @ V3)) @ (V0 @ (cNat.Suc @ V3)))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ (V0 @ (cNat.Suc @ V3))) @ (V0 @ V3))))))) @ ((cHOL.eq @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ (V0 @ V1)) @ (V0 @ V2))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ (V0 @ V2)) @ (V0 @ V1))))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TNat.dvd.order.order_iff_strict,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.dvd.order.strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TNat.linordered_idom.abs_of_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ ((((cNat.semiring_1.of_nat @ V7) @ V6) @ V3) @ V10))) @ ((((cNat.semiring_1.of_nat @ V7) @ V6) @ V3) @ V10))))))))))))))))))))))))))
(TNat.nat.size_nat_inst.size_nat,((c== @ cNat.nat.size_nat_inst.size_nat) @ cNat.nat.size_nat_inst.size_nat))
(TNat.semiring_1_class.Nats_mult,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cNat.semiring_1_class.Nats)) @ ((c==> @ ((cSet.member @ V1) @ cNat.semiring_1_class.Nats)) @ ((cSet.member @ ((cGroups.times_class.times @ V0) @ V1)) @ cNat.semiring_1_class.Nats))))))))
(TNat.semiring_char_0.inj_of_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cFun.inj_on @ (((cNat.semiring_1.of_nat @ V0) @ V2) @ V3)) @ cOrderings.top_class.top)))))))))))
(TNitpick.arity_term_of_pair_box,(cCode_Evaluation.term_of_class @ cTYPE))
(TNitpick.arity_typerep_pair_box,(cTyperep.typerep_class @ cTYPE))
(TNitpick.fun_box.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cNitpick.fun_box.fun_box_case @ V2) @ V0)) @ ((cNitpick.fun_box.fun_box_case @ V2) @ V1))))))))))
(TNitpick.norm_frac_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.norm_frac_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac_graph @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V4) @ V5)) @ (^[V6]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V4) @ V6)) @ ((cDivides.div_int_inst.div_int @ V5) @ V6)))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.norm_frac_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac_graph @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V1)) @ (cInt.uminus_int_inst.uminus_int @ V0))) @ (V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V1)) @ (cInt.uminus_int_inst.uminus_int @ V0)))))) @ ((cNitpick.norm_frac_graph @ ((cProduct_Type.Pair @ V1) @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ (V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V1)) @ (cInt.uminus_int_inst.uminus_int @ V0)))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V1) @ V0)) @ (^[V3]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V1) @ V3)) @ ((cDivides.div_int_inst.div_int @ V0) @ V3)))))))))))))))
(TNitpick.random_aux_fun_box_def,((c== @ cNitpick.random_aux_fun_box) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.fun_box.FunBox) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.fun_box.FunBox) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TNum.class.semiring_numeral_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cRings.class.semiring @ V2) @ V1))))))))))
(TNum.neg_numeral.is_num.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ (V6 @ V4)) @ ((c==> @ (call @ (^[V7]: ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V7)) @ ((c==> @ (V6 @ V7)) @ (V6 @ (V3 @ V7))))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V7)) @ ((c==> @ (V6 @ V7)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V8)) @ ((c==> @ (V6 @ V8)) @ (V6 @ ((V1 @ V7) @ V8))))))))))) @ (V6 @ V5)))))))))))))))))))))
(TNum.neg_numeral.is_num_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))))))))))))))))
(TNum.num.size_num_inst.size_num,((c== @ cNum.num.size_num_inst.size_num) @ cNum.num.size_num_inst.size_num))
(TNum.numeral_class.numeral_code_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))) @ ((cHOL.Let @ (cNum.numeral_class.numeral @ V0)) @ (^[V1]: ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V1) @ V1)) @ cGroups.one_class.one)))))))
(TNum.numeral_class.numeral_code_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))) @ ((cHOL.Let @ (cNum.numeral_class.numeral @ V0)) @ (^[V1]: ((cGroups.plus_class.plus @ V1) @ V1)))))))
(TNum.numeral_class.numeral_code_1,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ cGroups.one_class.one))
(TNum.ring_1.not_iszero_Numeral1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ cNum.num.One)))))))))))))))))
(TNum.semiring_numeral_class_def,((c== @ (cNum.semiring_numeral_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.monoid_mult_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE))))
(TNumeral_Simprocs.semiring_norm_163,(cHOL.Not @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ cNum.num.One))))
(TNumeral_Simprocs.semiring_norm_162,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_161,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_160,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_159,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_158,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0)))))))
(TNumeral_Simprocs.semiring_norm_157,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One)))))))
(TNumeral_Simprocs.semiring_norm_156,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0))))))
(TNumeral_Simprocs.semiring_norm_155,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ V0) @ cNum.num.One))))))
(TNumeral_Simprocs.semiring_norm_154,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ V1) @ V0))))))))
(TNumeral_Simprocs.semiring_norm_153,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)))))))))
(TNumeral_Simprocs.semiring_norm_152,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)))))))))
(TNumeral_Simprocs.semiring_norm_151,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_150,(call @ (^[V0]: ((cHOL.eq @ (cNat.Suc @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ V0) @ cNat.one_nat_inst.one_nat)))))
(TNumeral_Simprocs.semiring_norm_149,((cHOL.eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ cNum.num.One)))
(TNumeral_Simprocs.semiring_norm_148,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_147,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_146,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_145,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_144,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_143,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ ((cNum.neg_numeral_class.sub @ V1) @ V0)) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_142,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ ((cNum.neg_numeral_class.sub @ V0) @ V1)) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_141,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V1)) @ V2))) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))) @ V2)))))))))
(TNumeral_Simprocs.semiring_norm_140,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cNat.Suc @ V0)) @ V1)) @ (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_139,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TNumeral_Simprocs.semiring_norm_138,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cHOL.If @ cHOL.True) @ V0) @ V1)) @ V0))))))
(TNumeral_Simprocs.semiring_norm_137,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cHOL.If @ cHOL.False) @ V0) @ V1)) @ V1))))))
(TNumeral_Simprocs.semiring_norm_136,(cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNumeral_Simprocs.semiring_norm_135,(cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ cGroups.one_class.one)))
(TNumeral_Simprocs.semiring_norm_134,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNumeral_Simprocs.semiring_norm_133,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_132,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)))))
(TNumeral_Simprocs.semiring_norm_131,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_130,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TNumeral_Simprocs.semiring_norm_129,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNumeral_Simprocs.semiring_norm_128,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_127,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_126,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNumeral_Simprocs.semiring_norm_125,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cHOL.eq @ cNum.num.One) @ V0)))))
(TNumeral_Simprocs.semiring_norm_124,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ cNum.num.One)))))
(TNumeral_Simprocs.semiring_norm_123,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_122,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ cGroups.one_class.one)))
(TNumeral_Simprocs.semiring_norm_121,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ cGroups.zero_class.zero)))
(TNumeral_Simprocs.semiring_norm_120,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNumeral_Simprocs.semiring_norm_119,((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TNumeral_Simprocs.semiring_norm_118,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_117,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNumeral_Simprocs.semiring_norm_116,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_115,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNumeral_Simprocs.semiring_norm_114,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNumeral_Simprocs.semiring_norm_113,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNumeral_Simprocs.semiring_norm_112,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V1) @ V0)))))))
(TNumeral_Simprocs.semiring_norm_111,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNumeral_Simprocs.semiring_norm_110,(call @ (^[V0]: ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TNumeral_Simprocs.semiring_norm_109,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)))))
(TNumeral_Simprocs.semiring_norm_108,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ V0)))))
(TNumeral_Simprocs.semiring_norm_107,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_106,((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ cGroups.one_class.one))
(TNumeral_Simprocs.semiring_norm_105,((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ cGroups.zero_class.zero))
(TNumeral_Simprocs.semiring_norm_104,(cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNumeral_Simprocs.semiring_norm_103,((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TNumeral_Simprocs.semiring_norm_102,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_101,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNumeral_Simprocs.semiring_norm_100,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNumeral_Simprocs.semiring_norm_99,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNumeral_Simprocs.semiring_norm_98,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNumeral_Simprocs.semiring_norm_97,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNumeral_Simprocs.semiring_norm_96,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V1) @ V0)))))))
(TNumeral_Simprocs.semiring_norm_95,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNumeral_Simprocs.semiring_norm_94,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TNumeral_Simprocs.semiring_norm_93,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ cNum.num.One)))))
(TNumeral_Simprocs.semiring_norm_92,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0)))))
(TNumeral_Simprocs.semiring_norm_91,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_90,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_89,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ cHOL.False))))))
(TNumeral_Simprocs.semiring_norm_88,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ cHOL.False))))))
(TNumeral_Simprocs.semiring_norm_87,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_86,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNumeral_Simprocs.semiring_norm_85,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNumeral_Simprocs.semiring_norm_84,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ cHOL.False))))
(TNumeral_Simprocs.semiring_norm_83,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ cHOL.False))))
(TNumeral_Simprocs.semiring_norm_82,((cHOL.eq @ ((cHOL.eq @ cNum.num.One) @ cNum.num.One)) @ cHOL.True))
(TNumeral_Simprocs.semiring_norm_81,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_80,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_79,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_78,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_77,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ cHOL.True))))
(TNumeral_Simprocs.semiring_norm_76,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ cHOL.True))))
(TNumeral_Simprocs.semiring_norm_75,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_num @ V0) @ cNum.num.One)) @ cHOL.False))))
(TNumeral_Simprocs.semiring_norm_74,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_73,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_72,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_71,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_70,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNumeral_Simprocs.semiring_norm_69,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ cHOL.False))))
(TNumeral_Simprocs.semiring_norm_68,(call @ (^[V0]: ((cHOL.eq @ ((cNum.ord_num_inst.less_eq_num @ cNum.num.One) @ V0)) @ cHOL.True))))
(TNumeral_Simprocs.semiring_norm_67,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TNumeral_Simprocs.semiring_norm_66,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNumeral_Simprocs.semiring_norm_65,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNumeral_Simprocs.semiring_norm_64,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TNumeral_Simprocs.semiring_norm_63,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TNumeral_Simprocs.semiring_norm_62,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_61,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_60,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_59,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_58,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TNumeral_Simprocs.semiring_norm_57,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.zero_class.zero) @ V0)) @ (cGroups.uminus_class.uminus @ V0)))))
(TNumeral_Simprocs.semiring_norm_56,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNumeral_Simprocs.semiring_norm_55,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_54,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_53,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_52,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNumeral_Simprocs.semiring_norm_51,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNumeral_Simprocs.semiring_norm_50,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNumeral_Simprocs.semiring_norm_49,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TNumeral_Simprocs.semiring_norm_48,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TNumeral_Simprocs.semiring_norm_47,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TNumeral_Simprocs.semiring_norm_46,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_45,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNumeral_Simprocs.semiring_norm_44,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TNumeral_Simprocs.semiring_norm_43,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_42,((cHOL.eq @ (cGroups.abs_class.abs @ cGroups.one_class.one)) @ cGroups.one_class.one))
(TNumeral_Simprocs.semiring_norm_41,((cHOL.eq @ (cGroups.abs_class.abs @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNumeral_Simprocs.semiring_norm_40,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))))))
(TNumeral_Simprocs.semiring_norm_39,((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ cGroups.one_class.one)) @ cGroups.one_class.one))
(TNumeral_Simprocs.semiring_norm_38,((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ cGroups.zero_class.zero)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNumeral_Simprocs.semiring_norm_37,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit1 @ V0))))))
(TNumeral_Simprocs.semiring_norm_36,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))))))
(TNumeral_Simprocs.semiring_norm_35,((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))))
(TNumeral_Simprocs.semiring_norm_34,((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ cGroups.zero_class.zero)) @ cGroups.one_class.one))
(TNumeral_Simprocs.semiring_norm_33,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.BitM @ V0))))))
(TNumeral_Simprocs.semiring_norm_32,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))))))
(TNumeral_Simprocs.semiring_norm_31,((cHOL.eq @ (cNum.neg_numeral_class.dbl @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNumeral_Simprocs.semiring_norm_30,((cHOL.eq @ (cNum.neg_numeral_class.dbl @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNumeral_Simprocs.semiring_norm_29,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit0 @ V0))))))
(TNumeral_Simprocs.semiring_norm_28,(call @ (^[V0]: ((cHOL.eq @ (cNum.BitM @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ V0))))))
(TNumeral_Simprocs.semiring_norm_27,(call @ (^[V0]: ((cHOL.eq @ (cNum.BitM @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit1 @ (cNum.BitM @ V0))))))
(TNumeral_Simprocs.semiring_norm_26,((cHOL.eq @ (cNum.BitM @ cNum.num.One)) @ cNum.num.One))
(TNumeral_Simprocs.semiring_norm_25,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.neg_numeral_class.dbl @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_24,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.neg_numeral_class.dbl_inc @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_23,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.neg_numeral_class.dbl_dec @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_22,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.neg_numeral_class.dbl @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_21,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))))))
(TNumeral_Simprocs.semiring_norm_20,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))))))
(TNumeral_Simprocs.semiring_norm_19,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit0 @ V0))))))
(TNumeral_Simprocs.semiring_norm_18,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.BitM @ V0))))))
(TNumeral_Simprocs.semiring_norm_17,((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ cNum.num.One)) @ cGroups.zero_class.zero))
(TNumeral_Simprocs.semiring_norm_16,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))))
(TNumeral_Simprocs.semiring_norm_15,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit1 @ V0)) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_14,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ (cNum.num.Bit1 @ V1)))))))))
(TNumeral_Simprocs.semiring_norm_13,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ ((cNum.times_num_inst.times_num @ V0) @ V1)))))))))
(TNumeral_Simprocs.semiring_norm_12,(call @ (^[V0]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ cNum.num.One) @ V0)) @ V0))))
(TNumeral_Simprocs.semiring_norm_11,(call @ (^[V0]: ((cHOL.eq @ ((cNum.times_num_inst.times_num @ V0) @ cNum.num.One)) @ V0))))
(TNumeral_Simprocs.semiring_norm_10,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)) @ cNum.num.One))))))))
(TNumeral_Simprocs.semiring_norm_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_8,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNumeral_Simprocs.semiring_norm_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.num.Bit1 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNumeral_Simprocs.semiring_norm_5,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cNum.num.Bit1 @ V0)))))
(TNumeral_Simprocs.semiring_norm_4,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cNum.num.Bit0 @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNumeral_Simprocs.semiring_norm_3,(call @ (^[V0]: ((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cNum.num.Bit1 @ V0)))))
(TNumeral_Simprocs.semiring_norm_2,((cHOL.eq @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ cNum.num.One)) @ (cNum.num.Bit0 @ cNum.num.One)))
(TNumeral_Simprocs.semiring_norm_1,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.Let @ V0) @ V1)) @ (V1 @ V0)))))))
(TOption.option.Abs_option_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cOption.Abs_option @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cOption.option.option_rep_set))) @ V1))))) @ V1))))))
(TOption.option.Rep_option_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cOption.option.option_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cOption.Rep_option @ V2))) @ V1)))) @ V1)))))))
(TOrderings.arity_order_bot_bool,(cOrderings.order_bot_class @ cTYPE))
(TOrderings.arity_order_top_bool,(cOrderings.order_top_class @ cTYPE))
(TOrderings.bot_fun_inst.bot_fun,((c== @ cOrderings.bot_fun_inst.bot_fun) @ cOrderings.bot_fun_inst.bot_fun))
(TOrderings.class.linorder.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (cOrderings.class.linorder_axioms @ V0)) @ ((cOrderings.class.linorder @ V0) @ V1))))))))
(TOrderings.class.preorder.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((V0 @ V2) @ V3)) @ ((cHOL.conj @ ((V1 @ V2) @ V3)) @ (cHOL.Not @ ((V1 @ V3) @ V2))))))))) @ ((c==> @ (call @ (^[V2]: ((V1 @ V2) @ V2)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))) @ ((cOrderings.class.preorder @ V1) @ V0)))))))))
(TOrderings.linorder.less_linear,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.disj @ ((V1 @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ V3)) @ ((V1 @ V3) @ V2)))))))))))))
(TOrderings.linorder.max_of_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.mono @ V0) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ (V2 @ V3)) @ (V2 @ V4))) @ (V2 @ (((cOrderings.ord.max @ V0) @ V3) @ V4))))))))))))))))
(TOrderings.linorder.min_of_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.mono @ V0) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ (V2 @ V3)) @ (V2 @ V4))) @ (V2 @ (((cOrderings.ord.min @ V0) @ V3) @ V4))))))))))))))))
(TOrderings.linorder_class.intro,((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ (cOrderings.class.linorder_axioms @ cOrderings.ord_class.less_eq)) @ (cOrderings.linorder_class @ cTYPE))))
(TOrderings.linorder_class.super,((c==> @ (cOrderings.linorder_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TOrderings.linorder_less_linear,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.order.Least_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (V2 @ V4)) @ ((V0 @ V3) @ V4))))) @ ((cHOL.eq @ ((cOrderings.ord.Least @ V0) @ V2)) @ V3)))))))))))))
(TOrderings.order_bot.bot_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ V3) @ V0)) @ ((cHOL.eq @ V3) @ V0))))))))))))
(TOrderings.order_class.mono_def,(call @ (^[V0]: ((cHOL.eq @ (cOrderings.order_class.mono @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TOrderings.order_le_less_subst1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_le_less_subst2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_less_le_subst1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ (V1 @ V5)))))))) @ ((cOrderings.ord_class.less @ V0) @ (V1 @ V3))))))))))))))
(TOrderings.order_less_le_subst2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less @ V4) @ V5)) @ ((cOrderings.ord_class.less @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((cOrderings.ord_class.less @ (V2 @ V0)) @ V3)))))))))))))
(TOrderings.order_top.top_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V3) @ V2))))))))))))
(TOrderings.preorder.less_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((V0 @ V2) @ V3))))))))))))
(TOrderings.preorder.less_irrefl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ (cHOL.Not @ ((V1 @ V2) @ V2))))))))))
(TOrderings.preorder.order_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V2) @ V4)))))))))))))))
(TOrderings.preorder_class.intro,((c==> @ (cOrderings.ord_class @ cTYPE)) @ ((c==> @ ((cOrderings.class.preorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less)) @ (cOrderings.preorder_class @ cTYPE))))
(TOrderings.preorder_class.super,((c==> @ (cOrderings.preorder_class @ cTYPE)) @ (cOrderings.ord_class @ cTYPE)))
(TOrderings.top_fun_inst.top_fun,((c== @ cOrderings.top_fun_inst.top_fun) @ cOrderings.top_fun_inst.top_fun))
(TOrderings.wellorder.LeastI2_ex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (cHOL.Ex @ (^[V4]: (V2 @ V4)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ (V2 @ V4)) @ (V3 @ V4))))) @ (V3 @ ((cOrderings.ord.Least @ V0) @ V2))))))))))))))
(TPower.idom_class.power2_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ V1)))))))))
(TPower.monoid_mult.power_odd_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3)))) @ ((V1 @ V2) @ ((((cPower.power.power @ V0) @ V1) @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))
(TPower.ring_1.power_minus1_even,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ cNum.num.One)) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V6))) @ V0)))))))))))))))))
(TPower.ring_1_class.power_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cGroups.times_class.times @ ((cPower.power_class.power @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ V1)) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPredicate.iterate_upto.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cPredicate.iterate_upto_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cPredicate.iterate_upto_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ (((V3 @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TPredicate.iterate_upto_rel_def,((c== @ cPredicate.iterate_upto_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))))))))))))))))))
(TPredicate.map.compositionality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.map @ V0) @ ((cPredicate.map @ V1) @ V2))) @ ((cPredicate.map @ ((cFun.comp @ V0) @ V1)) @ V2)))))))))
(TPredicate.pred.Abs_pred_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cPredicate.pred.pred_rep_set))) @ (V0 @ (cPredicate.Abs_pred @ V2)))))) @ (V0 @ V1)))))))
(TPredicate.pred.Abs_pred_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.pred.pred_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cPredicate.pred.pred_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cPredicate.Abs_pred @ V0)) @ (cPredicate.Abs_pred @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TPredicate.pred.Rep_pred_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.pred.pred_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cPredicate.Rep_pred @ V2))))) @ (V1 @ V0))))))))
(TPredicate.pred.Rep_pred_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cPredicate.Rep_pred @ V0)) @ (cPredicate.Rep_pred @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TPredicate.pred.arity_size_pred,(cNat.size_class @ cTYPE))
(TPredicate.pred_of_set_fold_sup,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cPredicate.pred_of_set @ V0)) @ (((cFinite_Set.fold @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ ((cSet.image @ cPredicate.single) @ V0)))))))
(TPredicate.singleton_undefinedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cHOL.Ex1 @ (^[V2]: ((cPredicate.eval @ V0) @ V2))))) @ ((cHOL.eq @ ((cPredicate.singleton @ V1) @ V0)) @ (V1 @ cProduct_Type.Unity))))))))
(TPredicate.type_definition_pred,(((cTypedef.type_definition @ cPredicate.Rep_pred) @ cPredicate.Abs_pred) @ (cSet.Collect @ cPredicate.pred.pred_rep_set)))
(TPredicate_Compile.contains_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate_Compile.contains @ V0) @ V1)) @ ((cSet.member @ V1) @ V0)))))))
(TPredicate_Compile.pred_of_setE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.eval @ (cPredicate.pred_of_set @ V0)) @ V1)) @ ((c==> @ ((c==> @ ((cPredicate_Compile.contains @ V0) @ V1)) @ V2)) @ V2)))))))))
(TPredicate_Compile.pred_of_setI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPredicate_Compile.contains @ V0) @ V1)) @ ((cPredicate.eval @ (cPredicate.pred_of_set @ V0)) @ V1)))))))
(TProduct_Type.Compl_Times_UNIV1,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cProduct_Type.Sigma @ cOrderings.top_class.top) @ (^[V1]: V0)))) @ ((cProduct_Type.Sigma @ cOrderings.top_class.top) @ (^[V1]: (cGroups.uminus_class.uminus @ V0)))))))
(TProduct_Type.Compl_Times_UNIV2,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cProduct_Type.Sigma @ V0) @ (^[V1]: cOrderings.top_class.top)))) @ ((cProduct_Type.Sigma @ (cGroups.uminus_class.uminus @ V0)) @ (^[V1]: cOrderings.top_class.top))))))
(TProduct_Type.SetCompr_Sigma_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cHOL.conj @ (V0 @ V2)) @ ((V1 @ V2) @ V3))))))) @ ((cProduct_Type.Sigma @ (cSet.Collect @ V0)) @ (^[V2]: (cSet.Collect @ (V1 @ V2))))))))))
(TProduct_Type.Sigma_Un_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.sup_class.sup @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TProduct_Type.Sigma_Un_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cLattices.sup_class.sup @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TProduct_Type.Times_Un_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: V2))) @ ((cLattices.sup_class.sup @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: V2))) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: V2)))))))))))
(TProduct_Type.bool.bool_rec_def,((c== @ cProduct_Type.bool.bool_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cProduct_Type.bool.bool_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TProduct_Type.case_prod_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V1 @ V3) @ V4)))) @ V2))) @ ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (V0 @ ((V1 @ V3) @ V4))))) @ V2)))))))))
(TProduct_Type.fst_comp_map_pair,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ cProduct_Type.fst) @ ((cProduct_Type.map_pair @ V0) @ V1))) @ ((cFun.comp @ V0) @ cProduct_Type.fst)))))))
(TProduct_Type.map_pair.identity,((cHOL.eq @ ((cProduct_Type.map_pair @ (^[V0]: V0)) @ (^[V0]: V0))) @ cFun.id))
(TProduct_Type.prod.prod_rec_def,((c== @ cProduct_Type.prod.prod_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cProduct_Type.prod.prod_rec_set @ V0) @ V1) @ V2)))))))
(TProduct_Type.snd_comp_map_pair,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ cProduct_Type.snd) @ ((cProduct_Type.map_pair @ V0) @ V1))) @ ((cFun.comp @ V1) @ cProduct_Type.snd)))))))
(TProduct_Type.unit.unit_rec_def,((c== @ cProduct_Type.unit.unit_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cProduct_Type.unit.unit_rec_set @ V0) @ V1) @ V2)))))))
(TProduct_Type.unit_abs_eta_conv,(call @ (^[V0]: ((cHOL.eq @ (^[V1]: (V0 @ cProduct_Type.Unity))) @ V0))))
(TQuickcheck_Narrowing.apply_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.apply @ V0) @ V1) @ V2)) @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ (^[V3]: (^[V4]: ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ (^[V5]: ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ (^[V6]: (^[V7]: ((cHOL.Let @ ((cHOL.conj @ ((cCode_Numeral.ord_integer_inst.less_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ V2)) @ (cQuickcheck_Narrowing.non_empty @ V6))) @ (^[V8]: ((cHOL.Let @ (((cHOL.If @ V8) @ ((cList.map @ (^[V9]: (^[V10]: (((cList.list.list_case @ cHOL.undefined) @ (^[V11]: (^[V12]: ((V9 @ V12) @ ((cQuickcheck_Narrowing.conv @ V7) @ V11))))) @ V10)))) @ V4)) @ cList.list.Nil)) @ (^[V9]: ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ (((cHOL.If @ V8) @ ((cList.map @ (^[V10]: ((cList.list.Cons @ V6) @ V10))) @ V5)) @ cList.list.Nil))) @ V9)))))))) @ (V1 @ ((cCode_Numeral.minus_integer_inst.minus_integer @ V2) @ cCode_Numeral.one_integer_inst.one_integer))))) @ V3)))) @ (V0 @ V2))))))))))
(TQuickcheck_Narrowing.cfun.recs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.cfun.cfun_rec @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.cfun.size_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cQuickcheck_Narrowing.cfun.Constant @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Narrowing.cfun.size_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.cfun.cfun_size @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Narrowing.empty_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.empty @ V0)) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ cList.list.Nil)) @ cList.list.Nil)))))
(TQuickcheck_Narrowing.ffun.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_rec @ V0) @ V1) @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4))) @ ((((V1 @ V2) @ V3) @ V4) @ (((cQuickcheck_Narrowing.ffun.ffun_rec @ V0) @ V1) @ V4))))))))))))))
(TQuickcheck_Narrowing.ffun.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_rec @ V0) @ V1) @ (cQuickcheck_Narrowing.ffun.Constant @ V2))) @ (V0 @ V2)))))))))
(TQuickcheck_Narrowing.ffun.size_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cNat.size_class.size @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ (cNat.size_class.size @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TQuickcheck_Narrowing.ffun.size_3,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cQuickcheck_Narrowing.ffun.Constant @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Narrowing.ffun.size_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_size @ V0) @ V1) @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (V1 @ V3))) @ (((cQuickcheck_Narrowing.ffun.ffun_size @ V0) @ V1) @ V4))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))))))
(TQuickcheck_Narrowing.ffun.size_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_size @ V0) @ V1) @ (cQuickcheck_Narrowing.ffun.Constant @ V2))) @ ((cNat.plus_nat_inst.plus_nat @ (V1 @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))))
(TQuickcheck_Random.collapse_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.collapse @ V0)) @ ((cProduct_Type.scomp @ V0) @ cFun.id)))))
(TQuotient.Quotient3_part_equivp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ (cEquiv_Relations.part_equivp @ V0)))))))))
(TQuotient.Quotient3_to_Quotient,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ (V1 @ V4)) @ V5)))))) @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3))))))))))))
(TQuotient.quot_type.abs_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ ((c==> @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V0 @ V4) @ V4)) @ ((cHOL.eq @ V3) @ (cSet.Collect @ (V0 @ V4))))))) @ ((cHOL.eq @ (V2 @ (V1 @ V3))) @ V3))))))))))))
(TQuotient.quot_type.rep_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (V1 @ (V2 @ V3))) @ V3)))))))))))
(TRandom.select_weight_cons_zero,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ V1))) @ (cRandom.select_weight @ V1)))))))
(TRandom.select_weight_drop_zero,(call @ (^[V0]: ((cHOL.eq @ (cRandom.select_weight @ ((cList.filter @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1))))) @ V0))) @ (cRandom.select_weight @ V0)))))
(TRandom_Pred.iter'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Pred.iter'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ ((cQuickcheck_Random.random_class.random @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((cRandom_Pred.iter'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))))))))))))))))))))))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ ((cQuickcheck_Random.random_class.random @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))))))))))))))))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V6) @ V7)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cPredicate.Seq @ (^[V11]: ((cPredicate.seq.Insert @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V10)))))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Pred.iter'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V5) @ ((cQuickcheck_Random.random_class.random @ V1) @ V2))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V6) @ V7)) @ V5)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V6)) @ ((cRandom_Pred.iter'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V1) @ V10)))) @ (V4 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V1) @ V10)))))))))))))))))))))))) @ ((cRandom_Pred.iter'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V1) @ V2)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (^[V7]: (cPredicate.Seq @ (^[V8]: ((cPredicate.seq.Insert @ V5) @ (V4 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V1) @ V7)))))))))))))))))))))))))))
(TRandom_Pred.not_randompred_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Pred.not_randompred @ V0)) @ (^[V1]: ((cHOL.Let @ (V0 @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (((cHOL.If @ ((cPredicate.eval @ V2) @ cProduct_Type.Unity)) @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ V3)) @ ((cProduct_Type.Pair @ (cPredicate.single @ cProduct_Type.Unity)) @ V3)))))))))))
(TRandom_Sequence.Random.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.Random_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cRandom_Sequence.Random_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.Random_rel_def,((c== @ cRandom_Sequence.Random_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))))))
(TRandom_Sequence.iter_graph_def,((c== @ cRandom_Sequence.iter_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: ((cHOL.Let @ (V4 @ V6)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cOption.option.Some @ ((cProduct_Type.Pair @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V10)))))))))))))))) @ (cHOL.induct_forall @ (^[V7]: (cHOL.induct_forall @ (^[V8]: (cHOL.induct_forall @ (^[V9]: (cHOL.induct_forall @ (^[V10]: (cHOL.induct_forall @ (^[V11]: (cHOL.induct_forall @ (^[V12]: (cHOL.induct_forall @ (^[V13]: ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.induct_implies @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((cHOL.induct_implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((cHOL.induct_implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))))))))))))))))))))))))))))))))))))))
(TRandom_Sequence.iter_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.iter_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V12)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V7) @ (V3 @ V5))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ V2))))))))))))))))))))))))))) @ V2)))))))))
(TRandom_Sequence.iter_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.iter_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ V11)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ (V2 @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ ((cProduct_Type.Pair @ V7) @ V8)) @ V6)) @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V7))))))))))))))))))))))))))))))))
(TRandom_Sequence.neg_single_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.neg_single @ V0)) @ (^[V1]: (^[V2]: (^[V3]: (cLimited_Sequence.neg_single @ V0))))))))
(TRandom_Sequence.pos_Random_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.pos_Random @ V0)) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: (((cRandom_Sequence.iter @ (V0 @ V2)) @ V1) @ V3)))))))))
(TRandom_Sequence.pos_single_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.pos_single @ V0)) @ (^[V1]: (^[V2]: (^[V3]: (cLimited_Sequence.pos_single @ V0))))))))
(TRecord.isomorphic_tuple.intros_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V4)) @ V5))) @ V6)) @ ((cHOL.eq @ ((cHOL.conj @ ((cHOL.eq @ (((cRecord.iso_tuple_cons @ V0) @ V1) @ V3)) @ (((cRecord.iso_tuple_cons @ V0) @ V2) @ V4))) @ V5)) @ V6))))))))))))))))))
(TRecord.isomorphic_tuple.intros_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V1) @ V2)) @ ((cRecord.iso_tuple_update_accessor_cong_assist @ ((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_snd @ V0))))))))))))
(TRecord.isomorphic_tuple.intros_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V1) @ V2)) @ ((cRecord.iso_tuple_update_accessor_cong_assist @ ((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_fst @ V0))))))))))))
(TRecord.isomorphic_tuple.intros_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ ((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_snd @ V0))) @ (((cRecord.iso_tuple_cons @ V0) @ V7) @ V3)) @ V4) @ (((cRecord.iso_tuple_cons @ V0) @ V7) @ V5)) @ V6))))))))))))))))))))
(TRecord.isomorphic_tuple.intros_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ ((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_fst @ V0))) @ (((cRecord.iso_tuple_cons @ V0) @ V3) @ V7)) @ V4) @ (((cRecord.iso_tuple_cons @ V0) @ V5) @ V7)) @ V6))))))))))))))))))))
(TRecord.isomorphic_tuple.intros_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ (((cRecord.iso_tuple_surjective_proof_assist @ V1) @ V2) @ ((cFun.comp @ (cRecord.iso_tuple_fst @ V0)) @ V3))) @ ((c==> @ (((cRecord.iso_tuple_surjective_proof_assist @ V1) @ V4) @ ((cFun.comp @ (cRecord.iso_tuple_snd @ V0)) @ V3))) @ (((cRecord.iso_tuple_surjective_proof_assist @ V1) @ (((cRecord.iso_tuple_cons @ V0) @ V2) @ V4)) @ V3)))))))))))))))
(TRecord.isomorphic_tuple.intros_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ (V5 @ ((cFun.comp @ V2) @ V4)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4))) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V5) @ ((cFun.comp @ V2) @ V4))))))))))))))))))
(TRecord.isomorphic_tuple.intros_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ (V5 @ ((cFun.comp @ V2) @ V4)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4))) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V5) @ ((cFun.comp @ V2) @ V4))))))))))))))))))
(TRecord.isomorphic_tuple.intros_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)))))))))))))))
(TRecord.isomorphic_tuple.intros_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)))))))))))))))
(TRecord.isomorphic_tuple.intros_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ ((cFun.comp @ (V3 @ V4)) @ (V1 @ V2)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2))))))))))))))))
(TRecord.isomorphic_tuple.intros_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ ((cFun.comp @ (V3 @ V4)) @ (V1 @ V2)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2))))))))))))))))
(TRecord.isomorphic_tuple.intros_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ cFun.id) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0))))))))))))))
(TRecord.isomorphic_tuple.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ cFun.id) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0))))))))))))))
(TRecord.isomorphic_tuple.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ V1) @ (V2 @ V3))) @ ((cFun.comp @ V4) @ V1))) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ V4) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0)))))))))))))))))
(TRecord.isomorphic_tuple.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ V1) @ (V2 @ V3))) @ ((cFun.comp @ V4) @ V1))) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ V4) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0)))))))))))))))))
(TRecord.tuple_isomorphism.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V0) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TRecord.tuple_isomorphism.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRecord.tuple_isomorphism.tuple_isomorphism_rec @ V0) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TRecord.tuple_isomorphism.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V0) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TRecord.tuple_isomorphism.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1)) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TRecord.tuple_isomorphism.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TRelation.conversep_converse_eq,(call @ (^[V0]: ((cHOL.eq @ (cRelation.conversep @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cRelation.converse @ V0))))))))
(TRelation.relcomp_UNION_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcomp @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V2))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cRelation.relcomp @ V0) @ (V2 @ V3))))))))))))
(TRelation.single_valued_relcomp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.single_valued @ V0)) @ ((c==> @ (cRelation.single_valued @ V1)) @ (cRelation.single_valued @ ((cRelation.relcomp @ V0) @ V1)))))))))
(TRings.class.comm_ring_1.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cRings.class.zero_neq_one @ V1) @ V3)))))))))))))))
(TRings.class.comm_ring_1.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cRings.class.comm_ring @ V2) @ V3) @ V4) @ V5) @ V0)))))))))))))))
(TRings.class.comm_ring_1.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)))))))))))))))
(TRings.class.ordered_ring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ (((((cRings.class.ring @ V0) @ V1) @ V5) @ V6) @ V4)) @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6))))))))))))))))))
(TRings.class.zero_neq_one.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cRings.class.zero_neq_one @ V1) @ V0)))))))
(TRings.comm_semiring_1.dvd_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V5)) @ (((cRings.dvd.dvd @ V0) @ V4) @ ((V0 @ V6) @ V5)))))))))))))))))))
(TRings.comm_semiring_1.dvd_refl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cRings.dvd.dvd @ V0) @ V4) @ V4)))))))))))))
(TRings.idom_class.square_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cGroups.times_class.times @ V1) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ V1)))))))))
(TRings.linordered_idom.abs_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ ((V9 @ V10) @ V11))) @ ((V9 @ (V0 @ V10)) @ (V0 @ V11)))))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ (V8 @ V10)) @ V3)) @ ((V5 @ V10) @ V3))))))))))))))))))))))))))
(TRings.mult_zero.mult_zero_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.class.mult_zero @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V1)))))))))
(TRings.ordered_ring.le_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((V2 @ ((V0 @ ((V4 @ V7) @ V8)) @ V9)) @ ((V0 @ ((V4 @ V10) @ V8)) @ V11))) @ ((V2 @ ((V0 @ ((V4 @ ((V5 @ V7) @ V10)) @ V8)) @ V9)) @ V11))))))))))))))))))))))))))))
(TRings.ordered_ring.le_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((V2 @ ((V0 @ ((V4 @ V7) @ V8)) @ V9)) @ ((V0 @ ((V4 @ V10) @ V8)) @ V11))) @ ((V2 @ V9) @ ((V0 @ ((V4 @ ((V5 @ V10) @ V7)) @ V8)) @ V11)))))))))))))))))))))))))))))
(TRings.ordered_ring_class.intro,((c==> @ (cRings.ordered_cancel_semiring_class @ cTYPE)) @ ((c==> @ (cRings.ring_class @ cTYPE)) @ (cRings.ordered_ring_class @ cTYPE))))
(TRings.ordered_ring_class.super_2,((c==> @ (cRings.ordered_ring_class @ cTYPE)) @ (cRings.ring_class @ cTYPE)))
(TRings.ordered_ring_class.super_1,((c==> @ (cRings.ordered_ring_class @ cTYPE)) @ (cRings.ordered_cancel_semiring_class @ cTYPE)))
(TRings.ring_class.ring_distribs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TRings.ring_class.ring_distribs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TRings.ring_class.ring_distribs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TRings.ring_class.ring_distribs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TRings.zero_neq_one_class.intro,((c==> @ (cGroups.one_class @ cTYPE)) @ ((c==> @ (cGroups.zero_class @ cTYPE)) @ ((c==> @ ((cRings.class.zero_neq_one @ cGroups.one_class.one) @ cGroups.zero_class.zero)) @ (cRings.zero_neq_one_class @ cTYPE)))))
(TRings.zero_neq_one_class.super_2,((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TRings.zero_neq_one_class.super_1,((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cGroups.one_class @ cTYPE)))
(TSMT.pattern.Abs_pattern_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set))) @ (V0 @ (cSMT.Abs_pattern @ V2)))))) @ (V0 @ V1)))))))
(TSMT.pattern.Abs_pattern_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cSMT.Abs_pattern @ V0)) @ (cSMT.Abs_pattern @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TSMT.pattern.Rep_pattern_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cSMT.Rep_pattern @ V2))))) @ (V1 @ V0))))))))
(TSMT.pattern.Rep_pattern_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSMT.Rep_pattern @ V0)) @ (cSMT.Rep_pattern @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSMT.pattern.arity_size_pattern,(cNat.size_class @ cTYPE))
(TSet.uminus_set_inst.uminus_set,((c== @ cSet.uminus_set_inst.uminus_set) @ cSet.uminus_set_inst.uminus_set))
(TSet_Interval.Compl_greaterThan,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cSet_Interval.ord_class.greaterThan @ V0))) @ (cSet_Interval.ord_class.atMost @ V0)))))
(TSet_Interval.UN_finite2_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V3)) @ (^[V4]: (V0 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V1))) @ (^[V4]: (V2 @ V4))))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V3]: (V0 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V3]: (V2 @ V3))))))))))))
(TSet_Interval.atMost_subset_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.atMost @ V0)) @ (cSet_Interval.ord_class.atMost @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet_Interval.bij_betw_iff_card,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (cHOL.Ex @ (^[V2]: (((cFun.bij_betw @ V2) @ V0) @ V1)))) @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))))))))))
(TSet_Interval.setsum_atMost_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V0 @ V2))) @ (cSet_Interval.ord_class.atMost @ (cNat.Suc @ V1)))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V0 @ V2))) @ (cSet_Interval.ord_class.atMost @ V1))) @ (V0 @ (cNat.Suc @ V1)))))))))
(TSet_Interval.setsum_cl_ivl_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ (cNat.Suc @ V2)))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ (cNat.Suc @ V2)) @ V1)) @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ (V0 @ (cNat.Suc @ V2))))))))))))
(TSet_Interval.setsum_multicount,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V4]: ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V5]: ((cHOL.conj @ ((cSet.member @ V5) @ V0)) @ ((V2 @ V5) @ V4)))))) @ V3)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (cFinite_Set.card @ (cSet.Collect @ (^[V5]: ((cHOL.conj @ ((cSet.member @ V5) @ V1)) @ ((V2 @ V4) @ V5))))))) @ V0)) @ ((cNat.times_nat_inst.times_nat @ V3) @ (cFinite_Set.card @ V1)))))))))))))))
(TSet_Interval.setsum_op_ivl_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ (cNat.Suc @ V2)))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V2) @ V1)) @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ (V0 @ V2)))))))))))
(TSet_Interval.setsum_ub_add_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ cNat.one_nat_inst.one_nat))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3)))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cNat.plus_nat_inst.plus_nat @ V1) @ cNat.one_nat_inst.one_nat)) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V3)))))))))))))))
(TString.char.char_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cString.char.char_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cString.char.Char @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V2) @ ((V0 @ V4) @ V5))) @ V3))))))) @ V3)))))))))))
(TString.char.char_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cString.char.char_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cString.char.Char @ V3) @ V4))) @ ((cHOL.eq @ V2) @ ((V0 @ V3) @ V4)))))))))))))))
(TString.literal.explode_inverse,(call @ (^[V0]: ((cHOL.eq @ (cString.STR @ (cString.explode @ V0))) @ V0))))
(TString.nibble.Abs_nibble_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cString.Abs_nibble @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cString.nibble.nibble_rep_set))) @ V1))))) @ V1))))))
(TString.nibble.Rep_nibble_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.nibble.nibble_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cString.Rep_nibble @ V2))) @ V1)))) @ V1)))))))
(TString.nibble_of_nat_of_nibble,(call @ (^[V0]: ((cHOL.eq @ (cString.nibble_of_nat @ (cString.nat_of_nibble @ V0))) @ V0))))
(TString.type_definition_literal,(((cTypedef.type_definition @ cString.explode) @ cString.STR) @ cOrderings.top_class.top))
(TSum_Type.sum.sum_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cSum_Type.sum.sum_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ (cSum_Type.Inl @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ (V0 @ V5))) @ V4))))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ (cSum_Type.Inr @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ (V1 @ V5))) @ V4))))) @ V4))))))))))))))
(TSum_Type.sum.sum_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cSum_Type.sum.sum_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cSum_Type.Inl @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4)))))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cSum_Type.Inr @ V4))) @ ((cHOL.eq @ V3) @ (V1 @ V4))))))))))))))))
(TTransfer.right_unique_transfer,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_total @ V0)) @ ((c==> @ (cTransfer.right_total @ V1)) @ ((c==> @ (cTransfer.bi_unique @ V1)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq))) @ cHOL.implies) @ cTransfer.right_unique) @ cTransfer.right_unique)))))))))
(TTransfer.transfer_prover_start,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (((cTransfer.Rel @ V2) @ V1) @ V3)) @ (((cTransfer.Rel @ V2) @ V0) @ V3))))))))))))
(TTransitive_Closure.acyclic_def,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.acyclic @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ (cTransitive_Closure.trancl @ V0)))))))))
(TTransitive_Closure.ntrancl_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cTransitive_Closure.ntrancl @ (cNat.Suc @ V0)) @ V1)) @ ((cRelation.relcomp @ ((cTransitive_Closure.ntrancl @ V0) @ V1)) @ ((cLattices.sup_class.sup @ cRelation.Id) @ V1))))))))
(TTransitive_Closure.ntrancl_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cTransitive_Closure.ntrancl @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ (cNat.Suc @ V0)))))) @ (^[V2]: ((cNat.compow @ V2) @ V1)))))))))
(TTransitive_Closure.refl_reflcl,(call @ (^[V0]: ((cRelation.refl_on @ cOrderings.top_class.top) @ ((cLattices.sup_class.sup @ V0) @ cRelation.Id)))))
(TTransitive_Closure.relpowp_0_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ V3)) @ V3)))))))))))
(TTransitive_Closure.relpowp_0_I,(call @ (^[V0]: (call @ (^[V1]: ((((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V0) @ V1) @ V1))))))
(TTransitive_Closure.relpowp_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.compow @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1)) @ V2)) @ ((cRelation.relcompp @ ((cNat.compow @ V0) @ V2)) @ ((cNat.compow @ V1) @ V2))))))))))
(TTransitive_Closure.relpowp_bot,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cNat.compow @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot)))))
(TTransitive_Closure.relpowp_def,((c== @ cNat.compow) @ (^[V0]: (((cNat.nat.nat_rec @ (^[V1]: cHOL.eq)) @ (^[V1]: (^[V2]: (^[V3]: ((cRelation.relcompp @ (V2 @ V3)) @ V3))))) @ V0))))
(TTransitive_Closure.rtrancl_def,((c== @ cTransitive_Closure.rtrancl) @ (^[V0]: (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (((cTransitive_Closure.rtranclp @ (^[V3]: (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V0)))) @ V1) @ V2))))))))
(TTransitive_Closure.sym_rtrancl,(call @ (^[V0]: ((c==> @ (cRelation.sym @ V0)) @ (cRelation.sym @ (cTransitive_Closure.rtrancl @ V0))))))
(TTransitive_Closure.trancl_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cTransitive_Closure.trancl @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cSet.member @ V0) @ (cTransitive_Closure.trancl @ V2)))))))))))
(TTransitive_Closure.tranclp_def,((c== @ cTransitive_Closure.tranclp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.disj @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V5)) @ ((V0 @ V4) @ V5)))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V6)) @ ((cHOL.conj @ ((V1 @ V4) @ V5)) @ ((V0 @ V5) @ V6))))))))))))))))))
(TTyperep.arity_typerep_finite_1,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_finite_2,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_finite_3,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_finite_4,(cTyperep.typerep_class @ cTYPE))
(TTyperep.arity_typerep_finite_5,(cTyperep.typerep_class @ cTYPE))
(TTyperep.typerep.typerep_of_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cTyperep.typerep.typerep_of @ V0) @ V1)) @ (V0 @ cTYPE)))))))
(TTyperep.typerep.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cTyperep.typerep.typerep_case @ V2) @ V0)) @ ((cTyperep.typerep.typerep_case @ V2) @ V1))))))))))
(TWellfounded.accp_downwards_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((cHOL.implies @ ((cWellfounded.accp @ V0) @ V2)) @ ((cWellfounded.accp @ V0) @ V1))))))))))
(TWellfounded.accp_subset_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (cWellfounded.accp @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V0 @ V4)) @ ((c==> @ ((V1 @ V5) @ V4)) @ (V0 @ V5)))))))) @ ((c==> @ (V0 @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((V1 @ V5) @ V4)) @ (V3 @ V5))))) @ (V3 @ V4)))))) @ (V3 @ V2))))))))))))))
(TWellfounded.finite_psubset_def,((cHOL.eq @ cWellfounded.finite_psubset) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cFinite_Set.finite @ V1))))))))
(TWellfounded.wellorder_class.wf,(cWellfounded.wf @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V0) @ V1)))))))
(TWellfounded.wf_bounded_measure,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V3)) @ V0)) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ (V1 @ V4)) @ (V1 @ V3))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ V4)) @ (V1 @ V3))) @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V3)) @ (V2 @ V4)))))))))) @ (cWellfounded.wf @ V0)))))))))
(TWellfounded.wf_converse_trancl,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ (cRelation.converse @ V0))) @ (cWellfounded.wf @ (cRelation.converse @ (cTransitive_Closure.trancl @ V0)))))))
(TBig_Operators.linorder.Max_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((V0 @ ((cBig_Operators.linorder.Max @ V0) @ V2)) @ ((cBig_Operators.linorder.Max @ V0) @ V3)))))))))))))))
(TBig_Operators.linorder.dual_Max,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cBig_Operators.linorder.Max @ (^[V2]: (^[V3]: ((V0 @ V3) @ V2))))) @ (cBig_Operators.linorder.Min @ V0))))))))
(TBig_Operators.linorder.dual_Min,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cBig_Operators.linorder.Min @ (^[V2]: (^[V3]: ((V0 @ V3) @ V2))))) @ (cBig_Operators.linorder.Max @ V0))))))))
(TBig_Operators.linorder.dual_max,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cOrderings.ord.max @ (^[V2]: (^[V3]: ((V0 @ V3) @ V2))))) @ (cOrderings.ord.min @ V0))))))))
(TBig_Operators.linorder.dual_min,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cOrderings.ord.min @ (^[V2]: (^[V3]: ((V0 @ V3) @ V2))))) @ (cOrderings.ord.max @ V0))))))))
(TBig_Operators.linorder.le_maxI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((V0 @ V2) @ (((cOrderings.ord.max @ V0) @ V2) @ V3))))))))))))
(TBig_Operators.linorder.le_maxI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((V0 @ V2) @ (((cOrderings.ord.max @ V0) @ V3) @ V2))))))))))))
(TBig_Operators.setprod_gen_delta,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V4]: (((cHOL.If @ ((cHOL.eq @ V4) @ V1)) @ (V2 @ V4)) @ V3))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ ((cGroups.times_class.times @ (V2 @ V1)) @ ((cPower.power_class.power @ V3) @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V0)) @ cNat.one_nat_inst.one_nat)))) @ ((cPower.power_class.power @ V3) @ (cFinite_Set.card @ V0))))))))))))))
(TBig_Operators.setsum_diff1_ring,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ ((cGroups.minus_class.minus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ (V2 @ V1))))))))))))
(TCode_Evaluation.arity_type_term,(cHOL.type_class @ cTYPE))
(TCode_Evaluation.term_of_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))))
(TCode_Evaluation.typerep_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TCode_Numeral.abs_integer.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.abs_integer_inst.abs_integer @ (cCode_Numeral.integer_of_int @ V0))) @ (cCode_Numeral.integer_of_int @ (cInt.abs_int_inst.abs_int @ V0))))))
(TCode_Numeral.abs_integer.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.abs_integer_inst.abs_integer @ V0))) @ (cInt.abs_int_inst.abs_int @ (cCode_Numeral.int_of_integer @ V0))))))
(TCode_Numeral.arity_type_integer,(cHOL.type_class @ cTYPE))
(TCode_Numeral.arity_type_natural,(cHOL.type_class @ cTYPE))
(TCode_Numeral.div_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.div_integer_inst.div_integer @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ (cCode_Numeral.integer_of_int @ ((cDivides.div_int_inst.div_int @ V0) @ V1))))))))
(TCode_Numeral.div_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cCode_Numeral.div_integer_inst.div_integer @ V0) @ V1))) @ ((cDivides.div_int_inst.div_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.div_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.div_natural_inst.div_natural @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ (cCode_Numeral.natural_of_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1))))))))
(TCode_Numeral.div_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ ((cCode_Numeral.div_natural_inst.div_natural @ V0) @ V1))) @ ((cDivides.div_nat_inst.div_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.divmod_integer_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.divmod_integer @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cCode_Numeral.div_integer_inst.div_integer @ V0) @ V1)) @ ((cCode_Numeral.div_integer_inst.mod_integer @ V0) @ V1))))))))
(TCode_Numeral.equal_integer_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Neg @ V1))) @ ((cHOL.equal_class.equal @ V0) @ V1)))))))
(TCode_Numeral.equal_integer_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Pos @ V1))) @ cHOL.False))))))
(TCode_Numeral.equal_integer_code_7,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.Neg @ V0)) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.False))))
(TCode_Numeral.equal_integer_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Neg @ V1))) @ cHOL.False))))))
(TCode_Numeral.equal_integer_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Pos @ V1))) @ ((cHOL.equal_class.equal @ V0) @ V1)))))))
(TCode_Numeral.equal_integer_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.Pos @ V0)) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.False))))
(TCode_Numeral.equal_integer_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.Neg @ V0))) @ cHOL.False))))
(TCode_Numeral.equal_integer_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.Pos @ V0))) @ cHOL.False))))
(TCode_Numeral.equal_integer_code_1,((cHOL.eq @ ((cHOL.equal_class.equal @ cCode_Numeral.zero_integer_inst.zero_integer) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.True))
(TCode_Numeral.equal_integer_refl,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TCode_Numeral.int_of_integer_max,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.max @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.int_of_integer_min,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.min @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.int_of_integer_sub,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cNum.neg_numeral_class.sub @ V0) @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TCode_Numeral.integer_of_nat.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cNat.semiring_1_class.of_nat) @ cNat.semiring_1_class.of_nat))
(TCode_Numeral.integer_of_nat_def,((c== @ cCode_Numeral.integer_of_nat) @ (((cFun.map_fun @ cFun.id) @ cCode_Numeral.integer_of_int) @ cNat.semiring_1_class.of_nat)))
(TCode_Numeral.integer_of_num.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cNum.numeral_class.numeral) @ cNum.numeral_class.numeral))
(TCode_Numeral.integer_of_num_def,((c== @ cCode_Numeral.integer_of_num) @ (((cFun.map_fun @ cFun.id) @ cCode_Numeral.integer_of_int) @ cNum.numeral_class.numeral)))
(TCode_Numeral.minus_integer_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Neg @ V1))) @ ((cCode_Numeral.sub @ V1) @ V0)))))))
(TCode_Numeral.minus_integer_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Pos @ V1))) @ (cCode_Numeral.Neg @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TCode_Numeral.minus_integer_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Neg @ V1))) @ (cCode_Numeral.Pos @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TCode_Numeral.minus_integer_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Pos @ V1))) @ ((cCode_Numeral.sub @ V0) @ V1)))))))
(TCode_Numeral.minus_integer_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.minus_integer_inst.minus_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ V0)) @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ V0)))))
(TCode_Numeral.minus_integer_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.minus_integer_inst.minus_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ V0))))
(TCode_Numeral.mod_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.div_integer_inst.mod_integer @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ (cCode_Numeral.integer_of_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))))))))
(TCode_Numeral.mod_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cCode_Numeral.div_integer_inst.mod_integer @ V0) @ V1))) @ ((cDivides.div_int_inst.mod_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.mod_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.div_natural_inst.mod_natural @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ (cCode_Numeral.natural_of_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))))))))
(TCode_Numeral.mod_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ ((cCode_Numeral.div_natural_inst.mod_natural @ V0) @ V1))) @ ((cDivides.div_nat_inst.mod_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.nat_of_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cInt.nat) @ cInt.nat))
(TCode_Numeral.nat_of_integer_def,((c== @ cCode_Numeral.nat_of_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cFun.id) @ cInt.nat)))
(TCode_Numeral.nat_of_natural_max,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.max @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.nat_of_natural_min,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.min @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.num_of_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ ((cFun.comp @ cNum.num_of_nat) @ cInt.nat)) @ ((cFun.comp @ cNum.num_of_nat) @ cInt.nat)))
(TCode_Numeral.num_of_integer_def,((c== @ cCode_Numeral.num_of_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cFun.id) @ ((cFun.comp @ cNum.num_of_nat) @ cInt.nat))))
(TCode_Numeral.one_integer.abs_eq,((cHOL.eq @ cCode_Numeral.one_integer_inst.one_integer) @ (cCode_Numeral.integer_of_int @ cInt.one_int_inst.one_int)))
(TCode_Numeral.one_integer.rep_eq,((cHOL.eq @ (cCode_Numeral.int_of_integer @ cCode_Numeral.one_integer_inst.one_integer)) @ cInt.one_int_inst.one_int))
(TCode_Numeral.one_natural.abs_eq,((cHOL.eq @ cCode_Numeral.one_natural_inst.one_natural) @ (cCode_Numeral.natural_of_nat @ cNat.one_nat_inst.one_nat)))
(TCode_Numeral.one_natural.rep_eq,((cHOL.eq @ (cCode_Numeral.nat_of_natural @ cCode_Numeral.one_natural_inst.one_natural)) @ cNat.one_nat_inst.one_nat))
(TCode_Numeral.sgn_integer.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.sgn_integer_inst.sgn_integer @ (cCode_Numeral.integer_of_int @ V0))) @ (cCode_Numeral.integer_of_int @ (cInt.sgn_int_inst.sgn_int @ V0))))))
(TCode_Numeral.sgn_integer.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.sgn_integer_inst.sgn_integer @ V0))) @ (cInt.sgn_int_inst.sgn_int @ (cCode_Numeral.int_of_integer @ V0))))))
(TCode_Numeral.times_integer_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.times_integer_inst.times_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Neg @ V1))) @ (cCode_Numeral.Pos @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TCode_Numeral.times_integer_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.times_integer_inst.times_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Pos @ V1))) @ (cCode_Numeral.Neg @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TCode_Numeral.times_integer_code_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.times_integer_inst.times_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Neg @ V1))) @ (cCode_Numeral.Neg @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TCode_Numeral.times_integer_code_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.times_integer_inst.times_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Pos @ V1))) @ (cCode_Numeral.Pos @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TCode_Numeral.times_integer_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.times_integer_inst.times_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ V0)) @ cCode_Numeral.zero_integer_inst.zero_integer))))
(TCode_Numeral.times_integer_code_1,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.times_integer_inst.times_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cCode_Numeral.zero_integer_inst.zero_integer))))
(TCode_Numeral.uminus_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cInt.uminus_int_inst.uminus_int) @ cInt.uminus_int_inst.uminus_int))
(TCode_Numeral.uminus_integer_def,((c== @ cCode_Numeral.uminus_integer_inst.uminus_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int) @ cInt.uminus_int_inst.uminus_int)))
(TComplete_Lattices.Collect_ex_eq,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (cSet.Collect @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TComplete_Lattices.INT_anti_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.Inf_class_def,((c== @ (cComplete_Lattices.Inf_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TComplete_Lattices.Sup_class_def,((c== @ (cComplete_Lattices.Sup_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TComplete_Lattices.UN_Pow_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (cSet.Pow @ (V1 @ V2))))) @ (cSet.Pow @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2))))))))))
(TComplete_Lattices.UN_UN_flatten,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.SUPR @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))))))))))
(TComplete_Lattices.UN_Un_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.UN_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cSet.Ball @ V0) @ (^[V3]: ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V2)))))))))))
(TDivides.divmod_nat_rel_mult1_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (((cDivides.divmod_nat_rel @ ((cNat.times_nat_inst.times_nat @ V4) @ V0)) @ V1) @ ((cProduct_Type.Pair @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V4) @ V2)) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V4) @ V3)) @ V1))) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.times_nat_inst.times_nat @ V4) @ V3)) @ V1)))))))))))))))
(TDivides.divmod_nat_rel_mult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (((cDivides.divmod_nat_rel @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V4)) @ ((cProduct_Type.Pair @ ((cDivides.div_nat_inst.div_nat @ V2) @ V4)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ ((cDivides.div_nat_inst.mod_nat @ V2) @ V4))) @ V3)))))))))))))))
(TDivides.dvd_eq_mod_eq_0_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ ((cDivides.div_class.mod @ (cNum.numeral_class.numeral @ V1)) @ (cNum.numeral_class.numeral @ V0))) @ cGroups.zero_class.zero)))))))
(TDivides.negDivAlg_eqn_1_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.negDivAlg @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0)))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0)))) @ ((cDivides.adjust @ (cNum.numeral_class.numeral @ V0)) @ ((cDivides.negDivAlg @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNum.numeral_class.numeral @ V0)))))))))
(TDivides.negDivAlg_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.negDivAlg_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.negDivAlg_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cInt.plus_int_inst.plus_int @ V4) @ V5))) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.neg_imp_zdiv_nonneg_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ ((cInt.ord_int_inst.less_eq_int @ V1) @ cInt.zero_int_inst.zero_int))))))))
(TDivides.posDivAlg_eqn_1_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.posDivAlg @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ cInt.one_int_inst.one_int) @ (cNum.numeral_class.numeral @ V0))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cDivides.adjust @ (cNum.numeral_class.numeral @ V0)) @ ((cDivides.posDivAlg @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNum.numeral_class.numeral @ V0)))))))))
(TDivides.posDivAlg_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cDivides.posDivAlg_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((cDivides.posDivAlg_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.disj @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ ((cInt.ord_int_inst.less_eq_int @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cDivides.adjust @ V5) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TDivides.pos_imp_zdiv_nonneg_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.div_int @ V1) @ V0))) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1))))))))
(TDivides.ring_div.mod_minus_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ ((V2 @ V8) @ V9)) @ ((V2 @ V10) @ V9))) @ ((cHOL.eq @ ((V2 @ (V7 @ V8)) @ V9)) @ ((V2 @ (V7 @ V10)) @ V9)))))))))))))))))))))))))))
(TDivides.semiring_div.mod_add_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ V7)) @ V8)) @ ((V2 @ ((V3 @ ((V2 @ V6) @ V8)) @ ((V2 @ V7) @ V8))) @ V8))))))))))))))))))))))
(TDivides.zmod_le_nonneg_dividend,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)) @ V0)))))))
(TEnum.enum.card_UNIV_length_enum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cFinite_Set.card @ cOrderings.top_class.top)) @ (cNat.size_class.size @ V0))))))))))
(TEnum.enum_fun_inst.enum_all_fun,((c== @ cEnum.enum_fun_inst.enum_all_fun) @ cEnum.enum_fun_inst.enum_all_fun))
(TEnum.enum_set_inst.enum_all_set,((c== @ cEnum.enum_set_inst.enum_all_set) @ cEnum.enum_set_inst.enum_all_set))
(TEnum.enum_sum_inst.enum_all_sum,((c== @ cEnum.enum_sum_inst.enum_all_sum) @ cEnum.enum_sum_inst.enum_all_sum))
(TEnum.finite_1.finite_1_case_def,((c== @ cEnum.finite_1.finite_1_case) @ (^[V0]: (cEnum.finite_1.finite_1_rec @ V0))))
(TEnum.finite_1.finite_1_size_def,((c== @ cEnum.finite_1.finite_1_size) @ (cEnum.finite_1.finite_1_rec @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_2.finite_2_case_def,((c== @ cEnum.finite_2.finite_2_case) @ (^[V0]: (^[V1]: ((cEnum.finite_2.finite_2_rec @ V0) @ V1)))))
(TEnum.finite_2.finite_2_size_def,((c== @ cEnum.finite_2.finite_2_size) @ ((cEnum.finite_2.finite_2_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_3.finite_3_case_def,((c== @ cEnum.finite_3.finite_3_case) @ (^[V0]: (^[V1]: (^[V2]: (((cEnum.finite_3.finite_3_rec @ V0) @ V1) @ V2))))))
(TEnum.finite_3.finite_3_size_def,((c== @ cEnum.finite_3.finite_3_size) @ (((cEnum.finite_3.finite_3_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_4.finite_4_case_def,((c== @ cEnum.finite_4.finite_4_case) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((((cEnum.finite_4.finite_4_rec @ V0) @ V1) @ V2) @ V3)))))))
(TEnum.finite_4.finite_4_size_def,((c== @ cEnum.finite_4.finite_4_size) @ ((((cEnum.finite_4.finite_4_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_5.finite_5_case_def,((c== @ cEnum.finite_5.finite_5_case) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (((((cEnum.finite_5.finite_5_rec @ V0) @ V1) @ V2) @ V3) @ V4))))))))
(TEnum.finite_5.finite_5_size_def,((c== @ cEnum.finite_5.finite_5_size) @ (((((cEnum.finite_5.finite_5_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEquiv_Relations.UN_equiv_class2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cEquiv_Relations.equiv @ V2) @ V3)) @ ((c==> @ (((cEquiv_Relations.congruent2 @ V1) @ V3) @ V4)) @ ((c==> @ ((cSet.member @ V5) @ V0)) @ ((c==> @ ((cSet.member @ V6) @ V2)) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cRelation.Image @ V1) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ (^[V7]: ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cRelation.Image @ V3) @ ((cSet.insert @ V6) @ cOrderings.bot_class.bot))) @ (^[V8]: ((V4 @ V7) @ V8)))))) @ ((V4 @ V5) @ V6))))))))))))))))))))))
(TEquiv_Relations.finite_quotient,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V0)))) @ (cFinite_Set.finite @ ((cEquiv_Relations.quotient @ V0) @ V1)))))))))
(TEquiv_Relations.identity_equivp,(cEquiv_Relations.equivp @ cHOL.eq))
(TEquiv_Relations.part_equivp_def,(call @ (^[V0]: ((cHOL.eq @ (cEquiv_Relations.part_equivp @ V0)) @ ((cHOL.conj @ (cHOL.Ex @ (^[V1]: ((V0 @ V1) @ V1)))) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((cHOL.conj @ ((V0 @ V1) @ V1)) @ ((cHOL.conj @ ((V0 @ V2) @ V2)) @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2))))))))))))))
(TEquiv_Relations.quotient_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ ((cSet.member @ V3) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ ((c==> @ ((cSet.member @ V5) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V2) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1))))))))))))))))))))
(TFields.class.field_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.eq @ ((V1 @ (V2 @ V5)) @ V5)) @ V3))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ ((V4 @ V5) @ V6)) @ ((V1 @ V5) @ (V2 @ V6)))))))) @ (((((cFields.class.field_axioms @ V2) @ V4) @ V1) @ V3) @ V0))))))))))))))
(TFields.field.diff_divide_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V6 @ V9) @ ((V1 @ V10) @ V8))) @ ((V1 @ ((V6 @ ((V2 @ V8) @ V9)) @ V10)) @ V8)))))))))))))))))))))))))))
(TFields.field.divide_diff_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V6 @ ((V1 @ V9) @ V8)) @ V10)) @ ((V1 @ ((V6 @ V9) @ ((V2 @ V8) @ V10))) @ V8)))))))))))))))))))))))))))
(TFields.field_class.diff_frac_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cFields.inverse_class.divide @ V2) @ V0)) @ ((cFields.inverse_class.divide @ V3) @ V1))) @ ((cFields.inverse_class.divide @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V3) @ V0))) @ ((cGroups.times_class.times @ V0) @ V1))))))))))))))
(TFields.field_class.field_axioms,((((((((cFields.class.field @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TFields.linordered_field.frac_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V5) @ V12)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V10 @ V5) @ V14)) @ ((c==> @ ((V9 @ V14) @ V15)) @ ((V9 @ ((V1 @ V12) @ V15)) @ ((V1 @ V13) @ V14))))))))))))))))))))))))))))))))))))))))
(TFinite_Set.card_Diff_subset_Int,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cHOL.eq @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ ((cLattices.inf_class.inf @ V0) @ V1))))))))))
(TFinite_Set.card_insert_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ (cFinite_Set.card @ ((cSet.insert @ V1) @ V0))) @ (cNat.Suc @ (cFinite_Set.card @ V0))))))))))
(TFinite_Set.comp_fun_commute_def,(call @ (^[V0]: ((c== @ (cFinite_Set.comp_fun_commute @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V2))) @ ((cFun.comp @ (V0 @ V2)) @ (V0 @ V1)))))))))))
(TFinite_Set.comp_fun_idem.axioms_2,(call @ (^[V0]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ (cFinite_Set.comp_fun_idem_axioms @ V0)))))
(TFinite_Set.comp_fun_idem.axioms_1,(call @ (^[V0]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ (cFinite_Set.comp_fun_commute @ V0)))))
(TFinite_Set.comp_fun_idem_insert,(cFinite_Set.comp_fun_idem @ cSet.insert))
(TFinite_Set.comp_fun_idem_remove,(cFinite_Set.comp_fun_idem @ cSet.remove))
(TFinite_Set.finite_Collect_conjI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (V0 @ V2))))) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (V1 @ V2)))))) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V2)))))))))))
(TFinite_Set.finite_Collect_disjI,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ (V1 @ V2)))))) @ ((cHOL.conj @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (V0 @ V2))))) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (V1 @ V2)))))))))))
(TFinite_Set.finite_Plus_UNIV_iff,((cHOL.eq @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((cHOL.conj @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ (cFinite_Set.finite @ cOrderings.top_class.top))))
(TFinite_Set.finite_UNIV_inj_surj,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))))))
(TFinite_Set.finite_UNIV_surj_inj,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top))))))
(TFinite_Set.finite_subset_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (V2 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V3) @ V4))) @ ((c==> @ (V2 @ V4)) @ (V2 @ ((cSet.insert @ V3) @ V4))))))))))) @ (V2 @ V0))))))))))))
(TFinite_Set.infinite_UNIV_char_0,(cHOL.Not @ (cFinite_Set.finite @ cOrderings.top_class.top)))
(TGroups.ab_group_add.diff_add_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V2 @ V4) @ V5)) @ V6)) @ ((V2 @ ((V0 @ V4) @ V6)) @ V5))))))))))))))))))
(TGroups.ab_group_add_class.intro,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.minus_class @ cTYPE)) @ ((c==> @ (cGroups.uminus_class @ cTYPE)) @ ((c==> @ ((((cGroups.class.ab_group_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus)) @ (cGroups.ab_group_add_class @ cTYPE))))))
(TGroups.ab_group_add_class.super_3,((c==> @ (cGroups.ab_group_add_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE)))
(TGroups.ab_group_add_class.super_2,((c==> @ (cGroups.ab_group_add_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TGroups.ab_group_add_class.super_1,((c==> @ (cGroups.ab_group_add_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TGroups.class.ab_group_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((((cGroups.class.ab_group_add_axioms @ V0) @ V1) @ V2) @ V3)) @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3))))))))))))
(TGroups.class.monoid_mult.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cGroups.class.monoid_mult_axioms @ V0) @ V1)))))))
(TGroups.class.monoid_mult.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ (cGroups.class.semigroup_mult @ V1)))))))
(TGroups.class.semigroup_mult_def,(call @ (^[V0]: ((c== @ (cGroups.class.semigroup_mult @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TGroups.comm_monoid.comm_neutral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.comm_monoid @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))))))))
(TGroups.comm_monoid_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))) @ ((cGroups.comm_monoid_axioms @ V0) @ V1)))))))
(TGroups.group_add.right_minus_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ V2)) @ ((cHOL.eq @ V4) @ V5))))))))))))))))
(TGroups.monoid_mult.mult_1_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V2) @ V0)) @ V2)))))))))
(TGroups.monoid_mult_class.axioms,((cGroups.class.monoid_mult_axioms @ cGroups.one_class.one) @ cGroups.times_class.times))
(TGroups.semigroup_mult_class_def,((c== @ (cGroups.semigroup_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.times_class @ cTYPE)) @ (cGroups.class.semigroup_mult @ cGroups.times_class.times))))
(THilbert_Choice.Cantor_Bernstein,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((c==> @ ((cFun.inj_on @ V3) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V3) @ V2)) @ V1)) @ (cHOL.Ex @ (^[V4]: (((cFun.bij_betw @ V4) @ V1) @ V2))))))))))))))))
(THilbert_Choice.GreatestM_nat_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V4)) @ V3))))) @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ V1)) @ (V2 @ ((cHilbert_Choice.GreatestM @ V2) @ V0))))))))))))))
(THilbert_Choice.LeastM_nat_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((cHOL.conj @ (V0 @ ((cHilbert_Choice.LeastM @ V2) @ V0))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (V0 @ V3)) @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ ((cHilbert_Choice.LeastM @ V2) @ V0))) @ (V2 @ V3))))))))))))))
(THilbert_Choice.bacc_upper_bound,(call @ (^[V0]: ((cHOL.eq @ ((cHilbert_Choice.bacc @ V0) @ (cFinite_Set.card @ cOrderings.top_class.top))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: ((cHilbert_Choice.bacc @ V0) @ V1)))))))
(THilbert_Choice.ex_has_least_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ (V0 @ V3)) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ V3)) @ (V2 @ V4))))))))))))))))
(THilbert_Choice.inj_imp_surj_inv,(call @ (^[V0]: ((c==> @ ((cFun.inj_on @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)))))
(THilbert_Choice.split_paired_Eps,(call @ (^[V0]: ((cHOL.eq @ (cHilbert_Choice.Eps @ (^[V1]: (V0 @ V1)))) @ (cHilbert_Choice.Eps @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (V0 @ ((cProduct_Type.Pair @ V1) @ V2))))))))))
(THilbert_Choice.surj_imp_inj_inv,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cFun.inj_on @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ cOrderings.top_class.top)))))
(TInt.mult_le_cancel_left_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))))
(TInt.ring_1_class.of_int_numeral,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TInt.ring_char_0.of_int_0_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V3) @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6))) @ ((cHOL.eq @ V6) @ cInt.zero_int_inst.zero_int))))))))))))))))))
(TInt.ring_char_0.of_int_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (((((cInt.ring_1.of_int @ V0) @ V2) @ V3) @ V4) @ V6)) @ V3)) @ ((cHOL.eq @ V6) @ cInt.zero_int_inst.zero_int))))))))))))))))))
(TLattices.inf_bool_inst.inf_bool,((c== @ cLattices.inf_bool_inst.inf_bool) @ cLattices.inf_bool_inst.inf_bool))
(TLattices.lattice.distrib_inf_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ ((V3 @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6))) @ ((V0 @ V4) @ ((V3 @ V5) @ V6)))))))))))))))))))
(TLattices.lattice.distrib_sup_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ ((V3 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V3 @ V4) @ V5)) @ ((V3 @ V4) @ V6)))))))))))))))))))
(TLattices.lattice.inf_sup_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V3 @ V4) @ V5))) @ V4)))))))))))))))
(TLattices.lattice.sup_inf_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ V4) @ ((V0 @ V4) @ V5))) @ V4)))))))))))))))
(TLattices.semilattice.right_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cLattices.semilattice @ V0)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TLattices.semilattice_axioms_def,(call @ (^[V0]: ((c== @ (cLattices.semilattice_axioms @ V0)) @ (cHOL.All @ (^[V1]: ((cHOL.eq @ ((V0 @ V1) @ V1)) @ V1)))))))
(TLattices.semilattice_order.mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V6)) @ ((V1 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TLattices.sup_bool_inst.sup_bool,((c== @ cLattices.sup_bool_inst.sup_bool) @ cLattices.sup_bool_inst.sup_bool))
(TLazy_Sequence.Lazy_Sequence_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.Lazy_Sequence @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ (((cOption.option.option_case @ cList.list.Nil) @ (^[V1]: ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cList.list.Cons @ V2) @ (cLazy_Sequence.list_of_lazy_sequence @ V3))))) @ V1))) @ (V0 @ cProduct_Type.Unity)))))))
(TLazy_Sequence.lazy_sequence_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ V0)) @ (cLazy_Sequence.list_of_lazy_sequence @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TLazy_Sequence.lazy_sequence_rec,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_rec @ V0) @ V1)) @ (V0 @ (cLazy_Sequence.list_of_lazy_sequence @ V1))))))))
(TLazy_Sequence.small_lazy'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TLazy_Sequence.small_lazy'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cLazy_Sequence.small_lazy' @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V5)) @ ((cLazy_Sequence.small_lazy' @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))) @ V3)))))))) @ V3)))))))))))
(TLazy_Sequence.small_lazy'.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.small_lazy' @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V1)) @ ((cLazy_Sequence.small_lazy' @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))))))))))
(TLifting.left_unique_composition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_unique @ V0)) @ ((c==> @ (cLifting.left_unique @ V1)) @ (cLifting.left_unique @ ((cRelation.relcompp @ V0) @ V1)))))))))
(TLifting_Option.option_rel_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLifting_Option.option_rel @ V0) @ (cOption.option.Some @ V1)) @ (cOption.option.Some @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TLifting_Option.option_rel_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cLifting_Option.option_rel @ V0) @ cOption.option.None) @ (cOption.option.Some @ V1))) @ cHOL.False))))))
(TLifting_Option.option_rel_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cLifting_Option.option_rel @ V0) @ (cOption.option.Some @ V1)) @ cOption.option.None)) @ cHOL.False))))))
(TLifting_Option.option_rel_simps_1,(call @ (^[V0]: ((cHOL.eq @ (((cLifting_Option.option_rel @ V0) @ cOption.option.None) @ cOption.option.None)) @ cHOL.True))))
(TLifting_Option.reflp_option_rel,(call @ (^[V0]: ((c==> @ (cRelation.reflp @ V0)) @ (cRelation.reflp @ (cLifting_Option.option_rel @ V0))))))
(TLifting_Product.prod_pred_apply,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cLifting_Product.prod_pred @ V0) @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V3))))))))))))
(TLifting_Set.left_unique_set_rel,(call @ (^[V0]: ((c==> @ (cLifting.left_unique @ V0)) @ (cLifting.left_unique @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Set.right_total_set_rel,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ (cTransfer.right_total @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Sum.left_unique_sum_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_unique @ V0)) @ ((c==> @ (cLifting.left_unique @ V1)) @ (cLifting.left_unique @ ((cLifting_Sum.sum_rel @ V0) @ V1)))))))))
(TLifting_Sum.right_total_sum_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_total @ V0)) @ ((c==> @ (cTransfer.right_total @ V1)) @ (cTransfer.right_total @ ((cLifting_Sum.sum_rel @ V0) @ V1)))))))))
(TLimited_Sequence.neg_if_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.neg_if_seq @ V0)) @ (((cHOL.If @ V0) @ (cLimited_Sequence.neg_single @ cProduct_Type.Unity)) @ cLimited_Sequence.neg_empty)))))
(TLimited_Sequence.neg_single_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.neg_single @ V0)) @ (^[V1]: (cLazy_Sequence.hb_single @ V0))))))
(TLimited_Sequence.pos_if_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.pos_if_seq @ V0)) @ (((cHOL.If @ V0) @ (cLimited_Sequence.pos_single @ cProduct_Type.Unity)) @ cLimited_Sequence.pos_empty)))))
(TLimited_Sequence.pos_single_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.pos_single @ V0)) @ (^[V1]: (cLazy_Sequence.single @ V0))))))
(TList.distinct_remove1_removeAll,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ ((cList.remove1 @ V1) @ V0)) @ ((cList.removeAll @ V1) @ V0))))))))
(TList.equal_list_inst.equal_list,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TList.linorder.set_insort_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cList.set @ ((((cList.linorder.insort_insert_key @ V0) @ (^[V4]: V4)) @ V2) @ V3))) @ ((cSet.insert @ V2) @ (cList.set @ V3)))))))))))))
(TList.linorder.sorted_insort_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4)))) @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ V4)))))))))))))))
(TList.linorder_class.filter_sort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.filter @ V0) @ ((cList.linorder_class.sort_key @ V1) @ V2))) @ ((cList.linorder_class.sort_key @ V1) @ ((cList.filter @ V0) @ V2))))))))))
(TList.linorder_class.length_sort,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cList.linorder_class.sort_key @ V0) @ V1))) @ (cNat.size_class.size @ V1)))))))
(TList.linorder_class.sorted.Cons,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V1) @ V2)))) @ ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ ((cList.list.Cons @ V1) @ V0)))))))))
(TList.linorder_class.sorted_Cons,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.linorder_class.sorted @ ((cList.list.Cons @ V0) @ V1))) @ ((cHOL.conj @ (cList.linorder_class.sorted @ V1)) @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TList.linorder_class.sorted_drop,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ ((cList.drop @ V1) @ V0))))))))
(TList.linorder_class.sorted_many,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cList.linorder_class.sorted @ ((cList.list.Cons @ V1) @ V2))) @ (cList.linorder_class.sorted @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2))))))))))))
(TList.linorder_class.sorted_same,(call @ (^[V0]: (call @ (^[V1]: (cList.linorder_class.sorted @ ((cList.filter @ (^[V2]: ((cHOL.eq @ V2) @ (V0 @ V1)))) @ V1)))))))
(TList.linorder_class.sorted_sort,(call @ (^[V0]: (cList.linorder_class.sorted @ ((cList.linorder_class.sort_key @ (^[V1]: V1)) @ V0)))))
(TList.linorder_class.sorted_take,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ ((cList.take @ V1) @ V0))))))))
(TList.listrel_reflcl_if_listrel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel1 @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ (cTransitive_Closure.rtrancl @ V2)))))))))))
(TList.map_tailrec_rev_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.map_tailrec_rev_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V5) @ ((cList.list.Cons @ (V3 @ V4)) @ V6)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ V6)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TList.map_tailrec_rev_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cList.map_tailrec_rev_rel @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cList.list.Cons @ (V0 @ V2)) @ V3)))) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V1)) @ V3))))))))))))
(TList.monoid_add_class.listsum_0,(call @ (^[V0]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V1]: cGroups.zero_class.zero)) @ V0))) @ cGroups.zero_class.zero))))
(TMap.finite_range_map_of_map_add,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cSet.image @ V0) @ cOrderings.top_class.top))) @ (cFinite_Set.finite @ ((cSet.image @ ((cMap.map_add @ V0) @ (cMap.map_of @ V1))) @ cOrderings.top_class.top))))))))
(TNat.class.semiring_char_0.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cNat.class.semiring_char_0_axioms @ V0) @ V2) @ V3)) @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3))))))))))))
(TNat.dvd.dual_order.strict_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V2)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))))
(TNat.nat.nat_size_overloaded_def,((c== @ cNat.nat.size_nat_inst.size_nat) @ ((cNat.nat.nat_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))
(TNat.semiring_1.of_nat_aux.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNat.semiring_1.of_nat_aux @ V4) @ (cNat.Suc @ V5)) @ V6)) @ (((cNat.semiring_1.of_nat_aux @ V4) @ V5) @ (V4 @ V6)))))))))))))))))))
(TNat.semiring_1.of_nat_aux.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cNat.semiring_1.of_nat_aux @ V4) @ cNat.zero_nat_inst.zero_nat) @ V5)) @ V5)))))))))))))))
(TNat.semiring_1_class.Nats_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cNat.semiring_1_class.Nats)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNat.semiring_1_class.of_nat @ V2))) @ V1)))) @ V1)))))))
(TNat.semiring_1_class.of_nat_Suc,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V0))) @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNat.semiring_1_class.of_nat @ V0))))))
(TNat.semiring_1_class.of_nat_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TNat.semiring_1_class.of_nat_def,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (((cNat.compow @ V0) @ (cGroups.plus_class.plus @ cGroups.one_class.one)) @ cGroups.zero_class.zero)))))
(TNat.semiring_char_0_class.intro,((c==> @ (cRings.semiring_1_class @ cTYPE)) @ ((c==> @ (((cNat.class.semiring_char_0_axioms @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)) @ (cNat.semiring_char_0_class @ cTYPE))))
(TNat.semiring_char_0_class.super,((c==> @ (cNat.semiring_char_0_class @ cTYPE)) @ (cRings.semiring_1_class @ cTYPE)))
(TNat_Transfer.transfer_morphismI,(call @ (^[V0]: (call @ (^[V1]: ((cNat_Transfer.transfer_morphism @ V0) @ V1))))))
(TNitpick.arity_type_unsigned_bit,(cHOL.type_class @ cTYPE))
(TNitpick.fun_box.fun_box_rec_def,((c== @ cNitpick.fun_box.fun_box_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cNitpick.fun_box.fun_box_rec_set @ V0) @ V1) @ V2)))))))
(TNitpick.norm_frac_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNitpick.norm_frac_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((cNitpick.norm_frac_graph @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))))) @ ((c==> @ ((c==> @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ ((V2 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5))) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ cInt.zero_int_inst.zero_int)) @ (V3 @ ((cProduct_Type.Pair @ (cInt.uminus_int_inst.uminus_int @ V4)) @ (cInt.uminus_int_inst.uminus_int @ V5)))) @ (((cHOL.If @ ((cHOL.disj @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cHOL.eq @ V5) @ cInt.zero_int_inst.zero_int))) @ ((cProduct_Type.Pair @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int)) @ ((cHOL.Let @ ((cNitpick.int_gcd @ V4) @ V5)) @ (^[V6]: ((cProduct_Type.Pair @ ((cDivides.div_int_inst.div_int @ V4) @ V6)) @ ((cDivides.div_int_inst.div_int @ V5) @ V6)))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TNitpick.pair_box.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cNitpick.pair_box.pair_box_case @ V2) @ V0)) @ ((cNitpick.pair_box.pair_box_case @ V2) @ V1))))))))))
(TNitpick.random_aux_pair_box_def,((c== @ cNitpick.random_aux_pair_box) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.pair_box.PairBox) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.pair_box.PairBox) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TNitpick.type_definition_fun_box,(((cTypedef.type_definition @ cNitpick.Rep_fun_box) @ cNitpick.Abs_fun_box) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set)))
(TNitpick.word.word_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cNitpick.word.word_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cNitpick.word.Word @ V4))) @ ((c==> @ ((cHOL.eq @ V2) @ (V0 @ V4))) @ V3))))) @ V3)))))))))))
(TNitpick.word.word_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNitpick.word.word_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cNitpick.word.Word @ V3))) @ ((cHOL.eq @ V2) @ (V0 @ V3)))))))))))))
(TNum.classrel_ring_1_neg_numeral,(cNum.neg_numeral_class @ cTYPE))
(TNum.linordered_idom.abs_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ (((cNum.numeral.numeral @ V7) @ V6) @ V10))) @ (((cNum.numeral.numeral @ V7) @ V6) @ V10))))))))))))))))))))))))))
(TNum.neg_numeral.neg_numeral_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5)) @ (V3 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5)))))))))))))))))
(TNum.neg_numeral_class.dbl_simps_4,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.neg_numeral_class.dbl_simps_3,((cHOL.eq @ (cNum.neg_numeral_class.dbl @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNum.neg_numeral_class.dbl_simps_2,((cHOL.eq @ (cNum.neg_numeral_class.dbl @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TNum.neg_numeral_class.dbl_simps_1,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.neg_numeral_class.minus_one,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNum.num.num_size_overloaded_def,((c== @ cNum.num.size_num_inst.size_num) @ (((cNum.num.num_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))
(TNum.numeral.add_numeral_special_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V1)) @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TNum.numeral.add_numeral_special_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ (((cNum.numeral.numeral @ V1) @ V0) @ V2))) @ (((cNum.numeral.numeral @ V1) @ V0) @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V2)))))))))))
(TNum.numeral.add_numeral_special_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ V1)) @ (((cNum.numeral.numeral @ V1) @ V0) @ ((cNum.plus_num_inst.plus_num @ V2) @ cNum.num.One)))))))))))
(TNum.numeral.numeral.numeral_One,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ cNum.num.One)) @ V1)))))))
(TNum.numeral_class.numeral.simps_3,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V0))) @ cGroups.one_class.one)))))
(TNum.numeral_class.numeral.simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V0))))))
(TNum.numeral_class.numeral.simps_1,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ cGroups.one_class.one))
(TOption.option.Abs_option_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cOption.option.option_rep_set))) @ (V0 @ (cOption.Abs_option @ V2)))))) @ (V0 @ V1)))))))
(TOption.option.Abs_option_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cOption.option.option_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cOption.option.option_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cOption.Abs_option @ V0)) @ (cOption.Abs_option @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TOption.option.Rep_option_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cOption.option.option_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cOption.Rep_option @ V2))))) @ (V1 @ V0))))))))
(TOption.option.Rep_option_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cOption.Rep_option @ V0)) @ (cOption.Rep_option @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TOption.option.arity_size_option,(cNat.size_class @ cTYPE))
(TOrderings.class.dense_order_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.dense_order @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.order @ V0) @ V1)) @ (cOrderings.class.dense_order_axioms @ V1))))))))
(TOrderings.class.linorder.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ (cOrderings.class.linorder_axioms @ V0)))))))
(TOrderings.class.linorder.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cOrderings.class.order @ V0) @ V1)))))))
(TOrderings.class.order_bot.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cOrderings.class.order_bot_axioms @ V2) @ V0)) @ (((cOrderings.class.order_bot @ V2) @ V0) @ V1))))))))))
(TOrderings.class.order_top.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cOrderings.class.order_top_axioms @ V0) @ V2)) @ (((cOrderings.class.order_top @ V0) @ V1) @ V2))))))))))
(TOrderings.class.wellorder.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cOrderings.class.wellorder_axioms @ V1)) @ ((cOrderings.class.wellorder @ V0) @ V1))))))))
(TOrderings.dense_order_class_def,((c== @ (cOrderings.dense_order_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ (cOrderings.class.dense_order_axioms @ cOrderings.ord_class.less))))
(TOrderings.linorder_class.axioms,(cOrderings.class.linorder_axioms @ cOrderings.ord_class.less_eq))
(TOrderings.linorder_class.linear,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TOrderings.linorder_class.not_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TOrderings.ord.ord_eq_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((V2 @ V1) @ V3)) @ ((V2 @ V0) @ V3))))))))))))
(TOrderings.ord.ord_less_eq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((V0 @ V1) @ V3))))))))))))
(TOrderings.ord_fun_inst.less_fun,((c== @ cOrderings.ord_fun_inst.less_fun) @ cOrderings.ord_fun_inst.less_fun))
(TOrderings.order.less_imp_not_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V2) @ V3)) @ cHOL.False))))))))))))
(TOrderings.order.strict_mono_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.order.strict_mono @ V1) @ V2)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V1 @ V3) @ V4)) @ ((cOrderings.ord_class.less @ (V2 @ V3)) @ (V2 @ V4))))))))))))))))
(TOrderings.order_bot_class.intro,((c==> @ (cOrderings.bot_class @ cTYPE)) @ ((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ ((cOrderings.class.order_bot_axioms @ cOrderings.bot_class.bot) @ cOrderings.ord_class.less_eq)) @ (cOrderings.order_bot_class @ cTYPE)))))
(TOrderings.order_bot_class.super_2,((c==> @ (cOrderings.order_bot_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TOrderings.order_bot_class.super_1,((c==> @ (cOrderings.order_bot_class @ cTYPE)) @ (cOrderings.bot_class @ cTYPE)))
(TOrderings.order_less_imp_not_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ cHOL.False)))))))
(TOrderings.order_top_class.intro,((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ (cOrderings.top_class @ cTYPE)) @ ((c==> @ ((cOrderings.class.order_top_axioms @ cOrderings.ord_class.less_eq) @ cOrderings.top_class.top)) @ (cOrderings.order_top_class @ cTYPE)))))
(TOrderings.order_top_class.super_2,((c==> @ (cOrderings.order_top_class @ cTYPE)) @ (cOrderings.top_class @ cTYPE)))
(TOrderings.order_top_class.super_1,((c==> @ (cOrderings.order_top_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TOrderings.ordering.strict_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.ordering_top.extremum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ ((V0 @ V3) @ V2)))))))))))
(TOrderings.preorder.less_not_sym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ (cHOL.Not @ ((V1 @ V3) @ V2)))))))))))))
(TOrderings.preorder_class.axioms,((cOrderings.class.preorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.wellorder.less_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (call @ (^[V5]: ((c==> @ ((V1 @ V5) @ V4)) @ (V2 @ V5))))) @ (V2 @ V4))))) @ (V2 @ V3))))))))))))
(TOrderings.wellorder_class.intro,((c==> @ (cOrderings.linorder_class @ cTYPE)) @ ((c==> @ (cOrderings.class.wellorder_axioms @ cOrderings.ord_class.less)) @ (cOrderings.wellorder_class @ cTYPE))))
(TOrderings.wellorder_class.super,((c==> @ (cOrderings.wellorder_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE)))
(TPartial_Function.admissible_fun,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (((cComplete_Partial_Order.ccpo.admissible @ V1) @ V0) @ (V2 @ V3))))) @ (((cComplete_Partial_Order.ccpo.admissible @ (cPartial_Function.fun_lub @ V1)) @ (cPartial_Function.fun_ord @ V0)) @ (^[V3]: (cHOL.All @ (^[V4]: ((V2 @ V4) @ (V3 @ V4)))))))))))))))
(TPower.comm_semiring_1.dvd_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V4)) @ ((cHOL.eq @ V5) @ V1))) @ (((cRings.dvd.dvd @ V0) @ V5) @ ((((cPower.power.power @ V1) @ V0) @ V5) @ V4)))))))))))))))))
(TPower.linordered_idom.power_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ V11))) @ ((((cPower.power.power @ V7) @ V9) @ (V0 @ V10)) @ V11))))))))))))))))))))))))))))
(TPower.monoid_mult.power_even_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3))) @ ((((cPower.power.power @ V0) @ V1) @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))
(TPower.power_class.power.power_0,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cGroups.one_class.one))))
(TPower.ring_1_class.power2_minus,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TPredicate.closure_of_bool_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ (^[V2]: cHOL.False))) @ (V1 @ V0))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ (^[V2]: cHOL.True))) @ (V1 @ V0))) @ (V1 @ V0))))))))
(TPredicate.iterate_upto_sumC_def,((c== @ cPredicate.iterate_upto_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cPredicate.iterate_upto_graph @ V0) @ V1))))))
(TPredicate.pred.Abs_pred_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cPredicate.pred.pred_rep_set))) @ ((cHOL.eq @ (cPredicate.Rep_pred @ (cPredicate.Abs_pred @ V0))) @ V0)))))
(TPredicate.pred.Rep_pred_inverse,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.Abs_pred @ (cPredicate.Rep_pred @ V0))) @ V0))))
(TPredicate.pred.pred_rec_set_def,((c== @ cPredicate.pred.pred_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cPredicate.pred.Pred @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4))))))))))))
(TPredicate.pred.pred_rep_set_def,((c== @ cPredicate.pred.pred_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.Leaf @ V2)))))))))
(TPredicate.seq.seq_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cPredicate.seq.Empty)) @ ((c==> @ ((cHOL.eq @ V4) @ V0)) @ V5))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V3) @ ((cPredicate.seq.Insert @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ V4) @ ((V1 @ V6) @ V7))) @ V5))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V3) @ ((cPredicate.seq.Join @ V8) @ V6))) @ ((c==> @ ((cHOL.eq @ V4) @ (((V2 @ V8) @ V6) @ V7))) @ ((c==> @ (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ V6) @ V7)) @ V5)))))))))) @ V5)))))))))))))))))
(TPredicate.seq.seq_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cPredicate.seq.Empty)) @ ((cHOL.eq @ V4) @ V0))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cPredicate.seq.Insert @ V5) @ V6))) @ ((cHOL.eq @ V4) @ ((V1 @ V5) @ V6)))))))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cPredicate.seq.Join @ V7) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ (((V2 @ V7) @ V5) @ V6))) @ (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ V5) @ V6)))))))))))))))))))))))
(TProduct_Type.Sigma_Int_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.inf_class.inf @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TProduct_Type.Sigma_Int_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cLattices.inf_class.inf @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TProduct_Type.Times_Int_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V3]: V2))) @ ((cLattices.inf_class.inf @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: V2))) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: V2)))))))))))
(TProduct_Type.arity_default_unit,(cHOL.default_class @ cTYPE))
(TProduct_Type.bool.bool_case_def,((c== @ cProduct_Type.bool.bool_case) @ (^[V0]: (^[V1]: ((cProduct_Type.bool.bool_rec @ V0) @ V1)))))
(TProduct_Type.internal_split_def,((c== @ cProduct_Type.prod.prod_case) @ cProduct_Type.prod.prod_case))
(TProduct_Type.prod.prod_case_def,((c== @ cProduct_Type.prod.prod_case) @ (^[V0]: (cProduct_Type.prod.prod_rec @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2)))))))
(TProduct_Type.prod.prod_size_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cProduct_Type.prod.prod_size @ V0) @ V1)) @ (cProduct_Type.prod.prod_rec @ (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (V1 @ V3))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))))
(TProduct_Type.split_eta_SetCompr,(call @ (^[V0]: ((cHOL.eq @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (V0 @ ((cProduct_Type.Pair @ V2) @ V3))))))))) @ V0))))
(TProduct_Type.surjective_pairing,(call @ (^[V0]: ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (cProduct_Type.fst @ V0)) @ (cProduct_Type.snd @ V0))))))
(TProduct_Type.unit.unit_case_def,((c== @ cProduct_Type.unit.unit_case) @ (^[V0]: (cProduct_Type.unit.unit_rec @ V0))))
(TProduct_Type.unit.unit_size_def,((c== @ cProduct_Type.unit.unit_size) @ (cProduct_Type.unit.unit_rec @ cNat.zero_nat_inst.zero_nat)))
(TQuickcheck_Narrowing.cfun.cases,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.cfun.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.cfun.cfun_rec @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.cfun.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.cfun.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.cfun.Constant @ V0)) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.cfun.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.cfun.Constant @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TQuickcheck_Narrowing.conv.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V3) @ V4)))) @ V1)))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V3) @ V4)))) @ V1)))))))) @ V1)))))))
(TQuickcheck_Narrowing.conv.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Narrowing.conv @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V5))))) @ V3)))))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ (((cQuickcheck_Narrowing.nth @ V4) @ V5) @ V6))) @ V3)))))))))) @ V3))))))))))))
(TQuickcheck_Narrowing.conv.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.conv @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V1) @ V2))) @ (((cQuickcheck_Narrowing.nth @ V0) @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.conv.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.conv @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V1) @ V2))) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V1)))))))))))
(TQuickcheck_Narrowing.exists_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.exists @ V0)) @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ (^[V1]: (^[V2]: (((cQuickcheck_Narrowing.property.Existential @ V1) @ (^[V3]: (V0 @ ((cQuickcheck_Narrowing.conv @ V2) @ V3)))) @ (cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ cTYPE))))) @ (cQuickcheck_Narrowing.narrowing_class.narrowing @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit1 @ cNum.num.One)))))))))))))
(TQuickcheck_Narrowing.ffun.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V0) @ V1) @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4))) @ (((V1 @ V2) @ V3) @ V4)))))))))))))
(TQuickcheck_Narrowing.ffun.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V0) @ V1) @ (cQuickcheck_Narrowing.ffun.Constant @ V2))) @ (V0 @ V2)))))))))
(TQuickcheck_Narrowing.ffun.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_rec @ V0) @ V1) @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4))) @ ((((V1 @ V2) @ V3) @ V4) @ (((cQuickcheck_Narrowing.ffun.ffun_rec @ V0) @ V1) @ V4))))))))))))))
(TQuickcheck_Narrowing.ffun.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_rec @ V0) @ V1) @ (cQuickcheck_Narrowing.ffun.Constant @ V2))) @ (V0 @ V2)))))))))
(TQuickcheck_Narrowing.ffun.simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V0) @ V1) @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4))) @ (((V1 @ V2) @ V3) @ V4)))))))))))))
(TQuickcheck_Narrowing.ffun.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V0) @ V1) @ (cQuickcheck_Narrowing.ffun.Constant @ V2))) @ (V0 @ V2)))))))))
(TQuickcheck_Narrowing.ffun.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.ffun.Constant @ V3))))))))))))
(TQuickcheck_Narrowing.ffun.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ (((cQuickcheck_Narrowing.ffun.Update @ V1) @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.ffun.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.ffun.Update @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.ffun.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ (cQuickcheck_Narrowing.ffun.Constant @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.ffun.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cQuickcheck_Narrowing.ffun.Constant @ V4))) @ (V0 @ (V1 @ V4)))))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.ffun.Update @ V4) @ V5) @ V6))) @ (V0 @ (((V2 @ V4) @ V5) @ V6))))))))))))))))))))
(TQuotient.quot_type.some_collect,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.quot_type @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V3)) @ ((cHOL.eq @ (V0 @ (cHilbert_Choice.Eps @ (^[V4]: ((cSet.member @ V4) @ (cSet.Collect @ (V0 @ V3))))))) @ (V0 @ V3)))))))))))))
(TRandom_Pred.iter'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Pred.iter'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ ((cQuickcheck_Random.random_class.random @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((cRandom_Pred.iter'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))))))))))))))))))))))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ ((cQuickcheck_Random.random_class.random @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V13)))))))))))))))))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOrderings.bot_class.bot) @ ((cHOL.Let @ ((cQuickcheck_Random.random_class.random @ V6) @ V7)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cPredicate.Seq @ (^[V11]: ((cPredicate.seq.Insert @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ ((cProduct_Type.Pair @ V6) @ V10)))))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.Random_sumC_def,((c== @ cRandom_Sequence.Random_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cRandom_Sequence.Random_graph @ V0) @ V1))))))
(TRandom_Sequence.iter_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.iter_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V7) @ (V3 @ V5))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V12))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.iter_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V1) @ (V2 @ V3))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V4) @ V5)) @ V1)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V6) @ V7)) @ V4)) @ ((cRandom_Sequence.iter_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V8))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V3))))))))))))))))))))))))))
(TRecord.iso_tuple_fst_update_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRecord.iso_tuple_fst_update @ V0) @ V1)) @ ((cFun.comp @ ((cFun.comp @ (cRecord.abst @ V0)) @ (cProduct_Type.apfst @ V1))) @ (cRecord.repr @ V0))))))))
(TRecord.iso_tuple_snd_update_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRecord.iso_tuple_snd_update @ V0) @ V1)) @ ((cFun.comp @ ((cFun.comp @ (cRecord.abst @ V0)) @ (cProduct_Type.apsnd @ V1))) @ (cRecord.repr @ V0))))))))
(TRecord.tuple_isomorphism.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TRecord.tuple_isomorphism.inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1)) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TRecord.tuple_isomorphism.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TRecord.tuple_isomorphism.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TRelation.relcomp_UNION_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRelation.relcomp @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cRelation.relcomp @ (V1 @ V3)) @ V2)))))))))))
(TRings.class.comm_semiring.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((c==> @ (cGroups.class.ab_semigroup_mult @ V1)) @ ((c==> @ ((cRings.class.comm_semiring_axioms @ V0) @ V1)) @ ((cRings.class.comm_semiring @ V0) @ V1)))))))))
(TRings.class.comm_semiring_0_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.comm_semiring_0 @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.conj @ ((cRings.class.comm_semiring @ V0) @ V2)) @ ((cRings.class.mult_zero @ V2) @ V1)))))))))))
(TRings.class.comm_semiring_1_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cHOL.conj @ (((cRings.class.comm_semiring_0 @ V2) @ V3) @ V0)) @ ((cRings.class.zero_neq_one @ V1) @ V3)))))))))))))
(TRings.class.linordered_idom_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c== @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.conj @ ((cHOL.conj @ ((((cGroups.class.abs_if @ V0) @ V2) @ V3) @ V5)) @ ((((((cGroups.class.ordered_ab_group_add @ V6) @ V3) @ V1) @ V2) @ V4) @ V5))) @ ((cHOL.conj @ (((((cGroups.class.sgn_if @ V7) @ V8) @ V2) @ V3) @ V5)) @ ((cHOL.conj @ ((((((cRings.class.comm_ring_1 @ V9) @ V7) @ V6) @ V3) @ V1) @ V2)) @ (((((cRings.class.linordered_comm_semiring_strict @ V6) @ V4) @ V5) @ V3) @ V9))))))))))))))))))))))))))
(TRings.class.linordered_ring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((cHOL.conj @ ((((cGroups.class.abs_if @ V0) @ V2) @ V3) @ V5)) @ ((((((cGroups.class.linordered_ab_group_add @ V6) @ V3) @ V1) @ V2) @ V4) @ V5))) @ ((cHOL.conj @ (((((cRings.class.linordered_semiring @ V6) @ V4) @ V5) @ V3) @ V7)) @ (((((cRings.class.ring @ V6) @ V3) @ V1) @ V2) @ V7)))))))))))))))))))))
(TRings.class.ordered_ring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (((((cRings.class.ring @ V0) @ V1) @ V5) @ V6) @ V4)))))))))))))))))
(TRings.class.ordered_ring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))))
(TRings.class.semiring_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.class.semiring_axioms @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V1 @ ((V0 @ V2) @ V3)) @ V4)) @ ((V0 @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V1 @ V2) @ ((V0 @ V3) @ V4))) @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V1 @ V2) @ V4))))))))))))))))
(TRings.comm_ring_1.dvd_minus_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ V6) @ (V5 @ V7))) @ (((cRings.dvd.dvd @ V0) @ V6) @ V7))))))))))))))))))))
(TRings.comm_ring_1.minus_dvd_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ (V5 @ V6)) @ V7)) @ (((cRings.dvd.dvd @ V0) @ V6) @ V7))))))))))))))))))))
(TRings.comm_semiring_0_class_def,((c== @ (cRings.comm_semiring_0_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_semiring_class @ cTYPE)) @ (cRings.mult_zero_class @ cTYPE)))))
(TRings.comm_semiring_1.dvd_mult2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V5)) @ (((cRings.dvd.dvd @ V0) @ V4) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TRings.comm_semiring_1.dvd_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V5) @ V6)) @ (((cRings.dvd.dvd @ V0) @ V4) @ V6)))))))))))))))))))
(TRings.comm_semiring_1_class_def,((c== @ (cRings.comm_semiring_1_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ (cRings.comm_semiring_0_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.dvd_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))))
(TRings.comm_semiring_class.intro,((c==> @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.ab_semigroup_mult_class @ cTYPE)) @ ((c==> @ ((cRings.class.comm_semiring_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times)) @ (cRings.comm_semiring_class @ cTYPE)))))
(TRings.comm_semiring_class.super_2,((c==> @ (cRings.comm_semiring_class @ cTYPE)) @ (cGroups.ab_semigroup_mult_class @ cTYPE)))
(TRings.comm_semiring_class.super_1,((c==> @ (cRings.comm_semiring_class @ cTYPE)) @ (cGroups.ab_semigroup_add_class @ cTYPE)))
(TRings.idom.dvd_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ ((V0 @ V6) @ V7)) @ ((V0 @ V6) @ V8))) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V3)) @ (((cRings.dvd.dvd @ V0) @ V7) @ V8)))))))))))))))))))))))
(TRings.linordered_idom.sgn_1_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((cHOL.eq @ (V8 @ V10)) @ (V2 @ V7))) @ ((V5 @ V10) @ V3))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_1_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((cHOL.eq @ (V8 @ V10)) @ V7)) @ ((V5 @ V3) @ V10))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_times,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V8 @ ((V9 @ V10) @ V11))) @ ((V9 @ (V8 @ V10)) @ (V8 @ V11)))))))))))))))))))))))))))))
(TRings.linordered_idom_class_def,((c== @ (cRings.linordered_idom_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.abs_if_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_class @ cTYPE))) @ ((cPure.conjunction @ (cGroups.sgn_if_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_ring_1_class @ cTYPE)) @ (cRings.linordered_comm_semiring_strict_class @ cTYPE))))))
(TRings.linordered_ring_class_def,((c== @ (cRings.linordered_ring_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.abs_if_class @ cTYPE)) @ (cGroups.linordered_ab_group_add_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.linordered_semiring_class @ cTYPE)) @ (cRings.ring_class @ cTYPE)))))
(TRings.mult_zero.mult_zero_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.class.mult_zero @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V1)))))))))
(TRings.zero_neq_one.one_neq_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.zero_neq_one @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))))
(TRings.zero_neq_one.zero_neq_one,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.zero_neq_one @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))))))))
(TRings.zero_neq_one_class.axioms,((cRings.class.zero_neq_one @ cGroups.one_class.one) @ cGroups.zero_class.zero))
(TSMT.pattern.Abs_pattern_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cSMT.pattern.pattern_rep_set))) @ ((cHOL.eq @ (cSMT.Rep_pattern @ (cSMT.Abs_pattern @ V0))) @ V0)))))
(TSMT.pattern.Rep_pattern_inverse,(call @ (^[V0]: ((cHOL.eq @ (cSMT.Abs_pattern @ (cSMT.Rep_pattern @ V0))) @ V0))))
(TSMT.pattern.pattern_rec_set_def,((c== @ cSMT.pattern.pattern_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ cSMT.pattern.Pattern)) @ ((cHOL.eq @ V3) @ V0)))))))))
(TSMT.pattern.pattern_rep_set_def,((c== @ cSMT.pattern.pattern_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.eq @ V1) @ cHOL.undefined))))))
(TSet_Interval.atLeastLessThanSuc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ (cNat.Suc @ V1))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cSet.insert @ V1) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ cOrderings.bot_class.bot)))))))
(TSet_Interval.atLeast_subset_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ (cSet_Interval.ord_class.atLeast @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet_Interval.atMost_Int_atLeast,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atMost @ V0)) @ (cSet_Interval.ord_class.atLeast @ V0))) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TSet_Interval.card_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ (cNat.Suc @ V1)) @ V0)))))))
(TSet_Interval.greaterThan_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cSet_Interval.ord_class.greaterThan @ V0)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TSet_Interval.inj_on_iff_card_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cFun.inj_on @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V2) @ V0)) @ V1))))) @ ((cNat.ord_nat_inst.less_eq_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))))))))))
(TSet_Interval.setsum_add_nat_ivl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2))))))))))))))
(TSet_Interval.setsum_le_included,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V5]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V2 @ V5))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V5]: ((cSet.Bex @ V1) @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ (V3 @ V6)) @ V5)) @ ((cOrderings.ord_class.less_eq @ (V4 @ V5)) @ (V2 @ V6)))))))) @ ((cOrderings.ord_class.less_eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V4) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)))))))))))))))))
(TString.char.char_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TString.char.char_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((cString.char.char_rec_set @ V0) @ ((cString.char.Char @ V1) @ V2)) @ ((V0 @ V1) @ V2)))))))))
(TString.char.char_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cString.char.char_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V2)) @ (cDatatype.Leaf @ V3)))))))) @ (V1 @ V0))))))))
(TString.char.char_rep_set.intros,(call @ (^[V0]: (call @ (^[V1]: (cString.char.char_rep_set @ ((cDatatype.Scons @ (cDatatype.Leaf @ V0)) @ (cDatatype.Leaf @ V1))))))))
(TString.char_of_nat_Char_nibbles,(call @ (^[V0]: ((cHOL.eq @ (cString.char_of_nat @ V0)) @ ((cString.char.Char @ (cString.nibble_of_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))) @ (cString.nibble_of_nat @ V0))))))
(TString.enum_char_inst.enum_char,((c== @ cString.enum_char_inst.enum_char) @ cString.enum_char_inst.enum_char))
(TString.nibble.Abs_nibble_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cString.nibble.nibble_rep_set))) @ (V0 @ (cString.Abs_nibble @ V2)))))) @ (V0 @ V1)))))))
(TString.nibble.Abs_nibble_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.nibble.nibble_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cString.nibble.nibble_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cString.Abs_nibble @ V0)) @ (cString.Abs_nibble @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TString.nibble.Rep_nibble_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.nibble.nibble_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cString.Rep_nibble @ V2))))) @ (V1 @ V0))))))))
(TString.nibble.Rep_nibble_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cString.Rep_nibble @ V0)) @ (cString.Rep_nibble @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TString.nibble.arity_size_nibble,(cNat.size_class @ cTYPE))
(TSum_Type.sum.sum_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TSum_Type.sum.sum_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cSum_Type.sum.sum_rec_set @ V0) @ V1) @ (cSum_Type.Inr @ V2)) @ (V1 @ V2)))))))))
(TSum_Type.sum.sum_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cSum_Type.sum.sum_rec_set @ V0) @ V1) @ (cSum_Type.Inl @ V2)) @ (V0 @ V2)))))))))
(TTransitive_Closure.ntrancl_Zero,(call @ (^[V0]: ((cHOL.eq @ ((cTransitive_Closure.ntrancl @ cNat.zero_nat_inst.zero_nat) @ V0)) @ V0))))
(TTransitive_Closure.refl_rtrancl,(call @ (^[V0]: ((cRelation.refl_on @ cOrderings.top_class.top) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.relpow.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ (cNat.Suc @ V0)) @ V1)) @ ((cRelation.relcomp @ ((cNat.compow @ V0) @ V1)) @ V1)))))))
(TTransitive_Closure.relpow.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cRelation.Id))))
(TTransitive_Closure.relpow_Suc_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ (cNat.Suc @ V2)) @ V3))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V5)) @ ((cNat.compow @ V2) @ V3))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ V3)) @ V4))))) @ V4)))))))))))))
(TTransitive_Closure.relpow_Suc_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ V2) @ V3))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V4)) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ ((cNat.compow @ (cNat.Suc @ V2)) @ V3)))))))))))))))
(TTransitive_Closure.relpow_empty,(call @ (^[V0]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cNat.compow @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot)))))
(TTransitive_Closure.rtrancl_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cTransitive_Closure.rtrancl @ V0)) @ (cTransitive_Closure.rtrancl @ V1))))))))
(TTransitive_Closure.rtranclp_def,((c== @ cTransitive_Closure.rtranclp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.eq @ V3) @ V4))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V6)) @ ((cHOL.conj @ ((V1 @ V4) @ V5)) @ ((V0 @ V5) @ V6))))))))))))))))))
(TTransitive_Closure.trancl.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ V3)))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ V3))))))))))) @ V3))))))))))))
(TTransitive_Closure.trancl.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V2)))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V5)) @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)))))))))))))))))))
(TTransitive_Closure.trancl_empty,((cHOL.eq @ (cTransitive_Closure.trancl @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TTransitive_Closure.trancl_power,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cTransitive_Closure.trancl @ V1))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cSet.member @ V0) @ ((cNat.compow @ V2) @ V1)))))))))))
(TTransitive_Closure.trancl_range,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Range @ (cTransitive_Closure.trancl @ V0))) @ (cRelation.Range @ V0)))))
(TTransitive_Closure.trancl_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.trans_trancl,(call @ (^[V0]: (cRelation.trans @ (cTransitive_Closure.trancl @ V0)))))
(TTyperep.type_definition_typerep,(((cTypedef.type_definition @ cTyperep.Rep_typerep) @ cTyperep.Abs_typerep) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1)))
(TWellfounded.max_extp_max_ext_eq,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.max_extp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cWellfounded.max_ext @ V0))))))))
(TWellfounded.wf_union_compatible,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (cWellfounded.wf @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ V0) @ V1)) @ V0)) @ (cWellfounded.wf @ ((cLattices.sup_class.sup @ V0) @ V1))))))))))
(TBig_Operators.lattice.Inf_le_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cOrderings.bot_class.bot))) @ ((V1 @ ((cBig_Operators.semilattice_inf.Inf_fin @ V0) @ V4)) @ ((cBig_Operators.semilattice_sup.Sup_fin @ V3) @ V4))))))))))))))))
(TBig_Operators.linorder.Least_Min,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ (cSet.Collect @ (^[V3]: (V2 @ V3))))) @ ((c==> @ (cHOL.Ex @ (^[V3]: (V2 @ V3)))) @ ((cHOL.eq @ ((cOrderings.ord.Least @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cBig_Operators.linorder.Min @ V0) @ (cSet.Collect @ (^[V3]: (V2 @ V3)))))))))))))))
(TBig_Operators.setsum_UN_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ V0) @ (^[V4]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V1 @ V4))) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ (V1 @ V3)))) @ V0))))))))))))
(TBig_Operators.setsum_Un_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)))))))))))))
(TBig_Operators.setsum_abs_ge_zero,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cGroups.abs_class.abs @ (V0 @ V2)))) @ V1)))))))
(TBig_Operators.setsum_eq_Suc0_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cSet.Bex @ V0) @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))) @ ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ (V1 @ V3)) @ cNat.zero_nat_inst.zero_nat))))))))))))))
(TBig_Operators.setsum_strict_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cOrderings.ord_class.less @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.setsum_subset_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.strong_setsum_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (V2 @ V4))) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (V3 @ V4))) @ V1)))))))))))))
(TCode_Evaluation.arity_equal_term,(cHOL.equal_class @ cTYPE))
(TCode_Evaluation.term_of_anything,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ V1))))))
(TCode_Evaluation.term_of_int_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_int_inst.term_of_int @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_nat_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_nat_inst.term_of_nat @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_num_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_num_inst.term_of_num @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_seq_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_set_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_sum_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.typerep_pred_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TCode_Evaluation.typerep_term_def,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.typerep_term_inst.typerep_term @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)))))
(TCode_Numeral.arity_equal_integer,(cHOL.equal_class @ cTYPE))
(TCode_Numeral.arity_equal_natural,(cHOL.equal_class @ cTYPE))
(TCode_Numeral.divmod_integer_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.divmod_integer @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ ((cProduct_Type.Pair @ cCode_Numeral.zero_integer_inst.zero_integer) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ ((cProduct_Type.Pair @ cCode_Numeral.zero_integer_inst.zero_integer) @ V0)) @ ((((cFun.comp @ ((cFun.comp @ cProduct_Type.apsnd) @ cCode_Numeral.times_integer_inst.times_integer)) @ cCode_Numeral.sgn_integer_inst.sgn_integer) @ V1) @ (((cHOL.If @ ((cHOL.eq @ (cCode_Numeral.sgn_integer_inst.sgn_integer @ V0)) @ (cCode_Numeral.sgn_integer_inst.sgn_integer @ V1))) @ ((cCode_Numeral.divmod_abs @ V0) @ V1)) @ ((cHOL.Let @ ((cCode_Numeral.divmod_abs @ V0) @ V1)) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ ((cProduct_Type.Pair @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ V2)) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ V2)) @ cCode_Numeral.one_integer_inst.one_integer)) @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.abs_integer_inst.abs_integer @ V1)) @ V3)))))))))))))))))
(TCode_Numeral.int_of_integer_code,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ V0)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ (cInt.uminus_int_inst.uminus_int @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ V0)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cInt.zero_int_inst.zero_int) @ ((cHOL.Let @ ((cCode_Numeral.divmod_integer @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.Let @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cCode_Numeral.int_of_integer @ V1))) @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ V3) @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int))))))))))))))
(TCode_Numeral.integer.right_total,(cTransfer.right_total @ cCode_Numeral.pcr_integer))
(TCode_Numeral.integer_of_int_code,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_int @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ (cCode_Numeral.integer_of_int @ (cInt.uminus_int_inst.uminus_int @ V0)))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ cCode_Numeral.zero_integer_inst.zero_integer) @ ((cHOL.Let @ ((cDivides.divmod_int @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.Let @ ((cCode_Numeral.times_integer_inst.times_integer @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cCode_Numeral.integer_of_int @ V1))) @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V2) @ cInt.zero_int_inst.zero_int)) @ V3) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V3) @ cCode_Numeral.one_integer_inst.one_integer))))))))))))))
(TCode_Numeral.less_eq_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cInt.ord_int_inst.less_eq_int) @ cInt.ord_int_inst.less_eq_int))
(TCode_Numeral.less_eq_integer_def,((c== @ cCode_Numeral.ord_integer_inst.less_eq_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ ((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cFun.id)) @ cInt.ord_int_inst.less_eq_int)))
(TCode_Numeral.less_eq_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cNat.ord_nat_inst.less_eq_nat) @ cNat.ord_nat_inst.less_eq_nat))
(TCode_Numeral.less_eq_natural_def,((c== @ cCode_Numeral.ord_natural_inst.less_eq_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ ((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cFun.id)) @ cNat.ord_nat_inst.less_eq_nat)))
(TCode_Numeral.less_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_integer @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ ((cInt.ord_int_inst.less_int @ V0) @ V1)))))))
(TCode_Numeral.less_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ V1)) @ ((cInt.ord_int_inst.less_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.less_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_natural_inst.less_natural @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TCode_Numeral.less_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.nat_of_integer_code,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_integer @ V0)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cNat.zero_nat_inst.zero_nat) @ ((cHOL.Let @ ((cCode_Numeral.divmod_integer @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.Let @ (cCode_Numeral.nat_of_integer @ V1)) @ (^[V3]: ((cHOL.Let @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V3)) @ (^[V4]: (((cHOL.If @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ V4) @ ((cNat.plus_nat_inst.plus_nat @ V4) @ cNat.one_nat_inst.one_nat)))))))))))))))
(TCode_Numeral.natural.right_total,(cTransfer.right_total @ cCode_Numeral.pcr_natural))
(TCode_Numeral.num_of_integer_code,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.num_of_integer @ V0)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ V0) @ cCode_Numeral.one_integer_inst.one_integer)) @ cNum.num.One) @ ((cHOL.Let @ ((cCode_Numeral.divmod_integer @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((cHOL.Let @ (cCode_Numeral.num_of_integer @ V1)) @ (^[V3]: ((cHOL.Let @ ((cNum.plus_num_inst.plus_num @ V3) @ V3)) @ (^[V4]: (((cHOL.If @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ V4) @ ((cNum.plus_num_inst.plus_num @ V4) @ cNum.num.One)))))))))))))))
(TCode_Numeral.plus_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.plus_integer_inst.plus_integer @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ (cCode_Numeral.integer_of_int @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))))))))
(TCode_Numeral.plus_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V0) @ V1))) @ ((cInt.plus_int_inst.plus_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.plus_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.plus_natural_inst.plus_natural @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ (cCode_Numeral.natural_of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TCode_Numeral.plus_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.uminus_integer_code_3,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ (cCode_Numeral.Neg @ V0))) @ (cCode_Numeral.Pos @ V0)))))
(TCode_Numeral.uminus_integer_code_2,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ (cCode_Numeral.Pos @ V0))) @ (cCode_Numeral.Neg @ V0)))))
(TCode_Numeral.uminus_integer_code_1,((cHOL.eq @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cCode_Numeral.zero_integer_inst.zero_integer))
(TCode_Numeral.zero_integer.abs_eq,((cHOL.eq @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.integer_of_int @ cInt.zero_int_inst.zero_int)))
(TCode_Numeral.zero_integer.rep_eq,((cHOL.eq @ (cCode_Numeral.int_of_integer @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cInt.zero_int_inst.zero_int))
(TCode_Numeral.zero_natural.abs_eq,((cHOL.eq @ cCode_Numeral.zero_natural_inst.zero_natural) @ (cCode_Numeral.natural_of_nat @ cNat.zero_nat_inst.zero_nat)))
(TCode_Numeral.zero_natural.rep_eq,((cHOL.eq @ (cCode_Numeral.nat_of_natural @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cNat.zero_nat_inst.zero_nat))
(TComplete_Lattices.Collect_all_eq,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: (cHOL.All @ (^[V2]: ((V0 @ V1) @ V2)))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ cOrderings.top_class.top) @ (^[V1]: (cSet.Collect @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TComplete_Lattices.Collect_bex_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cSet.Bex @ V0) @ (^[V3]: ((V1 @ V2) @ V3)))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (cSet.Collect @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TComplete_Lattices.INT_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cSet.Ball @ V1) @ (^[V3]: ((cOrderings.ord_class.less_eq @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.Int_UN_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cLattices.inf_class.inf @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.Inter_greatest,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cComplete_Lattices.Inf_class.Inf @ V0))))))))
(TComplete_Lattices.Inter_image_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cSet.image @ V0) @ V1))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V2]: (V0 @ V2)))))))))
(TComplete_Lattices.Un_INT_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cLattices.sup_class.sup @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.Un_Union_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ V1) @ V0))) @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ V2) @ V0)))))))))))
(TComplete_Lattices.Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ cOrderings.bot_class.bot)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V1)) @ cOrderings.bot_class.bot)))))))))
(TComplete_Lattices.Union_image_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ V0) @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: (V0 @ V2)))))))))
(TComplete_Lattices.strong_UN_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Partial_Order.chain_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Partial_Order.chain @ V0) @ V1)) @ ((cSet.Ball @ V1) @ (^[V2]: ((cSet.Ball @ V1) @ (^[V3]: ((cHOL.disj @ ((V0 @ V2) @ V3)) @ ((V0 @ V3) @ V2))))))))))))
(TComplete_Partial_Order.monotoneD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.monotone @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V1 @ (V2 @ V3)) @ (V2 @ V4)))))))))))))))
(TComplete_Partial_Order.monotoneI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((V1 @ (V2 @ V3)) @ (V2 @ V4)))))))) @ (((cComplete_Partial_Order.monotone @ V0) @ V1) @ V2)))))))))
(TDivides.class.semiring_div.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cRings.class.no_zero_divisors @ V2) @ V1)) @ ((c==> @ (((((cDivides.class.semiring_div_axioms @ V2) @ V4) @ V5) @ V0) @ V1)) @ ((((((cDivides.class.semiring_div @ V2) @ V4) @ V5) @ V0) @ V1) @ V3)))))))))))))))))
(TDivides.nonneg1_imp_zdiv_pos_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.div_int @ V0) @ V1))) @ ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ V1) @ V0)) @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V1)))))))))
(TDivides.ring_div.div_minus_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ (V7 @ V8)) @ (V7 @ V9))) @ ((V1 @ V8) @ V9))))))))))))))))))))))))
(TDivides.ring_div.div_minus_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ (V7 @ V9))) @ ((V1 @ (V7 @ V8)) @ V9))))))))))))))))))))))))
(TDivides.ring_div.mod_minus_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ (V7 @ V8)) @ (V7 @ V9))) @ (V7 @ ((V2 @ V8) @ V9)))))))))))))))))))))))))
(TDivides.ring_div.mod_minus_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V8) @ (V7 @ V9))) @ (V7 @ ((V2 @ (V7 @ V8)) @ V9)))))))))))))))))))))))))
(TDivides.semiring_div.div_dvd_div,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ ((V1 @ V7) @ V6)) @ ((V1 @ V8) @ V6))) @ (((cRings.dvd.dvd @ V0) @ V7) @ V8))))))))))))))))))))))))
(TDivides.semiring_div.dvd_mod_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ V6) @ ((V2 @ V8) @ V7))) @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)))))))))))))))))))))))
(TDivides.semiring_div.mod_mult_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ V8)) @ ((V2 @ ((V0 @ ((V2 @ V6) @ V8)) @ ((V2 @ V7) @ V8))) @ V8))))))))))))))))))))))
(TDivides.semiring_div_class.div_0,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.div @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TDivides.semiring_div_class.intro,((c==> @ (cDivides.div_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ ((c==> @ (cRings.no_zero_divisors_class @ cTYPE)) @ ((c==> @ (((((cDivides.class.semiring_div_axioms @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)) @ (cDivides.semiring_div_class @ cTYPE))))))
(TDivides.semiring_div_class.mod_0,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.mod @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TDivides.semiring_div_class.super_3,((c==> @ (cDivides.semiring_div_class @ cTYPE)) @ (cRings.no_zero_divisors_class @ cTYPE)))
(TDivides.semiring_div_class.super_2,((c==> @ (cDivides.semiring_div_class @ cTYPE)) @ (cRings.comm_semiring_1_cancel_class @ cTYPE)))
(TDivides.semiring_div_class.super_1,((c==> @ (cDivides.semiring_div_class @ cTYPE)) @ (cDivides.div_class @ cTYPE)))
(TEnum.enum_bool_inst.enum_ex_bool,((c== @ cEnum.enum_bool_inst.enum_ex_bool) @ cEnum.enum_bool_inst.enum_ex_bool))
(TEnum.enum_prod_inst.enum_ex_prod,((c== @ cEnum.enum_prod_inst.enum_ex_prod) @ cEnum.enum_prod_inst.enum_ex_prod))
(TEnum.enum_unit_inst.enum_ex_unit,((c== @ cEnum.enum_unit_inst.enum_ex_unit) @ cEnum.enum_unit_inst.enum_ex_unit))
(TEnum.finite_1.Abs_finite_1_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Abs_finite_1 @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set))) @ V1))))) @ V1))))))
(TEnum.finite_1.Rep_finite_1_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Rep_finite_1 @ V2))) @ V1)))) @ V1)))))))
(TEnum.finite_2.Abs_finite_2_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Abs_finite_2 @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set))) @ V1))))) @ V1))))))
(TEnum.finite_2.Rep_finite_2_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Rep_finite_2 @ V2))) @ V1)))) @ V1)))))))
(TEnum.finite_3.Abs_finite_3_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Abs_finite_3 @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set))) @ V1))))) @ V1))))))
(TEnum.finite_3.Rep_finite_3_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Rep_finite_3 @ V2))) @ V1)))) @ V1)))))))
(TEnum.finite_4.Abs_finite_4_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Abs_finite_4 @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set))) @ V1))))) @ V1))))))
(TEnum.finite_4.Rep_finite_4_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Rep_finite_4 @ V2))) @ V1)))) @ V1)))))))
(TEnum.finite_5.Abs_finite_5_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Abs_finite_5 @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set))) @ V1))))) @ V1))))))
(TEnum.finite_5.Rep_finite_5_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cEnum.Rep_finite_5 @ V2))) @ V1)))) @ V1)))))))
(TEquiv_Relations.equiv_class_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V2) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))))))))))
(TEquiv_Relations.part_equivp_symp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cEquiv_Relations.part_equivp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TFields.class.division_ring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((((cFields.class.division_ring_axioms @ V6) @ V7) @ V0) @ V1) @ V3)) @ ((((((((cFields.class.division_ring @ V6) @ V7) @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))))))
(TFields.division_ring.divide_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V1 @ V8) @ V8)) @ V2))))))))))))))))))))))
(TFields.division_ring_class.intro,((c==> @ (cFields.inverse_class @ cTYPE)) @ ((c==> @ (cRings.ring_1_class @ cTYPE)) @ ((c==> @ (((((cFields.class.division_ring_axioms @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.zero_class.zero)) @ (cFields.division_ring_class @ cTYPE)))))
(TFields.division_ring_class.super_2,((c==> @ (cFields.division_ring_class @ cTYPE)) @ (cRings.ring_1_class @ cTYPE)))
(TFields.division_ring_class.super_1,((c==> @ (cFields.division_ring_class @ cTYPE)) @ (cFields.inverse_class @ cTYPE)))
(TFields.field_class.field_inverse,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cFields.inverse_class.inverse @ V0)) @ V0)) @ cGroups.one_class.one)))))
(TFinite_Set.card.comp_fun_commute,((cHOL.eq @ ((cFun.comp @ cNat.Suc) @ cNat.Suc)) @ ((cFun.comp @ cNat.Suc) @ cNat.Suc)))
(TFinite_Set.card_Collect_less_nat,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V1]: ((cNat.ord_nat_inst.less_nat @ V1) @ V0))))) @ V0))))
(TFinite_Set.finite_Collect_le_nat,(call @ (^[V0]: (cFinite_Set.finite @ (cSet.Collect @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V0)))))))
(TFinite_Set.finite_UNIV_card_ge_0,((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (cFinite_Set.card @ cOrderings.top_class.top))))
(TFinite_Set.finite_imp_fold_graph,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V3]: ((((cFinite_Set.fold_graph @ V1) @ V2) @ V0) @ V3)))))))))))
(TFinite_Set.finite_psubset_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V3) @ V2)) @ (V1 @ V3))))) @ (V1 @ V2)))))) @ (V1 @ V0))))))))
(TFinite_Set.folding.insert_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (((cFinite_Set.folding.F @ V0) @ V2) @ ((cSet.insert @ V3) @ V1))) @ ((V0 @ V3) @ (((cFinite_Set.folding.F @ V0) @ V2) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))))))))))))))))
(TGroups.ab_group_add.diff_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V4) @ V5)) @ V6)) @ ((V2 @ V4) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TGroups.ab_group_add_class.axioms,((((cGroups.class.ab_group_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TGroups.ab_semigroup_mult.mult_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ V2) @ ((V0 @ V1) @ V3)))))))))))))
(TGroups.ab_semigroup_mult.mult_ac_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.ab_semigroup_mult.mult_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TGroups.abel_semigroup_axioms_def,(call @ (^[V0]: ((c== @ (cGroups.abel_semigroup_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.class.ab_group_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((((cGroups.class.ab_group_add_axioms @ V0) @ V1) @ V2) @ V3)))))))))))
(TGroups.class.ab_group_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))))))
(TGroups.class.comm_monoid_add_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cGroups.class.comm_monoid_add_axioms @ V0) @ V1))))))))
(TGroups.class.semigroup_add.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))) @ (cGroups.class.semigroup_add @ V0)))))
(TGroups.comm_monoid_add_class_def,((c== @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.zero_class @ cTYPE)) @ ((cGroups.class.comm_monoid_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))))
(TGroups.group_add.add_diff_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V1 @ V4) @ V5)) @ V5)) @ V4)))))))))))))))
(TGroups.group_add.diff_add_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ ((V0 @ V4) @ V5)) @ V5)) @ V4)))))))))))))))
(TGroups.group_add.diff_eq_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V0 @ V6) @ V7))) @ ((cHOL.eq @ ((cHOL.eq @ V4) @ V5)) @ ((cHOL.eq @ V6) @ V7)))))))))))))))))))))
(TGroups.group_add_class.diff_self,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V0)) @ cGroups.zero_class.zero))))
(TGroups.group_add_class.minus_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.plus_class.plus @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TGroups.semigroup_add_class.intro,((c==> @ (cGroups.plus_class @ cTYPE)) @ ((c==> @ (cGroups.class.semigroup_add @ cGroups.plus_class.plus)) @ (cGroups.semigroup_add_class @ cTYPE))))
(TGroups.semigroup_add_class.super,((c==> @ (cGroups.semigroup_add_class @ cTYPE)) @ (cGroups.plus_class @ cTYPE)))
(TGroups.semigroup_mult.mult_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.semigroup_mult @ V0)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(THilbert_Choice.Greatest_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cHOL.eq @ (cHilbert_Choice.Greatest @ (^[V2]: (V0 @ V2)))) @ V1))))))))
(THilbert_Choice.acc_subseteq_bacc,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cOrderings.ord_class.less_eq @ (cWellfounded.acc @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: ((cHilbert_Choice.bacc @ V0) @ V1))))))))
(THilbert_Choice.bacc_subseteq_acc,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cHilbert_Choice.bacc @ V0) @ V1)) @ (cWellfounded.acc @ V0)))))))
(THilbert_Choice.bij_betw_inv_into,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ (((cFun.bij_betw @ ((cHilbert_Choice.inv_into @ V1) @ V0)) @ V2) @ V1)))))))))
(THilbert_Choice.finite_fun_UNIVD1,((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ (cFinite_Set.card @ cOrderings.top_class.top)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))) @ (cFinite_Set.finite @ cOrderings.top_class.top))))
(TInductive.lfp_ordinal_induct_set,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V1 @ V2)) @ (V1 @ (V0 @ V2)))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.Ball @ V2) @ (^[V3]: (V1 @ V3)))) @ (V1 @ (cComplete_Lattices.Sup_class.Sup @ V2)))))) @ (V1 @ (cInductive.complete_lattice_class.lfp @ V0))))))))))
(TInt.mult_le_cancel_right_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ V1))) @ ((cGroups.times_class.times @ V2) @ (cNum.numeral_class.numeral @ V1)))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V1)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V2) @ V0)))))))))))
(TInt.ring_1_class.of_int.transfer,((((cTransfer.fun_rel @ cInt.cr_int) @ cHOL.eq) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cGroups.minus_class.minus @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1)))))) @ cInt.ring_1_class.of_int))
(TInt.zero_less_divide_iff_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ (cNum.numeral_class.numeral @ V0)) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)))))))))
(TLattices.boolean_algebra.diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V0 @ V8) @ V9)) @ ((V2 @ V8) @ (V1 @ V9)))))))))))))))))))))))))
(TLattices.distrib_lattice.distrib_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V3 @ V4) @ V5)) @ V6)) @ ((V3 @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.distrib_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V3 @ V5) @ V6))) @ ((V3 @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ ((V0 @ V4) @ V5)) @ V6)) @ ((V0 @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V3 @ V4) @ V5)) @ ((V3 @ V4) @ V6)))))))))))))))))))
(TLattices.linorder_class.max.idem,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V0)) @ V0))))
(TLattices.linorder_class.max.mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.max @ V1) @ V3)))))))))))))
(TLattices.linorder_class.min.idem,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V0)) @ V0))))
(TLattices.linorder_class.min.mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V3)))))))))))))
(TLattices.semilattice_inf.inf_aci_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V3) @ V4))) @ ((V0 @ V3) @ V4))))))))))))))
(TLattices.semilattice_inf.inf_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V4) @ V5))) @ ((V0 @ V4) @ ((V0 @ V3) @ V5)))))))))))))))))
(TLattices.semilattice_inf.inf_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V3) @ V4)) @ V5)) @ ((V0 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))
(TLattices.semilattice_inf.inf_aci_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))))))))))
(TLattices.semilattice_inf.inf_le1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((V1 @ ((V0 @ V3) @ V4)) @ V3)))))))))))))
(TLattices.semilattice_inf.inf_le2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((V1 @ ((V0 @ V3) @ V4)) @ V4)))))))))))))
(TLattices.semilattice_inf.le_infE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ ((V0 @ V4) @ V5))) @ ((c==> @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V3) @ V5)) @ V6))) @ V6))))))))))))))))))
(TLattices.semilattice_inf.le_infI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V3) @ V5)) @ ((V1 @ V3) @ ((V0 @ V4) @ V5))))))))))))))))))
(TLattices.semilattice_neutr.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLattices.semilattice @ V0)) @ ((c==> @ ((cGroups.comm_monoid @ V0) @ V1)) @ ((cLattices.semilattice_neutr @ V0) @ V1))))))))
(TLattices.semilattice_order.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cLattices.semilattice @ V0)) @ ((c==> @ (((cLattices.semilattice_order_axioms @ V0) @ V1) @ V2)) @ (((cLattices.semilattice_order @ V0) @ V1) @ V2))))))))))
(TLattices.semilattice_sup.le_supE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ ((V0 @ V3) @ V4)) @ V5)) @ ((c==> @ ((c==> @ ((V1 @ V3) @ V5)) @ ((c==> @ ((V1 @ V4) @ V5)) @ V6))) @ V6))))))))))))))))))
(TLattices.semilattice_sup.le_supI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V4)) @ ((V1 @ ((V0 @ V3) @ V5)) @ V4)))))))))))))))))
(TLattices.semilattice_sup.sup_aci_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V3) @ V4))) @ ((V0 @ V3) @ V4))))))))))))))
(TLattices.semilattice_sup.sup_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V4) @ V5))) @ ((V0 @ V4) @ ((V0 @ V3) @ V5)))))))))))))))))
(TLattices.semilattice_sup.sup_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V3) @ V4)) @ V5)) @ ((V0 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))
(TLattices.semilattice_sup.sup_aci_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))))))))))
(TLattices.semilattice_sup.sup_ge1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((V1 @ V3) @ ((V0 @ V3) @ V4))))))))))))))
(TLattices.semilattice_sup.sup_ge2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((V1 @ V3) @ ((V0 @ V4) @ V3))))))))))))))
(TLazy_Sequence.iterate_upto.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TLazy_Sequence.iterate_upto.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cLazy_Sequence.iterate_upto @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (cLazy_Sequence.Lazy_Sequence @ (^[V8]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V7) @ V6)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V5 @ V6)) @ (((cLazy_Sequence.iterate_upto @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7)))))))) @ V4))))))))))) @ V4)))))))))))))
(TLazy_Sequence.iterate_upto.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLazy_Sequence.iterate_upto @ V0) @ V1) @ V2)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V3]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ V1)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V0 @ V1)) @ (((cLazy_Sequence.iterate_upto @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2))))))))))))))
(TLazy_Sequence.lazy_sequence.recs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_rec @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence.size_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TLazy_Sequence.lazy_sequence.size_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_size @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ V0) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TLazy_Sequence.lazy_sequence_case,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V0) @ V1)) @ (V0 @ (cLazy_Sequence.list_of_lazy_sequence @ V1))))))))
(TLazy_Sequence.small_lazy'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))) @ ((V0 @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TLazy_Sequence.small_lazy'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cLazy_Sequence.small_lazy' @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy'_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V5)) @ ((cLazy_Sequence.small_lazy' @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))) @ ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy'_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TLazy_Sequence.small_lazy'.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy'_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cLazy_Sequence.small_lazy' @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V1)) @ ((cLazy_Sequence.small_lazy' @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))))))))))
(TLazy_Sequence.small_lazy_int_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.small_lazy_int_inst.small_lazy_int @ V0)) @ ((cLazy_Sequence.small_lazy' @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_natural @ V0))) @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_natural @ V0))))))))
(TLifting.Quotient_id_abs_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cRelation.reflp @ V0)) @ ((((cTransfer.fun_rel @ cHOL.eq) @ V3) @ (^[V4]: V4)) @ V1))))))))))))
(TLifting.Quotient_rel_eq_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((((cTransfer.fun_rel @ V3) @ ((cTransfer.fun_rel @ V3) @ cHOL.eq)) @ V0) @ cHOL.eq)))))))))))
(TLifting.UNIV_typedef_to_Quotient,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ cOrderings.top_class.top)) @ ((c==> @ ((c== @ V2) @ (^[V3]: (^[V4]: ((cHOL.eq @ V3) @ (V0 @ V4)))))) @ ((((cLifting.Quotient @ cHOL.eq) @ V1) @ V0) @ V2))))))))))
(TLifting.bi_total_conv_left_right,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_total @ V0)) @ ((cHOL.conj @ (cLifting.left_total @ V0)) @ (cTransfer.right_total @ V0))))))
(TLifting.open_typedef_to_Quotient,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ (cSet.Collect @ (^[V4]: (V2 @ V4))))) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ ((((cLifting.Quotient @ (cLifting.invariant @ V2)) @ V1) @ V0) @ V3))))))))))))
(TLifting_Set.right_unique_set_rel,(call @ (^[V0]: ((c==> @ (cTransfer.right_unique @ V0)) @ (cTransfer.right_unique @ (cLifting_Set.set_rel @ V0))))))
(TLifting_Sum.right_unique_sum_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((c==> @ (cTransfer.right_unique @ V1)) @ (cTransfer.right_unique @ ((cLifting_Sum.sum_rel @ V0) @ V1)))))))))
(TLimited_Sequence.neg_not_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.neg_not_seq @ V0)) @ (^[V1]: (((cOption.option.option_case @ (cLazy_Sequence.hb_single @ cProduct_Type.Unity)) @ (^[V2]: ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cProduct_Type.unit.unit_case @ cLazy_Sequence.empty) @ V3)))) @ V2))) @ (cLazy_Sequence.yield @ (V0 @ V1))))))))
(TLimited_Sequence.pos_not_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cLimited_Sequence.pos_not_seq @ V0)) @ (^[V1]: (cLazy_Sequence.hb_not_seq @ (V0 @ ((cCode_Numeral.times_natural_inst.times_natural @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V1))))))))
(TList.comm_monoid_add.listsum_rev,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ (cList.rev @ V2))) @ (((cList.monoid_add.listsum @ V0) @ V1) @ V2))))))))))
(TList.comp_fun_idem.fold_set_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V1) @ (cList.set @ V2))) @ (((cList.fold @ V0) @ V2) @ V1))))))))))
(TList.in_set_product_lists_length,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ (cList.product_lists @ V1)))) @ ((cHOL.eq @ (cNat.size_class.size @ V0)) @ (cNat.size_class.size @ V1))))))))
(TList.length_takeWhile_less_P_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V3) @ V0)) @ (V1 @ ((cList.nth @ V2) @ V3)))))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.size_class.size @ V2))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.size_class.size @ ((cList.takeWhile @ V1) @ V2))))))))))))
(TList.linorder.filter_insort_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ (V2 @ V3))) @ ((cHOL.eq @ ((cList.filter @ V2) @ ((((cList.linorder.insort_key @ V0) @ V4) @ V3) @ V5))) @ ((cList.filter @ V2) @ V5)))))))))))))))))
(TList.linorder.insort_insert_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (cList.set @ V3))) @ ((cHOL.eq @ ((((cList.linorder.insort_insert_key @ V0) @ (^[V4]: V4)) @ V2) @ V3)) @ V3))))))))))))
(TList.linorder.insort_key_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (cList.set @ V3))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V4) @ V3))) @ ((c==> @ ((cHOL.eq @ (cList.hd @ ((cList.filter @ (^[V5]: ((cHOL.eq @ (V4 @ V2)) @ (V4 @ V5)))) @ V3))) @ V2)) @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ V4) @ V2) @ ((cList.remove1 @ V2) @ V3))) @ V3))))))))))))))))
(TList.linorder.sort_key_conv_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ (cList.set @ V3))) @ ((cHOL.eq @ (((cList.linorder.sort_key @ V0) @ V2) @ V3)) @ (((cList.fold @ ((cList.linorder.insort_key @ V0) @ V2)) @ V3) @ cList.list.Nil)))))))))))))
(TList.linorder.sorted_list_of_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ (cList.set @ ((cList.linorder.sorted_list_of_set @ V0) @ V2))) @ V2)) @ ((cHOL.conj @ ((cList.linorder.sorted @ V0) @ ((cList.linorder.sorted_list_of_set @ V0) @ V2))) @ (cList.distinct @ ((cList.linorder.sorted_list_of_set @ V0) @ V2)))))))))))))
(TList.linorder.sorted_map_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ V3))) @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ ((cList.remove1 @ V4) @ V3))))))))))))))))
(TList.linorder.sorted_remdups_adj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ (cList.remdups_adj @ V2)))))))))))
(TList.linorder_class.sort_key_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.linorder_class.sort_key @ V0) @ V1)) @ (((cList.foldr @ (cList.linorder_class.insort_key @ V0)) @ V1) @ cList.list.Nil)))))))
(TList.linorder_class.sorted.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V1)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V3) @ V2))) @ ((c==> @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: ((cOrderings.ord_class.less_eq @ V3) @ V4)))) @ ((c==> @ (cList.linorder_class.sorted @ V2)) @ V1)))))))) @ V1))))))))
(TList.linorder_class.sorted.simps,(call @ (^[V0]: ((cHOL.eq @ (cList.linorder_class.sorted @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cList.list.Cons @ V2) @ V1))) @ ((cHOL.conj @ ((cSet.Ball @ (cList.set @ V1)) @ (^[V3]: ((cOrderings.ord_class.less_eq @ V2) @ V3)))) @ (cList.linorder_class.sorted @ V1))))))))))))
(TList.map_tailrec_rev.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ (V1 @ V2)) @ V4)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V3)) @ V4)))) @ V0)))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cList.map_tailrec_rev_rel) @ V1))))))))
(TList.map_tailrec_rev_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.map_tailrec_rev_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V5)))) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ V2))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V6)) @ V7)))) @ ((c==> @ ((cHOL.eq @ V1) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))) @ ((c==> @ ((cList.map_tailrec_rev_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))) @ V2)))))))))))))) @ V2))))))))))
(TList.map_tailrec_rev_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.map_tailrec_rev_graph @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V4)))) @ ((cHOL.eq @ V1) @ V4))))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V5) @ ((cList.list.Cons @ (V3 @ V4)) @ V6)))))) @ ((cList.map_tailrec_rev_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V5) @ ((cList.list.Cons @ (V3 @ V4)) @ V6)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V5) @ ((cList.list.Cons @ (V3 @ V4)) @ V6))))))))))))))))))))))))
(TList.map_tailrec_rev_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.map_tailrec_rev_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V5) @ ((cList.list.Cons @ (V3 @ V4)) @ V6)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V5)) @ V6)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TList.rtrancl_listrel1_if_listrel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cList.listrel @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V2)))))))))))
(TList.semilattice_set.set_eq_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ (cList.set @ ((cList.list.Cons @ V1) @ V2)))) @ (((cList.fold @ V0) @ V2) @ V1))))))))))
(TNat.arity_linordered_semidom_nat,(cRings.linordered_semidom_class @ cTYPE))
(TNat.class.semiring_char_0.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ (((cNat.class.semiring_char_0_axioms @ V0) @ V2) @ V3)))))))))))
(TNat.class.semiring_char_0.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)))))))))))
(TNat.dvd.dual_order.strict_trans1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V2)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))))
(TNat.dvd.dual_order.strict_trans2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((c==> @ ((cRings.dvd_class.dvd @ V2) @ V0)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))))
(TNat.order.lift_Suc_mono_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (call @ (^[V5]: ((V1 @ (V2 @ V5)) @ (V2 @ (cNat.Suc @ V5)))))) @ ((cHOL.eq @ ((V1 @ (V2 @ V3)) @ (V2 @ V4))) @ ((cNat.ord_nat_inst.less_nat @ V3) @ V4)))))))))))))))
(TNat.order_class.lift_Suc_mono_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cOrderings.ord_class.less_eq @ (V0 @ V3)) @ (V0 @ (cNat.Suc @ V3)))))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat.semiring_1_class.Nats_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cNat.semiring_1_class.Nats)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cNat.semiring_1_class.of_nat @ V2))))) @ (V1 @ V0))))))))
(TNat.semiring_1_class.of_nat_code,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (((cNat.semiring_1_class.of_nat_aux @ (^[V1]: ((cGroups.plus_class.plus @ V1) @ cGroups.one_class.one))) @ V0) @ cGroups.zero_class.zero)))))
(TNat.semiring_1_class.of_nat_mult,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TNat.semiring_char_0_class.axioms,(((cNat.class.semiring_char_0_axioms @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TNitpick.arity_narrowing_pair_box,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TNitpick.fun_box.fun_box_case_def,((c== @ cNitpick.fun_box.fun_box_case) @ (^[V0]: (cNitpick.fun_box.fun_box_rec @ (^[V1]: (V0 @ V1))))))
(TNitpick.fun_box.fun_box_size_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cNitpick.fun_box.fun_box_size @ V0) @ V1)) @ (cNitpick.fun_box.fun_box_rec @ (^[V2]: cNat.zero_nat_inst.zero_nat))))))))
(TNitpick.fun_box.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNitpick.random_aux_fun_box @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.fun_box.FunBox) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))))))))
(TNitpick.type_definition_pair_box,(((cTypedef.type_definition @ cNitpick.Rep_pair_box) @ cNitpick.Abs_pair_box) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set)))
(TNitpick.word.word_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TNitpick.word.word_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (((cNitpick.word.word_rec_set @ V0) @ (cNitpick.word.Word @ V1)) @ (V0 @ V1)))))))
(TNitpick.word.word_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNitpick.word.word_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TNitpick.word.word_rep_set.intros,(call @ (^[V0]: (cNitpick.word.word_rep_set @ (cDatatype.Leaf @ V0)))))
(TNum.class.semiring_numeral.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((c==> @ ((cRings.class.semiring @ V2) @ V1)) @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2))))))))))
(TNum.linordered_idom.sub_negative,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ (((((cNum.neg_numeral.sub @ V1) @ V6) @ V7) @ V10) @ V11)) @ V3)) @ ((cNum.ord_num_inst.less_num @ V10) @ V11))))))))))))))))))))))))))))
(TNum.linordered_idom.sub_positive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V3) @ (((((cNum.neg_numeral.sub @ V1) @ V6) @ V7) @ V10) @ V11))) @ ((cNum.ord_num_inst.less_num @ V11) @ V10))))))))))))))))))))))))))))
(TNum.neg_numeral.is_num_normalize_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ (V3 @ V4)) @ ((V1 @ V4) @ V5))) @ V5)))))))))))))))
(TNum.neg_numeral.is_num_normalize_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ V4) @ ((V1 @ (V3 @ V4)) @ V5))) @ V5)))))))))))))))
(TNum.neg_numeral.is_num_normalize_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ ((V1 @ V4) @ V5))) @ ((V1 @ (V3 @ V5)) @ (V3 @ V4)))))))))))))))))
(TNum.neg_numeral.is_num_normalize_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ (V3 @ V5)))))))))))))))))
(TNum.neg_numeral.is_num_normalize_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))))))))))))))))
(TNum.neg_numeral.is_num_normalize_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ ((V1 @ V5) @ V6))))))))))))))))))))
(TNum.neg_numeral.is_num_normalize_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ (V3 @ V5)))))))))))))))))
(TNum.neg_numeral.is_num_normalize_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V4)))))))))))))
(TNum.neg_numeral.is_num_normalize_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6)) @ ((cHOL.eq @ ((V1 @ V5) @ ((V1 @ V6) @ V7))) @ ((V1 @ V6) @ ((V1 @ V5) @ V7)))))))))))))))))))))))
(TNum.neg_numeral.is_num_normalize_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6)) @ ((cHOL.eq @ ((V1 @ V5) @ V6)) @ ((V1 @ V6) @ V5))))))))))))))))))))
(TNum.neg_numeral.is_num_normalize_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ ((V1 @ V4) @ V5)) @ V6)) @ ((V1 @ V4) @ ((V1 @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral_class.is_num_def,((c== @ cNum.neg_numeral_class.is_num) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ cGroups.one_class.one)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cGroups.uminus_class.uminus @ V2))) @ (V0 @ V2))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cGroups.plus_class.plus @ V2) @ V3))) @ ((cHOL.conj @ (V0 @ V2)) @ (V0 @ V3))))))))))))))
(TNum.numeral.numeral.numeral_Bit0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit0 @ V2))) @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)))))))))))
(TNum.numeral.numeral.numeral_Bit1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V1) @ V0) @ (cNum.num.Bit1 @ V2))) @ ((V0 @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (((cNum.numeral.numeral @ V1) @ V0) @ V2))) @ V1))))))))))
(TNum.numeral.numeral_plus_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ (((cNum.numeral.numeral @ V1) @ V0) @ V3))) @ (((cNum.numeral.numeral @ V1) @ V0) @ ((cNum.plus_num_inst.plus_num @ V2) @ V3)))))))))))))
(TNum.numeral_class.numeral_axioms,(cNum.class.numeral @ cGroups.plus_class.plus))
(TNum.ring_1.eq_numeral_iff_iszero_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6))) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ V3)) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6))) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)) @ V3)) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6))) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V6))))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ V0)) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.plus_num_inst.plus_num @ V6) @ cNum.num.One))))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6))) @ ((cNum.ring_1.iszero @ V3) @ (((((cNum.neg_numeral.sub @ V4) @ V2) @ V0) @ cNum.num.One) @ V6)))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)) @ V0)) @ ((cNum.ring_1.iszero @ V3) @ (((((cNum.neg_numeral.sub @ V4) @ V2) @ V0) @ V6) @ cNum.num.One)))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7))) @ ((cNum.ring_1.iszero @ V3) @ (((((cNum.neg_numeral.sub @ V4) @ V2) @ V0) @ V7) @ V6)))))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V7))) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.plus_num_inst.plus_num @ V6) @ V7))))))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7))) @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.plus_num_inst.plus_num @ V6) @ V7))))))))))))))))))))))
(TNum.ring_1.eq_numeral_iff_iszero_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V7))) @ ((cNum.ring_1.iszero @ V3) @ (((((cNum.neg_numeral.sub @ V4) @ V2) @ V0) @ V6) @ V7)))))))))))))))))))))
(TNum.semiring_numeral_class.intro,((c==> @ (cGroups.monoid_mult_class @ cTYPE)) @ ((c==> @ (cRings.semiring_class @ cTYPE)) @ (cNum.semiring_numeral_class @ cTYPE))))
(TNum.semiring_numeral_class.super_2,((c==> @ (cNum.semiring_numeral_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))
(TNum.semiring_numeral_class.super_1,((c==> @ (cNum.semiring_numeral_class @ cTYPE)) @ (cGroups.monoid_mult_class @ cTYPE)))
(TNumeral_Simprocs.nat_eq_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V4))) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V3)) @ V4))))))))))))))
(TNumeral_Simprocs.nat_eq_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V4))) @ ((cHOL.eq @ V3) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V4)))))))))))))))
(TNumeral_Simprocs.nat_le_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V4))) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V3)) @ V4))))))))))))))
(TNumeral_Simprocs.nat_le_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V4))) @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V4)))))))))))))))
(TOption.option.Abs_option_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cOption.option.option_rep_set))) @ ((cHOL.eq @ (cOption.Rep_option @ (cOption.Abs_option @ V0))) @ V0)))))
(TOption.option.Rep_option_inverse,(call @ (^[V0]: ((cHOL.eq @ (cOption.Abs_option @ (cOption.Rep_option @ V0))) @ V0))))
(TOption.option.option_rec_set_def,((c== @ cOption.option.option_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cOption.option.None)) @ ((cHOL.eq @ V4) @ V0))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cOption.option.Some @ V5))) @ ((cHOL.eq @ V4) @ (V1 @ V5))))))))))))))
(TOption.option.option_rep_set_def,((c== @ cOption.option.option_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.Leaf @ V2)))))))))))
(TOrderings.bot_bool_inst.bot_bool,((c== @ cOrderings.bot_bool_inst.bot_bool) @ cOrderings.bot_bool_inst.bot_bool))
(TOrderings.class.order_axioms_def,(call @ (^[V0]: ((c== @ (cOrderings.class.order_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((V0 @ V1) @ V2)) @ ((cHOL.implies @ ((V0 @ V2) @ V1)) @ ((cHOL.eq @ V1) @ V2)))))))))))
(TOrderings.class.order_bot.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((cOrderings.class.order_bot_axioms @ V0) @ V1)))))))))
(TOrderings.class.order_bot.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((cOrderings.class.order @ V1) @ V2)))))))))
(TOrderings.class.order_top.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((cOrderings.class.order_top_axioms @ V0) @ V2)))))))))
(TOrderings.class.order_top.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((cOrderings.class.order @ V0) @ V1)))))))))
(TOrderings.class.wellorder.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ (cOrderings.class.wellorder_axioms @ V1)))))))
(TOrderings.class.wellorder.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((cOrderings.class.linorder @ V0) @ V1)))))))
(TOrderings.linorder.antisym_conv1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((V1 @ V2) @ V3))) @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.linorder.antisym_conv2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ (cHOL.Not @ ((V1 @ V2) @ V3))) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.linorder.antisym_conv3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((V1 @ V2) @ V3))) @ ((cHOL.eq @ (cHOL.Not @ ((V1 @ V3) @ V2))) @ ((cHOL.eq @ V3) @ V2)))))))))))))
(TOrderings.linorder.dual_linorder,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cOrderings.class.linorder @ (^[V2]: (^[V3]: ((V0 @ V3) @ V2)))) @ (^[V2]: (^[V3]: ((V1 @ V3) @ V2))))))))))
(TOrderings.linorder_antisym_conv1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.linorder_antisym_conv2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.linorder_antisym_conv3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V1) @ V0))) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.linorder_class.neq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.linorder_class.not_leE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TOrderings.order.less_imp_not_eq2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V3) @ V2)) @ cHOL.False))))))))))))
(TOrderings.order.strict_mono_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.strict_mono @ V1) @ V2)) @ ((cOrderings.order.mono @ V0) @ V2))))))))))
(TOrderings.order_bot.not_less_bot,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ (cHOL.Not @ ((V2 @ V3) @ V0))))))))))))
(TOrderings.order_bot_class.axioms,((cOrderings.class.order_bot_axioms @ cOrderings.bot_class.bot) @ cOrderings.ord_class.less_eq))
(TOrderings.order_bot_class.le_bot,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TOrderings.order_class.dual_order,((cOrderings.class.order @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TOrderings.order_class.order.asym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ cHOL.False)))))))
(TOrderings.order_class.order.refl,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ V0))))
(TOrderings.order_less_imp_not_eq2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ V1) @ V0)) @ cHOL.False)))))))
(TOrderings.order_top.not_top_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ (cHOL.Not @ ((V1 @ V2) @ V3))))))))))))
(TOrderings.order_top.top_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((V0 @ V3) @ V2)))))))))))
(TOrderings.order_top_class.axioms,((cOrderings.class.order_top_axioms @ cOrderings.ord_class.less_eq) @ cOrderings.top_class.top))
(TOrderings.order_top_class.top_le,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ V0)) @ ((cHOL.eq @ V0) @ cOrderings.top_class.top)))))
(TOrderings.ordering.strict_trans1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.ordering.strict_trans2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.preorder.dual_preorder,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((cOrderings.class.preorder @ (^[V2]: (^[V3]: ((V0 @ V3) @ V2)))) @ (^[V2]: (^[V3]: ((V1 @ V3) @ V2))))))))))
(TOrderings.preorder.le_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.preorder.less_imp_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.implies @ ((V1 @ V3) @ V2)) @ V4)) @ cHOL.True))))))))))))))
(TOrderings.preorder.less_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.preorder_class.eq_refl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TOrderings.top_bool_inst.top_bool,((c== @ cOrderings.top_bool_inst.top_bool) @ cOrderings.top_bool_inst.top_bool))
(TOrderings.wellorder_class.LeastI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ (V0 @ (cOrderings.ord_class.Least @ (^[V2]: (V0 @ V2))))))))))
(TOrderings.wellorder_class.axioms,(cOrderings.class.wellorder_axioms @ cOrderings.ord_class.less))
(TPartial_Function.option.leq_refl,(call @ (^[V0]: (((cPartial_Function.flat_ord @ cOption.option.None) @ V0) @ V0))))
(TPower.classrel_monoid_mult_power,(cPower.power_class @ cTYPE))
(TPower.field.nonzero_power_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((((cPower.power.power @ V3) @ V2) @ ((V1 @ V9) @ V8)) @ V10)) @ ((V1 @ ((((cPower.power.power @ V3) @ V2) @ V9) @ V10)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V10))))))))))))))))))))))))))))
(TPower.linordered_idom.abs_power2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))))))))))))))))
(TPower.linordered_idom.power2_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((((cPower.power.power @ V7) @ V9) @ (V0 @ V10)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))))))))))))))))
(TPower.monoid_mult.power3_eq_cube,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One)))) @ ((V1 @ ((V1 @ V2) @ V2)) @ V2))))))))))
(TPower.monoid_mult.power_commutes,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3)) @ V2)) @ ((V1 @ V2) @ ((((cPower.power.power @ V0) @ V1) @ V2) @ V3)))))))))))))
(TPredicate.Inf_pred_inst.Inf_pred,((c== @ cPredicate.Inf_pred_inst.Inf_pred) @ cPredicate.Inf_pred_inst.Inf_pred))
(TPredicate.Sup_pred_inst.Sup_pred,((c== @ cPredicate.Sup_pred_inst.Sup_pred) @ cPredicate.Sup_pred_inst.Sup_pred))
(TPredicate.bot_pred_inst.bot_pred,((c== @ cPredicate.bot_pred_inst.bot_pred) @ cPredicate.bot_pred_inst.bot_pred))
(TPredicate.inf_pred_inst.inf_pred,((c== @ cPredicate.inf_pred_inst.inf_pred) @ cPredicate.inf_pred_inst.inf_pred))
(TPredicate.iterate_upto_graph_def,((c== @ cPredicate.iterate_upto_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (cPredicate.Seq @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))))))) @ (cHOL.induct_forall @ (^[V7]: ((cHOL.induct_implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))))))))))))))))
(TPredicate.iterate_upto_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.iterate_upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ V2)))))))))))) @ V2)))))))))
(TPredicate.iterate_upto_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.iterate_upto_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3))))))))))))))))))
(TPredicate.seq.seq_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TPredicate.seq.seq_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ ((cPredicate.seq.Join @ V5) @ V3)) @ (((V2 @ V5) @ V3) @ V4))))))))))))))))
(TPredicate.seq.seq_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ ((cPredicate.seq.Insert @ V3) @ V4)) @ ((V1 @ V3) @ V4)))))))))))))
(TPredicate.seq.seq_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cPredicate.seq.seq_rec_set @ V0) @ V1) @ V2) @ cPredicate.seq.Empty) @ V0))))))))
(TPredicate.seq.seq_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cPredicate.seq.seq_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cPredicate.seq.seq_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))) @ V2))))))))))) @ (V1 @ V0))))))))))
(TPredicate.seq.seq_rep_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cPredicate.seq.seq_rep_set @ V0)) @ (cPredicate.seq.seq_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1))) @ V0))))))))))
(TPredicate.seq.seq_rep_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (cPredicate.seq.seq_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1)))))))))))
(TPredicate.seq.seq_rep_set.intros_1,(cPredicate.seq.seq_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TPredicate.sup_pred_inst.sup_pred,((c== @ cPredicate.sup_pred_inst.sup_pred) @ cPredicate.sup_pred_inst.sup_pred))
(TPredicate.top_pred_inst.top_pred,((c== @ cPredicate.top_pred_inst.top_pred) @ cPredicate.top_pred_inst.top_pred))
(TPredicate_Compile.contains_predE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPredicate.eval @ ((cPredicate_Compile.contains_pred @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cPredicate_Compile.contains @ V0) @ V1)) @ V3)) @ V3)))))))))))
(TPredicate_Compile.contains_predI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPredicate_Compile.contains @ V0) @ V1)) @ ((cPredicate.eval @ ((cPredicate_Compile.contains_pred @ V0) @ V1)) @ cProduct_Type.Unity)))))))
(TPredicate_Compile.pred_of_set_eq,((c== @ cPredicate.pred_of_set) @ (^[V0]: (cPredicate.pred.Pred @ (cPredicate_Compile.contains @ V0)))))
(TProduct_Type.Sigma_Diff_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cGroups.minus_class.minus @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TProduct_Type.Sigma_Diff_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: ((cGroups.minus_class.minus @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cGroups.minus_class.minus @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TProduct_Type.Times_Diff_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.Sigma @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: V2))) @ ((cGroups.minus_class.minus @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: V2))) @ ((cProduct_Type.Sigma @ V1) @ (^[V3]: V2)))))))))))
(TProduct_Type.apsnd_apfst_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.apsnd @ V0) @ ((cProduct_Type.apfst @ V1) @ V2))) @ ((cProduct_Type.apfst @ V1) @ ((cProduct_Type.apsnd @ V0) @ V2))))))))))
(TProduct_Type.bool.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cProduct_Type.bool.bool_case @ V2) @ V3) @ V0)) @ (((cProduct_Type.bool.bool_case @ V2) @ V3) @ V1))))))))))))
(TProduct_Type.insert_times_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cProduct_Type.Sigma @ ((cSet.insert @ V0) @ V1)) @ (^[V4]: ((cSet.insert @ V2) @ V3)))) @ ((cSet.insert @ ((cProduct_Type.Pair @ V0) @ V2)) @ ((cLattices.sup_class.sup @ ((cProduct_Type.Sigma @ V1) @ (^[V4]: ((cSet.insert @ V2) @ V3)))) @ ((cProduct_Type.Sigma @ ((cSet.insert @ V0) @ V1)) @ (^[V4]: V3))))))))))))))
(TProduct_Type.internal_split_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cProduct_Type.internal_split @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.prod.Abs_prod_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cProduct_Type.Abs_prod @ V2))) @ ((c==> @ ((cSet.member @ V2) @ cProduct_Type.prod)) @ V1))))) @ V1))))))
(TProduct_Type.prod.Rep_prod_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cProduct_Type.prod)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cProduct_Type.Rep_prod @ V2))) @ V1)))) @ V1)))))))
(TProduct_Type.prod.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cProduct_Type.prod.prod_case @ V2) @ V0)) @ ((cProduct_Type.prod.prod_case @ V2) @ V1))))))))))
(TProduct_Type.split_eta_SetCompr2,(call @ (^[V0]: ((cHOL.eq @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ ((V0 @ V2) @ V3)))))))) @ (cProduct_Type.prod.prod_case @ V0)))))
(TProduct_Type.unit.Abs_unit_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cProduct_Type.Abs_unit @ V2))) @ ((c==> @ ((cSet.member @ V2) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))) @ V1))))) @ V1))))))
(TProduct_Type.unit.Rep_unit_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cProduct_Type.Rep_unit @ V2))) @ V1)))) @ V1)))))))
(TProduct_Type.unit.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cProduct_Type.unit.unit_case @ V2) @ V0)) @ ((cProduct_Type.unit.unit_case @ V2) @ V1))))))))))
(TQuickcheck_Exhaustive.cps_if_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.cps_if @ V0)) @ (((cHOL.If @ V0) @ (cQuickcheck_Exhaustive.cps_single @ cProduct_Type.Unity)) @ cQuickcheck_Exhaustive.cps_empty)))))
(TQuickcheck_Exhaustive.orelse_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.orelse @ V0) @ V1)) @ (((cOption.option.option_case @ V1) @ (^[V2]: (cOption.option.Some @ V2))) @ V0)))))))
(TQuickcheck_Exhaustive.setify_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.setify @ V0) @ V1)) @ (((cList.foldr @ (cQuickcheck_Exhaustive.term_syntax.termify_insert @ V0)) @ V1) @ (cQuickcheck_Exhaustive.term_syntax.term_emptyset @ V0))))))))
(TQuickcheck_Narrowing.cfun.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Narrowing.cfun.Constant @ V2))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.cfun.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.cfun.Constant @ V0)) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.cfun.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.cfun.Constant @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TQuickcheck_Narrowing.cfun.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.cfun.Constant @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TQuickcheck_Narrowing.conv.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V0 @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V0 @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5))))))))) @ ((V0 @ V1) @ V2))))))))))
(TQuickcheck_Narrowing.conv.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Narrowing.conv @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V5))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V5) @ V6)))) @ V3))))))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ (((cQuickcheck_Narrowing.nth @ V4) @ V5) @ V6))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V5) @ V6)))) @ V3))))))))))) @ V3)))))))))))))
(TQuickcheck_Narrowing.conv.psimps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V1) @ V2)))) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.conv @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V1) @ V2))) @ (((cQuickcheck_Narrowing.nth @ V0) @ V1) @ V2))))))))))
(TQuickcheck_Narrowing.conv.psimps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V1) @ V2)))) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.conv @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V1) @ V2))) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V1))))))))))))
(TQuickcheck_Narrowing.ffun.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Narrowing.ffun.Constant @ V2))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V0 @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4)))))))))) @ (V0 @ V1))))))))
(TQuickcheck_Narrowing.ffun.inject_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.ffun.Update @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.ffun.inject_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ (cQuickcheck_Narrowing.ffun.Constant @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.ffun.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Narrowing.ffun.Constant @ V4))) @ (cHOL.Not @ (V0 @ (V1 @ V4))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.ffun.Update @ V4) @ V5) @ V6))) @ (cHOL.Not @ (V0 @ (((V2 @ V4) @ V5) @ V6))))))))))))))))))))))
(TQuickcheck_Narrowing.ffun.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cQuickcheck_Narrowing.ffun.Constant @ V4))) @ (V0 @ (V1 @ V4)))))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.ffun.Update @ V4) @ V5) @ V6))) @ (V0 @ (((V2 @ V4) @ V5) @ V6))))))))))))))))))))
(TQuickcheck_Random.random_aux_rec,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V1 @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ (call @ (^[V3]: ((cHOL.eq @ (V0 @ (cCode_Numeral.Suc @ V3))) @ (V1 @ (cCode_Numeral.Suc @ V3)))))) @ ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2)))))))))))
(TQuickcheck_Random.random_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ (cQuickcheck_Random.random_fun_lift @ (cQuickcheck_Random.random_class.random @ V0))))))
(TQuickcheck_Random.random_int_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_int_inst.random_int @ V0)) @ ((cProduct_Type.scomp @ (cRandom.range @ ((cCode_Numeral.plus_natural_inst.plus_natural @ ((cCode_Numeral.times_natural_inst.times_natural @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ cCode_Numeral.one_natural_inst.one_natural))) @ (^[V1]: (cProduct_Type.Pair @ ((cHOL.Let @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ V1)) @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_natural @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ V0)))) @ (cInt.uminus_int_inst.uminus_int @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_natural @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ V1)))))) @ (^[V2]: ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V2))))))))))))
(TQuickcheck_Random.random_nat_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_nat_inst.random_nat @ V0)) @ ((cProduct_Type.scomp @ (cRandom.range @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (^[V1]: (cProduct_Type.Pair @ ((cHOL.Let @ (cCode_Numeral.nat_of_natural @ V1)) @ (^[V2]: ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_nat_inst.term_of_nat @ V2))))))))))))
(TQuickcheck_Random.random_num_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_num_inst.random_num @ V0)) @ ((cQuickcheck_Random.random_aux_num @ V0) @ V0)))))
(TQuickcheck_Random.random_seq_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_seq @ V0) @ V0)))))
(TQuickcheck_Random.random_set_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_set @ V0) @ V0)))))
(TQuickcheck_Random.random_sum_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_sum @ V0) @ V0)))))
(TRandom_Sequence.Random_graph_def,((c== @ cRandom_Sequence.Random_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V4 @ V6)) @ (^[V7]: ((cProduct_Type.scomp @ ((V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ V6)) @ (^[V8]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V7))) @ V8)))))))))) @ (cHOL.induct_forall @ (^[V6]: (cHOL.induct_forall @ (^[V7]: ((cHOL.induct_implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))))))
(TRandom_Sequence.Random_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.Random_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ V2)))))))))))) @ V2)))))))))
(TRandom_Sequence.Random_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.Random_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))))))
(TRandom_Sequence.iter.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V5) @ (V1 @ V3))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V6) @ V7)) @ V5)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V6)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ V10))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0)))))))))))))))))))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cRandom_Sequence.iter_rel) @ V1))))))))
(TRandom_Sequence.iter_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.iter_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: ((cHOL.Let @ (V4 @ V6)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cOption.option.Some @ ((cProduct_Type.Pair @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V10)))))))))))))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((cRandom_Sequence.iter_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))))))))))))))))))))))) @ V2)))))))))))) @ V2)))))))))
(TRandom_Sequence.iter_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.iter_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V6]: ((cHOL.Let @ (V3 @ V5)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (^[V9]: (cOption.option.Some @ ((cProduct_Type.Pair @ V7) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V9)))))))))))))))) @ (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: (cHOL.All @ (^[V8]: (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: (cHOL.All @ (^[V11]: (cHOL.All @ (^[V12]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cHOL.implies @ ((cHOL.eq @ V7) @ (V3 @ V5))) @ ((cHOL.implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((cHOL.implies @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ ((cRandom_Sequence.iter_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V12))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V12))))))))))))))))))))))))))))))))))))))
(TRandom_Sequence.iter_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.iter_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V7) @ (V3 @ V5))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V7)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V10) @ V11)) @ V8)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V12))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRecord.isomorphic_tuple.abst_inj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cRecord.abst @ V0) @ V1)) @ ((cRecord.abst @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TRecord.isomorphic_tuple.abst_inv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cRecord.repr @ V0) @ ((cRecord.abst @ V0) @ V1))) @ V1)))))))
(TRecord.isomorphic_tuple.repr_inj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cRecord.repr @ V0) @ V1)) @ ((cRecord.repr @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TRecord.isomorphic_tuple.repr_inv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cRecord.abst @ V0) @ ((cRecord.repr @ V0) @ V1))) @ V1)))))))
(TRecord.tuple_isomorphism.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TRecord.tuple_isomorphism.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V2) @ V3))) @ V1)))))) @ V1))))))
(TRecord.tuple_isomorphism.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TRelation.transp_relcompp_less_eq,(call @ (^[V0]: ((c==> @ (cRelation.transp @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcompp @ V0) @ V0)) @ V0)))))
(TRings.class.comm_semiring.axioms_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.comm_semiring @ V0) @ V1)) @ ((cRings.class.comm_semiring_axioms @ V0) @ V1)))))))
(TRings.class.comm_semiring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.comm_semiring @ V0) @ V1)) @ (cGroups.class.ab_semigroup_mult @ V1)))))))
(TRings.class.comm_semiring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.class.comm_semiring @ V0) @ V1)) @ (cGroups.class.ab_semigroup_add @ V0)))))))
(TRings.class.no_zero_divisors_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.class.no_zero_divisors @ V0) @ V1)) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V1))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V1))) @ (cHOL.Not @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ V1))))))))))))))
(TRings.class.ordered_ring_abs_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cRings.class.ordered_ring_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.conj @ (((((((cRings.class.ordered_ring @ V1) @ V2) @ V5) @ V6) @ V7) @ V3) @ V4)) @ ((((cRings.class.ordered_ring_abs_axioms @ V0) @ V2) @ V5) @ V7)))))))))))))))))))))
(TRings.class.ordered_semiring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cHOL.conj @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V2) @ V3))) @ ((cHOL.conj @ ((cRings.class.semiring @ V0) @ V4)) @ (((cRings.class.ordered_semiring_axioms @ V1) @ V2) @ V4)))))))))))))))
(TRings.comm_ring_1_class.dvd_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2)))))))))))
(TRings.comm_semiring_1.dvd_0_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V3) @ V4)) @ ((cHOL.eq @ V4) @ V3))))))))))))))
(TRings.comm_semiring_class.axioms,((cRings.class.comm_semiring_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times))
(TRings.idom.dvd_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ ((V0 @ V6) @ V7)) @ ((V0 @ V8) @ V7))) @ ((cHOL.disj @ ((cHOL.eq @ V7) @ V3)) @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)))))))))))))))))))))))
(TRings.no_zero_divisors_class_def,((c== @ (cRings.no_zero_divisors_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.times_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.zero_class @ cTYPE)) @ ((cRings.class.no_zero_divisors @ cGroups.times_class.times) @ cGroups.zero_class.zero)))))
(TRings.ordered_ring.less_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((V3 @ ((V0 @ ((V4 @ V7) @ V8)) @ V9)) @ ((V0 @ ((V4 @ V10) @ V8)) @ V11))) @ ((V3 @ ((V0 @ ((V4 @ ((V5 @ V7) @ V10)) @ V8)) @ V9)) @ V11))))))))))))))))))))))))))))
(TRings.ordered_ring.less_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((V3 @ ((V0 @ ((V4 @ V7) @ V8)) @ V9)) @ ((V0 @ ((V4 @ V10) @ V8)) @ V11))) @ ((V3 @ V9) @ ((V0 @ ((V4 @ ((V5 @ V10) @ V7)) @ V8)) @ V11)))))))))))))))))))))))))))))
(TRings.ordered_ring_abs_class_def,((c== @ (cRings.ordered_ring_abs_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_ab_group_add_abs_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.ordered_ring_class @ cTYPE)) @ ((((cRings.class.ordered_ring_abs_axioms @ cGroups.abs_class.abs) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cGroups.times_class.times)))))
(TRings.ordered_semiring.mult_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((c==> @ ((V2 @ V7) @ V8)) @ ((c==> @ ((V2 @ V1) @ V6)) @ ((c==> @ ((V2 @ V1) @ V7)) @ ((V2 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V8))))))))))))))))))))))))))
(TRings.ordered_semiring_class_def,((c== @ (cRings.ordered_semiring_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.comm_monoid_add_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.semiring_class @ cTYPE)) @ (((cRings.class.ordered_semiring_axioms @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cGroups.times_class.times)))))
(TRings.ring_1_class.ring_1_axioms,((((((cRings.class.ring_1 @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TRings.ring_class.minus_mult_left,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cGroups.times_class.times @ (cGroups.uminus_class.uminus @ V0)) @ V1)))))))
(TRings.ring_class.mult_minus_left,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ (cGroups.uminus_class.uminus @ ((cGroups.times_class.times @ V0) @ V1))))))))
(TSMT.partial_term_of_pattern_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSMT.partial_term_of_pattern_inst.partial_term_of_pattern @ V0) @ V1)) @ cHOL.undefined))))))
(TSet_Interval.Sup_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ V1)))))))
(TSet_Interval.atLeastLessThan_inj_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cHOL.eq @ V1) @ V3)))))))))))))
(TSet_Interval.atLeastLessThan_inj_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cHOL.eq @ V0) @ V2)))))))))))))
(TSet_Interval.dvd.greaterThan_def,(call @ (^[V0]: ((c== @ ((cSet_Interval.ord.greaterThan @ (^[V1]: (^[V2]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V1)))))) @ V0)) @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))))))))
(TSet_Interval.dvd.greaterThan_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.greaterThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))))
(TSet_Interval.lessThan_Suc_atMost,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.lessThan @ (cNat.Suc @ V0))) @ (cSet_Interval.ord_class.atMost @ V0)))))
(TSet_Interval.lessThan_subset_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.lessThan @ V0)) @ (cSet_Interval.ord_class.lessThan @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet_Interval.linorder.Int_atMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ ((cSet_Interval.ord.atMost @ V0) @ V3))) @ ((cSet_Interval.ord.atMost @ V0) @ (((cOrderings.ord.min @ V0) @ V2) @ V3)))))))))))))
(TSet_Interval.ord.greaterThan_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord.greaterThan @ V0) @ V1)) @ (cSet.Collect @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TSet_Interval.ord.greaterThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord.greaterThan @ V1) @ V2))) @ ((V1 @ V2) @ V0)))))))))
(TSet_Interval.setsum_diff_nat_ivl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))))))))))))))
(TSet_Interval.setsum_head_upt_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (V2 @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet_Interval.ord_class.atLeastLessThan @ (cNat.Suc @ V0)) @ V1))))))))))))
(TSet_Interval.setsum_lessThan_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V0 @ V2))) @ (cSet_Interval.ord_class.lessThan @ (cNat.Suc @ V1)))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V0 @ V2))) @ (cSet_Interval.ord_class.lessThan @ V1))) @ (V0 @ V1))))))))
(TString.char.char_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cString.char.char_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V2)) @ (cDatatype.Leaf @ V3)))))))) @ (V1 @ V0))))))))
(TString.nibble.Abs_nibble_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cString.nibble.nibble_rep_set))) @ ((cHOL.eq @ (cString.Rep_nibble @ (cString.Abs_nibble @ V0))) @ V0)))))
(TString.nibble.Rep_nibble_inverse,(call @ (^[V0]: ((cHOL.eq @ (cString.Abs_nibble @ (cString.Rep_nibble @ V0))) @ V0))))
(TString.nibble.nibble_rec_set_def,((c== @ cString.nibble.nibble_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (^[V6]: (^[V7]: (^[V8]: (^[V9]: (^[V10]: (^[V11]: (^[V12]: (^[V13]: (^[V14]: (^[V15]: (cInductive.complete_lattice_class.lfp @ (^[V16]: (^[V17]: (^[V18]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble0)) @ ((cHOL.eq @ V18) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble1)) @ ((cHOL.eq @ V18) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble2)) @ ((cHOL.eq @ V18) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble3)) @ ((cHOL.eq @ V18) @ V3))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble4)) @ ((cHOL.eq @ V18) @ V4))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble5)) @ ((cHOL.eq @ V18) @ V5))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble6)) @ ((cHOL.eq @ V18) @ V6))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble7)) @ ((cHOL.eq @ V18) @ V7))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble8)) @ ((cHOL.eq @ V18) @ V8))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.Nibble9)) @ ((cHOL.eq @ V18) @ V9))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleA)) @ ((cHOL.eq @ V18) @ V10))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleB)) @ ((cHOL.eq @ V18) @ V11))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleC)) @ ((cHOL.eq @ V18) @ V12))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleD)) @ ((cHOL.eq @ V18) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleE)) @ ((cHOL.eq @ V18) @ V14))) @ ((cHOL.conj @ ((cHOL.eq @ V17) @ cString.nibble.NibbleF)) @ ((cHOL.eq @ V18) @ V15)))))))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rep_set_def,((c== @ cString.nibble.nibble_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))))))))))))))))))))))
(TString.nibble_of_nat_nat_of_char,(call @ (^[V0]: ((cHOL.eq @ (cString.nibble_of_nat @ (cString.nat_of_char @ V0))) @ ((cString.char.char_case @ (^[V1]: (^[V2]: V2))) @ V0)))))
(TTransfer.Domainp_forall_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ (cTransfer.transfer_bforall @ (cRelation.Domainp @ V0))) @ cTransfer.transfer_forall)))))
(TTransfer.right_total_Ex_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ (cSet.Bex @ (cSet.Collect @ (cRelation.Domainp @ V0)))) @ cHOL.Ex)))))
(TTransfer.transfer_bforall_unfold,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cTransfer.transfer_bforall @ V0) @ (^[V2]: (V1 @ V2)))) @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TTransitive_Closure.Range_rtrancl,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Range @ (cTransitive_Closure.rtrancl @ V0))) @ cOrderings.top_class.top))))
(TTransitive_Closure.finite_relpow,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ (cFinite_Set.finite @ ((cNat.compow @ V1) @ V0)))))))))
(TTransitive_Closure.finite_trancl,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ (cTransitive_Closure.trancl @ V0))) @ (cFinite_Set.finite @ V0)))))
(TTransitive_Closure.reflcl_set_eq,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)))) @ cHOL.eq)) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cLattices.sup_class.sup @ V0) @ cRelation.Id))))))))
(TTransitive_Closure.reflcl_trancl,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cTransitive_Closure.trancl @ V0)) @ cRelation.Id)) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.reflclp_idemp,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ cHOL.eq)) @ cHOL.eq)) @ ((cLattices.sup_class.sup @ V0) @ cHOL.eq)))))
(TTransitive_Closure.relpow_Suc_D2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ (cNat.Suc @ V2)) @ V3))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ V3)) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V1)) @ ((cNat.compow @ V2) @ V3)))))))))))))))
(TTransitive_Closure.relpow_Suc_E2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ (cNat.Suc @ V2)) @ V3))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V5)) @ V3)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ ((cNat.compow @ V2) @ V3))) @ V4))))) @ V4)))))))))))))
(TTransitive_Closure.relpow_Suc_I2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ ((cNat.compow @ V4) @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ ((cNat.compow @ (cNat.Suc @ V4)) @ V2)))))))))))))))
(TTransitive_Closure.relpowp.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ (cNat.Suc @ V0)) @ V1)) @ ((cRelation.relcompp @ ((cNat.compow @ V0) @ V1)) @ V1)))))))
(TTransitive_Closure.relpowp.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cNat.compow @ cNat.zero_nat_inst.zero_nat) @ V0)) @ cHOL.eq))))
(TTransitive_Closure.relpowp_Suc_E,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.compow @ (cNat.Suc @ V0)) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((((cNat.compow @ V0) @ V1) @ V2) @ V5)) @ ((c==> @ ((V1 @ V5) @ V3)) @ V4))))) @ V4)))))))))))))
(TTransitive_Closure.relpowp_Suc_I,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.compow @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((((cNat.compow @ (cNat.Suc @ V0)) @ V1) @ V2) @ V4))))))))))))))
(TTransitive_Closure.rtrancl.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V4)) @ V3))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ V3))))))))))) @ V3))))))))))))
(TTransitive_Closure.rtrancl.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.eq @ V1) @ V3))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V5)) @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)))))))))))))))))))
(TTransitive_Closure.rtrancl_empty,((cHOL.eq @ (cTransitive_Closure.rtrancl @ cOrderings.bot_class.bot)) @ cRelation.Id))
(TTransitive_Closure.rtrancl_idemp,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ (cTransitive_Closure.rtrancl @ V0))) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.rtrancl_power,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ V1))) @ (cHOL.Ex @ (^[V2]: ((cSet.member @ V0) @ ((cNat.compow @ V2) @ V1))))))))))
(TTransitive_Closure.rtrancl_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.rtranclp_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cTransitive_Closure.rtranclp @ V0)) @ (cTransitive_Closure.rtranclp @ V1))))))))
(TTransitive_Closure.trancl.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((V3 @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TTransitive_Closure.trancl.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.trancl.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))))))))))
(TTransitive_Closure.trancl_domain,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ (cTransitive_Closure.trancl @ V0))) @ (cRelation.Domain @ V0)))))
(TTransitive_Closure.trancl_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ V2)) @ (V3 @ V4))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ (V3 @ V4)) @ (V3 @ V5))))))))) @ (V3 @ V1)))))))))))))
(TTransitive_Closure.trancl_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cTransitive_Closure.trancl @ ((cSet.insert @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2))) @ ((cLattices.sup_class.sup @ (cTransitive_Closure.trancl @ V2)) @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V0)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V4)) @ (cTransitive_Closure.rtrancl @ V2))))))))))))))))
(TTransitive_Closure.trancl_reflcl,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.trancl @ ((cLattices.sup_class.sup @ V0) @ cRelation.Id))) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.trancl_unfold,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.trancl @ V0)) @ ((cLattices.sup_class.sup @ V0) @ ((cRelation.relcomp @ (cTransitive_Closure.trancl @ V0)) @ V0))))))
(TTransitive_Closure.tranclp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V5)) @ ((c==> @ ((V0 @ V4) @ V5)) @ V3)))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V6)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V4) @ V5)) @ ((c==> @ ((V0 @ V5) @ V6)) @ V3))))))))))) @ V3))))))))))))
(TTransitive_Closure.tranclp.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V4)) @ ((V0 @ V3) @ V4)))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V5)) @ ((cHOL.conj @ (((cTransitive_Closure.tranclp @ V0) @ V3) @ V4)) @ ((V0 @ V4) @ V5)))))))))))))))))))
(TTransitive_Closure.tranclp_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V3)) @ ((((cNat.compow @ V3) @ V0) @ V1) @ V2))))))))))))
(TTransitive_Closure.tranclp_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.trans_reflclI,(call @ (^[V0]: ((c==> @ (cRelation.trans @ V0)) @ (cRelation.trans @ ((cLattices.sup_class.sup @ V0) @ cRelation.Id))))))
(TTransitive_Closure.trans_rtrancl,(call @ (^[V0]: (cRelation.trans @ (cTransitive_Closure.rtrancl @ V0)))))
(TTyperep.typerep.typerep_case_def,((c== @ cTyperep.typerep.typerep_case) @ (^[V0]: (((cTyperep.typerep.typerep_rec_1 @ (^[V1]: (^[V2]: (^[V3]: ((V0 @ V1) @ V2))))) @ cHOL.undefined) @ cHOL.undefined))))
(TTyperep.typerep.typerep_size_def,((c== @ cTyperep.typerep.typerep_size) @ (((cTyperep.typerep.typerep_rec_1 @ (^[V0]: (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TWellfounded.trans_finite_psubset,(cRelation.trans @ cWellfounded.finite_psubset))
(TBig_Operators.card_Union_disjoint,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V1]: (cFinite_Set.finite @ V1)))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ V2)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ (cFinite_Set.card @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ cFinite_Set.card) @ V0))))))))
(TBig_Operators.comm_monoid_set_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((cGroups.comm_monoid @ V0) @ V1)))))))
(TBig_Operators.linorder.Max_ge_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ V3) @ ((cBig_Operators.linorder.Max @ V0) @ V2))) @ ((cSet.Bex @ V2) @ (^[V4]: ((V0 @ V3) @ V4))))))))))))))))
(TBig_Operators.linorder.Max_gr_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V1 @ V3) @ ((cBig_Operators.linorder.Max @ V0) @ V2))) @ ((cSet.Bex @ V2) @ (^[V4]: ((V1 @ V3) @ V4))))))))))))))))
(TBig_Operators.linorder.Max_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.linorder.Max @ V0) @ ((cSet.insert @ V3) @ V2))) @ (((cOrderings.ord.max @ V0) @ V3) @ ((cBig_Operators.linorder.Max @ V0) @ V2)))))))))))))))
(TBig_Operators.linorder.Max_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ ((cBig_Operators.linorder.Max @ V0) @ V2)) @ V3)) @ ((cSet.Ball @ V2) @ (^[V4]: ((V0 @ V4) @ V3))))))))))))))))
(TBig_Operators.linorder.Min_ge_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ V3) @ ((cBig_Operators.linorder.Min @ V0) @ V2))) @ ((cSet.Ball @ V2) @ (^[V4]: ((V0 @ V3) @ V4))))))))))))))))
(TBig_Operators.linorder.Min_gr_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V1 @ V3) @ ((cBig_Operators.linorder.Min @ V0) @ V2))) @ ((cSet.Ball @ V2) @ (^[V4]: ((V1 @ V3) @ V4))))))))))))))))
(TBig_Operators.linorder.Min_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.linorder.Min @ V0) @ ((cSet.insert @ V3) @ V2))) @ (((cOrderings.ord.min @ V0) @ V3) @ ((cBig_Operators.linorder.Min @ V0) @ V2)))))))))))))))
(TBig_Operators.linorder.Min_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ ((cBig_Operators.linorder.Min @ V0) @ V2)) @ V3)) @ ((cSet.Bex @ V2) @ (^[V4]: ((V0 @ V4) @ V3))))))))))))))))
(TBig_Operators.semilattice_set_def,(call @ (^[V0]: ((c== @ (cBig_Operators.semilattice_set @ V0)) @ (cLattices.semilattice @ V0)))))
(TBig_Operators.setprod_UN_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ V0) @ (^[V4]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V1 @ V4))) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ (V1 @ V3)))) @ V0))))))))))))
(TBig_Operators.setprod_Un_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)))))))))))))
(TBig_Operators.setprod_dvd_setprod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cRings.dvd_class.dvd @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cRings.dvd_class.dvd @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))
(TBig_Operators.setprod_pos_nat_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ (V1 @ V2)))))))))))
(TBig_Operators.setprod_subset_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))))
(TBig_Operators.setsum_left_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cGroups.times_class.times @ (V0 @ V3)) @ V2))) @ V1)))))))))
(TBig_Operators.strong_setprod_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)))))))))))))
(TCode_Evaluation.arity_term_of_fun,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_int,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_nat,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_num,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_seq,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_set,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_sum,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_typerep_seq,(cTyperep.typerep_class @ cTYPE))
(TCode_Evaluation.term.term_rec_def,((c== @ cCode_Evaluation.term.term_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cCode_Evaluation.term.term_rec_set @ V0) @ V1) @ V2)))))))
(TCode_Evaluation.term_of_bool_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_bool_inst.term_of_bool @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_char_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_char_inst.term_of_char @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_class_def,((c== @ (cCode_Evaluation.term_of_class @ cTYPE)) @ (cTyperep.typerep_class @ cTYPE)))
(TCode_Evaluation.term_of_list_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_pred_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_prod_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_term_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_term_inst.term_of_term @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_unit_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_unit_inst.term_of_unit @ V0)) @ cHOL.undefined))))
(TCode_Numeral.abs_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer) @ cInt.abs_int_inst.abs_int) @ cCode_Numeral.abs_integer_inst.abs_integer))
(TCode_Numeral.arity_ring_1_integer,(cRings.ring_1_class @ cTYPE))
(TCode_Numeral.div_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer)) @ cDivides.div_int_inst.div_int) @ cCode_Numeral.div_integer_inst.div_integer))
(TCode_Numeral.div_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cCode_Numeral.pcr_natural)) @ cDivides.div_nat_inst.div_nat) @ cCode_Numeral.div_natural_inst.div_natural))
(TCode_Numeral.equal_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ ((cHOL.equal_class.equal @ V0) @ V1)))))))
(TCode_Numeral.equal_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.equal_class.equal @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.equal_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ ((cHOL.equal_class.equal @ V0) @ V1)))))))
(TCode_Numeral.equal_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.equal_class.equal @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.integer.rep_transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cHOL.eq) @ (^[V0]: V0)) @ cCode_Numeral.int_of_integer))
(TCode_Numeral.integer.right_unique,(cTransfer.right_unique @ cCode_Numeral.pcr_integer))
(TCode_Numeral.less_eq_integer_code_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Neg @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V1) @ V0)))))))
(TCode_Numeral.less_eq_integer_code_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ (cCode_Numeral.Neg @ V0)) @ (cCode_Numeral.Pos @ V1))) @ cHOL.True))))))
(TCode_Numeral.less_eq_integer_code_7,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ (cCode_Numeral.Neg @ V0)) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.True))))
(TCode_Numeral.less_eq_integer_code_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Neg @ V1))) @ cHOL.False))))))
(TCode_Numeral.less_eq_integer_code_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ (cCode_Numeral.Pos @ V0)) @ (cCode_Numeral.Pos @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TCode_Numeral.less_eq_integer_code_4,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ (cCode_Numeral.Pos @ V0)) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.False))))
(TCode_Numeral.less_eq_integer_code_3,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.Neg @ V0))) @ cHOL.False))))
(TCode_Numeral.less_eq_integer_code_2,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ (cCode_Numeral.Pos @ V0))) @ cHOL.True))))
(TCode_Numeral.less_eq_integer_code_1,((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ cCode_Numeral.zero_integer_inst.zero_integer) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ cHOL.True))
(TCode_Numeral.minus_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.minus_integer_inst.minus_integer @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ (cCode_Numeral.integer_of_int @ ((cInt.minus_int_inst.minus_int @ V0) @ V1))))))))
(TCode_Numeral.minus_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cCode_Numeral.minus_integer_inst.minus_integer @ V0) @ V1))) @ ((cInt.minus_int_inst.minus_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.minus_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.minus_natural_inst.minus_natural @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ (cCode_Numeral.natural_of_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))))))))
(TCode_Numeral.minus_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.mod_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer)) @ cDivides.div_int_inst.mod_int) @ cCode_Numeral.div_integer_inst.mod_integer))
(TCode_Numeral.mod_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cCode_Numeral.pcr_natural)) @ cDivides.div_nat_inst.mod_nat) @ cCode_Numeral.div_natural_inst.mod_natural))
(TCode_Numeral.natural.rep_transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cHOL.eq) @ (^[V0]: V0)) @ cCode_Numeral.nat_of_natural))
(TCode_Numeral.natural.right_unique,(cTransfer.right_unique @ cCode_Numeral.pcr_natural))
(TCode_Numeral.one_integer.transfer,((cCode_Numeral.pcr_integer @ cInt.one_int_inst.one_int) @ cCode_Numeral.one_integer_inst.one_integer))
(TCode_Numeral.one_natural.transfer,((cCode_Numeral.pcr_natural @ cNat.one_nat_inst.one_nat) @ cCode_Numeral.one_natural_inst.one_natural))
(TCode_Numeral.sgn_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer) @ cInt.sgn_int_inst.sgn_int) @ cCode_Numeral.sgn_integer_inst.sgn_integer))
(TCode_Numeral.times_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.times_integer_inst.times_integer @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ (cCode_Numeral.integer_of_int @ ((cInt.times_int_inst.times_int @ V0) @ V1))))))))
(TCode_Numeral.times_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ ((cCode_Numeral.times_integer_inst.times_integer @ V0) @ V1))) @ ((cInt.times_int_inst.times_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.times_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.times_natural_inst.times_natural @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ (cCode_Numeral.natural_of_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))))))))
(TCode_Numeral.times_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ ((cCode_Numeral.times_natural_inst.times_natural @ V0) @ V1))) @ ((cNat.times_nat_inst.times_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TComplete_Lattices.Collect_ball_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((V1 @ V2) @ V3)))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (cSet.Collect @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TComplete_Lattices.INTER_UNIV_conv_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2)))) @ cOrderings.top_class.top)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.top_class.top)))))))))
(TComplete_Lattices.INTER_UNIV_conv_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.top_class.top) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.top_class.top)))))))))
(TComplete_Lattices.INT_Int_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.Inf_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cComplete_Lattices.Inf_class @ cTYPE)))
(TComplete_Lattices.Inf_class.super,((c==> @ (cComplete_Lattices.Inf_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TComplete_Lattices.Int_Inter_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Inf_class.Inf @ ((cSet.image @ V1) @ V0))) @ (cComplete_Lattices.Inf_class.Inf @ ((cSet.image @ V2) @ V0)))))))))))
(TComplete_Lattices.Int_UN_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V1 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V2) @ (^[V4]: (V3 @ V4))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V2) @ (^[V5]: ((cLattices.inf_class.inf @ (V1 @ V4)) @ (V3 @ V5))))))))))))))))
(TComplete_Lattices.Inter_UNIV_conv_2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.top_class.top) @ (cComplete_Lattices.Inf_class.Inf @ V0))) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.top_class.top)))))))
(TComplete_Lattices.Inter_UNIV_conv_1,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ cOrderings.top_class.top)) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.top_class.top)))))))
(TComplete_Lattices.Inter_Un_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ (cComplete_Lattices.Inf_class.Inf @ ((cLattices.inf_class.inf @ V0) @ V1))))))))
(TComplete_Lattices.Inter_anti_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V1)) @ (cComplete_Lattices.Inf_class.Inf @ V0))))))))
(TComplete_Lattices.Sup_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cComplete_Lattices.Sup_class @ cTYPE)))
(TComplete_Lattices.Sup_class.super,((c==> @ (cComplete_Lattices.Sup_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TComplete_Lattices.UN_extend_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet.image @ V2) @ V0)) @ (^[V3]: (V1 @ V3)))))))))))
(TComplete_Lattices.UN_extend_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.SUPR @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))))))))))
(TComplete_Lattices.UN_extend_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V2) @ (^[V3]: (V1 @ V3)))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V2]: (V1 @ V2)))))))))
(TComplete_Lattices.UN_extend_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cGroups.minus_class.minus @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.UN_extend_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cGroups.minus_class.minus @ (V1 @ V3)) @ V2)))))))))))
(TComplete_Lattices.UN_extend_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cLattices.inf_class.inf @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.UN_extend_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ V2)))))))))))
(TComplete_Lattices.UN_extend_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cLattices.sup_class.sup @ V0) @ (V2 @ V3)))))))))))))
(TComplete_Lattices.UN_extend_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ V2))))))))))))
(TComplete_Lattices.UN_extend_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.insert @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cSet.insert @ V0) @ (V2 @ V3)))))))))))))
(TComplete_Lattices.Un_INT_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V1 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ (^[V4]: (V3 @ V4))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ (^[V5]: ((cLattices.sup_class.sup @ (V1 @ V4)) @ (V3 @ V5))))))))))))))))
(TDivides.class.semiring_div.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cDivides.class.semiring_div_axioms @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))
(TDivides.class.semiring_div.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cRings.class.no_zero_divisors @ V0) @ V4)))))))))))))))
(TDivides.class.semiring_div.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cRings.class.comm_semiring_1_cancel @ V3) @ V4) @ V0) @ V5)))))))))))))))
(TDivides.divmod_nat_rel_divmod_nat,(call @ (^[V0]: (call @ (^[V1]: (((cDivides.divmod_nat_rel @ V0) @ V1) @ ((cDivides.divmod_nat @ V0) @ V1)))))))
(TDivides.neg_divmod_int_rel_mult_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ (((cDivides.divmod_int_rel @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)) @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (((cDivides.divmod_int_rel @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ ((cProduct_Type.Pair @ V2) @ ((cInt.minus_int_inst.minus_int @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3)) @ cInt.one_int_inst.one_int))))))))))))))
(TDivides.pos_divmod_int_rel_mult_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ (((cDivides.divmod_int_rel @ V1) @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (((cDivides.divmod_int_rel @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ ((cProduct_Type.Pair @ V2) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ ((cInt.times_int_inst.times_int @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3)))))))))))))))
(TDivides.ring_div.div_minus1_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ ((((cNum.neg_numeral.neg_numeral @ V3) @ V7) @ V5) @ cNum.num.One))) @ (V7 @ V8))))))))))))))))))))))
(TDivides.ring_div.mod_diff_left_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ ((V6 @ V8) @ V9)) @ V10)) @ ((V2 @ ((V6 @ ((V2 @ V8) @ V10)) @ V9)) @ V10))))))))))))))))))))))))))
(TDivides.ring_div.mod_minus1_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V8) @ ((((cNum.neg_numeral.neg_numeral @ V3) @ V7) @ V5) @ cNum.num.One))) @ V4)))))))))))))))))))))
(TDivides.semiring_div.dvd_div_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((V0 @ ((V1 @ V7) @ V6)) @ V8)) @ ((V1 @ ((V0 @ V7) @ V8)) @ V6)))))))))))))))))))))))
(TDivides.semiring_div.mod_add_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cHOL.eq @ ((V2 @ V6) @ V7)) @ ((V2 @ V8) @ V7))) @ ((c==> @ ((cHOL.eq @ ((V2 @ V9) @ V7)) @ ((V2 @ V10) @ V7))) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ V9)) @ V7)) @ ((V2 @ ((V3 @ V8) @ V10)) @ V7))))))))))))))))))))))))))))
(TDivides.semiring_div_class.axioms,(((((cDivides.class.semiring_div_axioms @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TDivides.unique_quotient_lemma_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V1)) @ V2)) @ ((cInt.plus_int_inst.plus_int @ ((cInt.times_int_inst.times_int @ V0) @ V3)) @ V4))) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V4) @ cInt.zero_int_inst.zero_int)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V4)) @ ((c==> @ ((cInt.ord_int_inst.less_int @ V0) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ V3) @ V1))))))))))))))))
(TEnum.enum_bool_inst.enum_all_bool,((c== @ cEnum.enum_bool_inst.enum_all_bool) @ cEnum.enum_bool_inst.enum_all_bool))
(TEnum.enum_option_inst.enum_option,((c== @ cEnum.enum_option_inst.enum_option) @ cEnum.enum_option_inst.enum_option))
(TEnum.enum_prod_inst.enum_all_prod,((c== @ cEnum.enum_prod_inst.enum_all_prod) @ cEnum.enum_prod_inst.enum_all_prod))
(TEnum.enum_unit_inst.enum_all_unit,((c== @ cEnum.enum_unit_inst.enum_all_unit) @ cEnum.enum_unit_inst.enum_all_unit))
(TEnum.finite_1.Abs_finite_1_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set))) @ (V0 @ (cEnum.Abs_finite_1 @ V2)))))) @ (V0 @ V1)))))))
(TEnum.finite_1.Abs_finite_1_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cEnum.Abs_finite_1 @ V0)) @ (cEnum.Abs_finite_1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TEnum.finite_1.Rep_finite_1_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cEnum.Rep_finite_1 @ V2))))) @ (V1 @ V0))))))))
(TEnum.finite_1.Rep_finite_1_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cEnum.Rep_finite_1 @ V0)) @ (cEnum.Rep_finite_1 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.finite_1.arity_size_finite_1,(cNat.size_class @ cTYPE))
(TEnum.finite_2.Abs_finite_2_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set))) @ (V0 @ (cEnum.Abs_finite_2 @ V2)))))) @ (V0 @ V1)))))))
(TEnum.finite_2.Abs_finite_2_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cEnum.Abs_finite_2 @ V0)) @ (cEnum.Abs_finite_2 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TEnum.finite_2.Rep_finite_2_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cEnum.Rep_finite_2 @ V2))))) @ (V1 @ V0))))))))
(TEnum.finite_2.Rep_finite_2_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cEnum.Rep_finite_2 @ V0)) @ (cEnum.Rep_finite_2 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.finite_2.arity_size_finite_2,(cNat.size_class @ cTYPE))
(TEnum.finite_3.Abs_finite_3_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set))) @ (V0 @ (cEnum.Abs_finite_3 @ V2)))))) @ (V0 @ V1)))))))
(TEnum.finite_3.Abs_finite_3_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cEnum.Abs_finite_3 @ V0)) @ (cEnum.Abs_finite_3 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TEnum.finite_3.Rep_finite_3_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cEnum.Rep_finite_3 @ V2))))) @ (V1 @ V0))))))))
(TEnum.finite_3.Rep_finite_3_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cEnum.Rep_finite_3 @ V0)) @ (cEnum.Rep_finite_3 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.finite_3.arity_size_finite_3,(cNat.size_class @ cTYPE))
(TEnum.finite_4.Abs_finite_4_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set))) @ (V0 @ (cEnum.Abs_finite_4 @ V2)))))) @ (V0 @ V1)))))))
(TEnum.finite_4.Abs_finite_4_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cEnum.Abs_finite_4 @ V0)) @ (cEnum.Abs_finite_4 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TEnum.finite_4.Rep_finite_4_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cEnum.Rep_finite_4 @ V2))))) @ (V1 @ V0))))))))
(TEnum.finite_4.Rep_finite_4_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cEnum.Rep_finite_4 @ V0)) @ (cEnum.Rep_finite_4 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.finite_4.arity_size_finite_4,(cNat.size_class @ cTYPE))
(TEnum.finite_5.Abs_finite_5_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set))) @ (V0 @ (cEnum.Abs_finite_5 @ V2)))))) @ (V0 @ V1)))))))
(TEnum.finite_5.Abs_finite_5_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cEnum.Abs_finite_5 @ V0)) @ (cEnum.Abs_finite_5 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TEnum.finite_5.Rep_finite_5_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cEnum.Rep_finite_5 @ V2))))) @ (V1 @ V0))))))))
(TEnum.finite_5.Rep_finite_5_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cEnum.Rep_finite_5 @ V0)) @ (cEnum.Rep_finite_5 @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TEnum.finite_5.arity_size_finite_5,(cNat.size_class @ cTYPE))
(TEquiv_Relations.quotient_is_empty,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cEquiv_Relations.quotient @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))))
(TExtraction.sumbool.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cExtraction.sumbool.sumbool_case @ V2) @ V3) @ V0)) @ (((cExtraction.sumbool.sumbool_case @ V2) @ V3) @ V1))))))))))))
(TFields.class.division_ring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cFields.class.division_ring_axioms @ V0) @ V1) @ V2) @ V3) @ V5)))))))))))))))))))
(TFields.class.division_ring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cRings.class.ring_1 @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TFields.class.linordered_field_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c== @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.conj @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((((cRings.class.linordered_idom @ V8) @ V6) @ V7) @ V5) @ V9) @ V10) @ V4) @ V3) @ V11) @ V2))))))))))))))))))))))))))))
(TFields.division_ring.left_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V3 @ (V0 @ V8)) @ V8)) @ V2))))))))))))))))))))))
(TFields.division_ring_class.axioms,(((((cFields.class.division_ring_axioms @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.zero_class.zero))
(TFields.field.field_divide_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ ((V2 @ V8) @ (V0 @ V9)))))))))))))))))))))))))
(TFields.field.times_divide_eq_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ ((V1 @ V8) @ V9)) @ V10)) @ ((V1 @ ((V2 @ V8) @ V10)) @ V9))))))))))))))))))))))))))
(TFields.linordered_field.frac_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V5) @ V12)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((c==> @ ((V10 @ V5) @ V14)) @ ((c==> @ ((V9 @ V14) @ V15)) @ ((V10 @ ((V1 @ V12) @ V15)) @ ((V1 @ V13) @ V14))))))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class_def,((c== @ (cFields.linordered_field_class @ cTYPE)) @ ((cPure.conjunction @ (cFields.field_class @ cTYPE)) @ (cRings.linordered_idom_class @ cTYPE))))
(TFinite_Set.card_Diff_singleton_if,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V0)) @ cNat.one_nat_inst.one_nat)) @ (cFinite_Set.card @ V0)))))))))
(TFinite_Set.comp_fun_commute.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V2))) @ ((cFun.comp @ (V0 @ V2)) @ (V0 @ V1)))))))) @ (cFinite_Set.comp_fun_commute @ V0)))))
(TFinite_Set.comp_fun_commute_const,(call @ (^[V0]: (cFinite_Set.comp_fun_commute @ (^[V1]: V0)))))
(TFinite_Set.diff_card_le_card_Diff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V1)) @ (cFinite_Set.card @ V0))) @ (cFinite_Set.card @ ((cGroups.minus_class.minus @ V1) @ V0)))))))))
(TFinite_Set.finite_Collect_subsets,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TFinite_Set.infinite_finite_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V2))) @ (V0 @ V2))))) @ ((c==> @ (V0 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((c==> @ (V0 @ V3)) @ (V0 @ ((cSet.insert @ V2) @ V3)))))))))) @ (V0 @ V1)))))))))
(TGroups.ab_group_add.ab_diff_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V0 @ V4) @ (V3 @ V5)))))))))))))))))
(TGroups.ab_group_add.ab_left_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ (V3 @ V4)) @ V4)) @ V1)))))))))))))
(TGroups.ab_semigroup_add_class_def,((c== @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.semigroup_add_class @ cTYPE)) @ (cGroups.class.ab_semigroup_add_axioms @ cGroups.plus_class.plus))))
(TGroups.abs_if_class.abs_if_axioms,((((cGroups.class.abs_if @ cGroups.abs_class.abs) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less))
(TGroups.class.ab_semigroup_add_def,(call @ (^[V0]: ((c== @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.conj @ (cGroups.class.semigroup_add @ V0)) @ (cGroups.class.ab_semigroup_add_axioms @ V0))))))
(TGroups.class.comm_monoid_diff_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ (((cGroups.class.comm_monoid_diff_axioms @ V0) @ V1) @ V2))))))))))
(TGroups.class.comm_monoid_mult_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((cGroups.class.comm_monoid_mult_axioms @ V0) @ V1))))))))
(TGroups.class.group_add_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cGroups.class.group_add_axioms @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V1 @ (V3 @ V4)) @ V4)) @ V2)))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ (V3 @ V5))))))))))))))))))
(TGroups.class.semigroup_mult.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))) @ (cGroups.class.semigroup_mult @ V0)))))
(TGroups.comm_monoid_diff.diff_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ V3) @ V1)) @ V3)))))))))))
(TGroups.comm_monoid_diff.zero_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ V1) @ V3)) @ V1)))))))))))
(TGroups.comm_monoid_diff_class_def,((c== @ (cGroups.comm_monoid_diff_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.minus_class @ cTYPE)) @ (((cGroups.class.comm_monoid_diff_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus)))))
(TGroups.comm_monoid_mult_class_def,((c== @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_semigroup_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.one_class @ cTYPE)) @ ((cGroups.class.comm_monoid_mult_axioms @ cGroups.times_class.times) @ cGroups.one_class.one)))))
(TGroups.group_add.add_minus_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ V4) @ ((V1 @ (V3 @ V4)) @ V5))) @ V5)))))))))))))))
(TGroups.group_add.eq_iff_diff_eq_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V4) @ V5)) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ V2))))))))))))))))
(TGroups.group_add.minus_add_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ (V3 @ V4)) @ ((V1 @ V4) @ V5))) @ V5)))))))))))))))
(TGroups.group_add_class.diff_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TGroups.group_add_class.diff_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TGroups.group_add_class.eq_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TGroups.group_add_class.left_minus,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ cGroups.zero_class.zero))))
(TGroups.group_add_class.minus_zero,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TGroups.semigroup_add_class.axioms,(cGroups.class.semigroup_add @ cGroups.plus_class.plus))
(TGroups.semigroup_mult_class.intro,((c==> @ (cGroups.times_class @ cTYPE)) @ ((c==> @ (cGroups.class.semigroup_mult @ cGroups.times_class.times)) @ (cGroups.semigroup_mult_class @ cTYPE))))
(TGroups.semigroup_mult_class.super,((c==> @ (cGroups.semigroup_mult_class @ cTYPE)) @ (cGroups.times_class @ cTYPE)))
(TGroups.sgn_if_class.sgn_if_axioms,(((((cGroups.class.sgn_if @ cGroups.one_class.one) @ cGroups.sgn_class.sgn) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less))
(THOL.bool.bool_size_overloaded_def,((c== @ cHOL.bool.size_bool_inst.size_bool) @ ((cProduct_Type.bool.bool_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(THOL.bool.size_bool_inst.size_bool,((c== @ cHOL.bool.size_bool_inst.size_bool) @ cHOL.bool.size_bool_inst.size_bool))
(THilbert_Choice.GreatestM_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V3)) @ (V2 @ V1)))))) @ ((cHOL.eq @ (V2 @ ((cHilbert_Choice.GreatestM @ V2) @ (^[V3]: (V0 @ V3))))) @ (V2 @ V1)))))))))))
(THilbert_Choice.image_surj_f_inv_f,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cSet.image @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ V1))) @ V1)))))))
(THilbert_Choice.inv_into_injective,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (((cHilbert_Choice.inv_into @ V0) @ V1) @ V2)) @ (((cHilbert_Choice.inv_into @ V0) @ V1) @ V3))) @ ((c==> @ ((cSet.member @ V2) @ ((cSet.image @ V1) @ V0))) @ ((c==> @ ((cSet.member @ V3) @ ((cSet.image @ V1) @ V0))) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TInt.inverse_eq_divide_neg_numeral,(call @ (^[V0]: ((cHOL.eq @ (cFields.inverse_class.inverse @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TInt.linordered_idom.of_int_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V10)) @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V11))) @ ((cInt.ord_int_inst.less_eq_int @ V10) @ V11))))))))))))))))))))))))))))
(TInt.mult_less_cancel_left_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ ((cOrderings.ord_class.less @ V1) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V1)))))))))))
(TInt.ring_1_class.of_int_of_nat_eq,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TLattices.linorder_class.max.assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TLattices.linorder_class.min.assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TLattices.minus_fun_inst.minus_fun,((c== @ cLattices.minus_fun_inst.minus_fun) @ cLattices.minus_fun_inst.minus_fun))
(TLattices.semilattice_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((cHOL.eq @ ((V0 @ V1) @ V1)) @ V1)))) @ (cLattices.semilattice_axioms @ V0)))))
(TLattices.semilattice_inf.inf_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ V3)) @ V3)))))))))))
(TLattices.semilattice_inf.inf_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V6)) @ ((V1 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TLattices.semilattice_inf.le_infI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ ((V0 @ V3) @ V5)) @ V4))))))))))))))))
(TLattices.semilattice_inf.le_infI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ ((V0 @ V5) @ V3)) @ V4))))))))))))))))
(TLattices.semilattice_inf.mono_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((cOrderings.order.mono @ V1) @ V3)) @ ((cOrderings.ord_class.less_eq @ (V3 @ ((V0 @ V4) @ V5))) @ ((cLattices.inf_class.inf @ (V3 @ V4)) @ (V3 @ V5))))))))))))))))))
(TLattices.semilattice_neutr.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cLattices.semilattice_neutr @ V0) @ V1)) @ ((cGroups.comm_monoid @ V0) @ V1)))))))
(TLattices.semilattice_neutr.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cLattices.semilattice_neutr @ V0) @ V1)) @ (cLattices.semilattice @ V0)))))))
(TLattices.semilattice_order.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ (((cLattices.semilattice_order_axioms @ V0) @ V1) @ V2)))))))))
(TLattices.semilattice_order.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ (cLattices.semilattice @ V0)))))))))
(TLattices.semilattice_order.orderE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ ((V0 @ V3) @ V4))) @ V5)) @ V5))))))))))))))))
(TLattices.semilattice_order.orderI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((cHOL.eq @ V3) @ ((V0 @ V3) @ V4))) @ ((V1 @ V3) @ V4))))))))))))))
(TLattices.semilattice_sup.le_supI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))
(TLattices.semilattice_sup.le_supI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V3) @ ((V0 @ V5) @ V4)))))))))))))))))
(TLattices.semilattice_sup.mono_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((cOrderings.order.mono @ V1) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (V3 @ V4)) @ (V3 @ V5))) @ (V3 @ ((V0 @ V4) @ V5))))))))))))))))))
(TLattices.semilattice_sup.sup_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ V3)) @ V3)))))))))))
(TLattices.semilattice_sup.sup_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V6)) @ ((V1 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TLazy_Sequence.iterate_upto.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ (((V0 @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TLazy_Sequence.iterate_upto.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cLazy_Sequence.iterate_upto @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.iterate_upto_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (cLazy_Sequence.Lazy_Sequence @ (^[V8]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V7) @ V6)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V5 @ V6)) @ (((cLazy_Sequence.iterate_upto @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7)))))))) @ ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.iterate_upto_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TLazy_Sequence.iterate_upto.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.iterate_upto_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cLazy_Sequence.iterate_upto @ V0) @ V1) @ V2)) @ (cLazy_Sequence.Lazy_Sequence @ (^[V3]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ V1)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V0 @ V1)) @ (((cLazy_Sequence.iterate_upto @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)))))))))))))))
(TLazy_Sequence.lazy_sequence.cases,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_rec @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TLazy_Sequence.lazy_sequence.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TLazy_Sequence.small_lazy'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy'_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy'_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))) @ ((V2 @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy'_rel_def,((c== @ cLazy_Sequence.small_lazy'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))))))))))))))
(TLazy_Sequence.small_lazy_list_def,((c== @ cLazy_Sequence.small_lazy_class.small_lazy) @ (^[V0]: (cLazy_Sequence.small_lazy_list_sumC @ V0))))
(TLazy_Sequence.small_lazy_prod_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.small_lazy_class.small_lazy @ V0)) @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ V0)) @ (cLazy_Sequence.small_lazy_class.small_lazy @ V0))))))
(TLazy_Sequence.small_lazy_unit_def,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.small_lazy_unit_inst.small_lazy_unit @ V0)) @ (cLazy_Sequence.single @ cProduct_Type.Unity)))))
(TLifting.Quotient_total_abs_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cRelation.reflp @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ (V1 @ V4)) @ (V1 @ V5))) @ ((V0 @ V4) @ V5)))))))))))))))))
(TLifting.Quotient_total_abs_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cRelation.reflp @ V0)) @ ((c==> @ (call @ (^[V6]: (V4 @ (V1 @ V6))))) @ (V4 @ V5)))))))))))))))))
(TLifting.bi_unique_conv_left_right,(call @ (^[V0]: ((cHOL.eq @ (cTransfer.bi_unique @ V0)) @ ((cHOL.conj @ (cLifting.left_unique @ V0)) @ (cTransfer.right_unique @ V0))))))
(TLifting_Product.bi_total_prod_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((c==> @ (cTransfer.bi_total @ V1)) @ (cTransfer.bi_total @ ((cLifting_Product.prod_rel @ V0) @ V1)))))))))
(TLifting_Product.map_pair_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V2) @ V3)) @ ((cTransfer.fun_rel @ ((cLifting_Product.prod_rel @ V0) @ V2)) @ ((cLifting_Product.prod_rel @ V1) @ V3)))) @ cProduct_Type.map_pair) @ cProduct_Type.map_pair))))))))))
(TLifting_Product.prod_rel_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq))) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V2) @ ((cTransfer.fun_rel @ V3) @ cHOL.eq))) @ ((cTransfer.fun_rel @ ((cLifting_Product.prod_rel @ V0) @ V2)) @ ((cTransfer.fun_rel @ ((cLifting_Product.prod_rel @ V1) @ V3)) @ cHOL.eq)))) @ cLifting_Product.prod_rel) @ cLifting_Product.prod_rel))))))))))
(TLifting_Set.set_invariant_commute,(call @ (^[V0]: ((cHOL.eq @ (cLifting_Set.set_rel @ (cLifting.invariant @ V0))) @ (cLifting.invariant @ (^[V1]: ((cSet.Ball @ V1) @ V0)))))))
(TLifting_Sum.sum_invariant_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLifting_Sum.sum_rel @ (cLifting.invariant @ V0)) @ (cLifting.invariant @ V1))) @ (cLifting.invariant @ ((cSum_Type.sum.sum_case @ V0) @ V1))))))))
(TList.comm_monoid_add.listsum_addf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ (^[V5]: ((V0 @ (V2 @ V5)) @ (V3 @ V5)))) @ V4))) @ ((V0 @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V2) @ V4))) @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V3) @ V4))))))))))))))))
(TList.linorder.sorted_rev_nth_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ (cList.rev @ V2))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V4)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V4) @ (cNat.size_class.size @ V2))) @ ((V0 @ ((cList.nth @ V2) @ V4)) @ ((cList.nth @ V2) @ V3)))))))))))))))))
(TList.linorder_class.distinct_sort,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.distinct @ ((cList.linorder_class.sort_key @ V0) @ V1))) @ (cList.distinct @ V1)))))))
(TList.linorder_class.filter_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ V1))) @ ((c==> @ (V2 @ V3)) @ ((cHOL.eq @ ((cList.filter @ V2) @ (((cList.linorder_class.insort_key @ V0) @ V3) @ V1))) @ (((cList.linorder_class.insort_key @ V0) @ V3) @ ((cList.filter @ V2) @ V1))))))))))))))
(TList.linorder_class.length_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cNat.size_class.size @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2))) @ (cNat.Suc @ (cNat.size_class.size @ V2))))))))))
(TList.linorder_class.sorted.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ ((c==> @ (V1 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: ((cOrderings.ord_class.less_eq @ V3) @ V4)))) @ ((c==> @ (cList.linorder_class.sorted @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ ((cList.list.Cons @ V3) @ V2)))))))))) @ (V1 @ V0)))))))))
(TList.linorder_class.sorted.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V1) @ V2)))) @ ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ ((cList.list.Cons @ V1) @ V0)))))))))
(TList.linorder_class.sorted.intros_1,(cList.linorder_class.sorted @ cList.list.Nil))
(TList.linorder_class.sorted_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.linorder_class.sorted @ ((cList.append @ V0) @ V1))) @ ((cHOL.conj @ (cList.linorder_class.sorted @ V0)) @ ((cHOL.conj @ (cList.linorder_class.sorted @ V1)) @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V2]: ((cSet.Ball @ (cList.set @ V1)) @ (^[V3]: ((cOrderings.ord_class.less_eq @ V2) @ V3)))))))))))))
(TList.linorder_class.sorted_filter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ V1))) @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ ((cList.filter @ V2) @ V1)))))))))))
(TList.linorder_class.sorted_insort,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.linorder_class.sorted @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V0) @ V1))) @ (cList.linorder_class.sorted @ V1)))))))
(TList.linorder_class.sorted_single,(call @ (^[V0]: (cList.linorder_class.sorted @ ((cList.list.Cons @ V0) @ cList.list.Nil)))))
(TList.map_tailrec_rev_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.map_tailrec_rev_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V5))) @ V5)))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cList.map_tailrec_rev_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V6)) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))))))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.map_tailrec_rev_graph.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cList.map_tailrec_rev_graph @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cList.list.Cons @ (V0 @ V2)) @ V3)))) @ (V4 @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cList.list.Cons @ (V0 @ V2)) @ V3)))))) @ ((cList.map_tailrec_rev_graph @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V1)) @ V3))) @ (V4 @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ ((cList.list.Cons @ (V0 @ V2)) @ V3)))))))))))))))))
(TList.map_tailrec_rev_graph.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((cList.map_tailrec_rev_graph @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V1))) @ V1))))))
(TList.monoid_add_class.listsum_def,(call @ (^[V0]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ V0)) @ (((cList.foldr @ cGroups.plus_class.plus) @ V0) @ cGroups.zero_class.zero)))))
(TMain.partial_term_of_sumbool_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMain.partial_term_of_sumbool_inst.partial_term_of_sumbool @ V0) @ V1)) @ cHOL.undefined))))))
(TNat.semiring_1_class.of_nat_simps_2,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cNat.Suc @ V0))) @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNat.semiring_1_class.of_nat @ V0))))))
(TNat.semiring_1_class.of_nat_simps_1,((cHOL.eq @ (cNat.semiring_1_class.of_nat @ cNat.zero_nat_inst.zero_nat)) @ cGroups.zero_class.zero))
(TNat.semiring_char_0.of_nat_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V5))) @ ((cHOL.eq @ V4) @ V5))))))))))))))))
(TNitpick.arity_type_bisim_iterator,(cHOL.type_class @ cTYPE))
(TNitpick.fun_box.Abs_fun_box_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.Abs_fun_box @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set))) @ V1))))) @ V1))))))
(TNitpick.fun_box.Rep_fun_box_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.Rep_fun_box @ V2))) @ V1)))) @ V1)))))))
(TNitpick.pair_box.pair_box_rec_def,((c== @ cNitpick.pair_box.pair_box_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cNitpick.pair_box.pair_box_rec_set @ V0) @ V1) @ V2)))))))
(TNitpick.pair_box.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNitpick.random_aux_pair_box @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNitpick.pair_box.PairBox) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))))))))
(TNitpick.partial_term_of_word_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TNitpick.word.narrowing_word.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cNitpick.word.Word)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)))
(TNitpick.word.word_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNitpick.word.word_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TNum.class.semiring_numeral.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cRings.class.semiring @ V2) @ V1)))))))))
(TNum.class.semiring_numeral.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cGroups.class.monoid_mult @ V0) @ V1)))))))))
(TNum.neg_numeral.minus_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))))))))))))))))
(TNum.neg_numeral_class.dbl_dec_def,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ V0)) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.one_class.one)))))
(TNum.neg_numeral_class.dbl_inc_def,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ V0)) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.one_class.one)))))
(TNum.ring_1.mult_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7))) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ ((cNum.times_num_inst.times_num @ V6) @ V7)))))))))))))))))))))
(TNum.ring_1.mult_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V7))) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ ((cNum.times_num_inst.times_num @ V6) @ V7)))))))))))))))))))))
(TNum.ring_1.mult_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7))) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.times_num_inst.times_num @ V6) @ V7)))))))))))))))))))))
(TNum.semiring_numeral.mult_2_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((V2 @ V3) @ V3))))))))))))
(TNum.semiring_numeral.numeral_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.times_num_inst.times_num @ V3) @ V4))) @ ((V1 @ (((cNum.numeral.numeral @ V0) @ V2) @ V3)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)))))))))))))))
(TNum.semiring_numeral_class.mult_2,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ ((cGroups.plus_class.plus @ V0) @ V0)))))
(TNumeral_Simprocs.nat_diff_add_eq1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V4))) @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V3)) @ V4))))))))))))))
(TNumeral_Simprocs.nat_diff_add_eq2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V4))) @ ((cNat.minus_nat_inst.minus_nat @ V3) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V4)))))))))))))))
(TOrderings.class.dense_order.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ (cOrderings.class.dense_order_axioms @ V1)) @ ((cOrderings.class.dense_order @ V0) @ V1))))))))
(TOrderings.class.no_bot_axioms_def,(call @ (^[V0]: ((c== @ (cOrderings.class.no_bot_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TOrderings.class.no_top_axioms_def,(call @ (^[V0]: ((c== @ (cOrderings.class.no_top_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TOrderings.dense_linorder.dense_ge,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V1 @ V2) @ V4)) @ ((V0 @ V3) @ V4))))) @ ((V0 @ V3) @ V2))))))))))))
(TOrderings.dense_linorder.dense_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V1 @ V4) @ V2)) @ ((V0 @ V4) @ V3))))) @ ((V0 @ V2) @ V3))))))))))))
(TOrderings.dense_order_class.dense,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V2)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.dense_order_class.intro,((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ (cOrderings.class.dense_order_axioms @ cOrderings.ord_class.less)) @ (cOrderings.dense_order_class @ cTYPE))))
(TOrderings.dense_order_class.super,((c==> @ (cOrderings.dense_order_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TOrderings.linorder.le_less_linear,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.disj @ ((V0 @ V2) @ V3)) @ ((V1 @ V3) @ V2))))))))))))
(TOrderings.linorder.linorder_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((c==> @ ((V1 @ V2) @ V3)) @ V4)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ V4)) @ ((c==> @ ((c==> @ ((V1 @ V3) @ V2)) @ V4)) @ V4)))))))))))))))
(TOrderings.linorder.strict_mono_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.strict_mono @ V1) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ (V2 @ V3)) @ (V2 @ V4))) @ ((cHOL.eq @ V3) @ V4)))))))))))))))
(TOrderings.linorder_class.le_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ V2)) @ V2)))))))))
(TOrderings.linorder_class.not_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TOrderings.linorder_le_less_linear,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TOrderings.ord_bool_inst.less_bool,((c== @ cOrderings.ord_bool_inst.less_bool) @ cOrderings.ord_bool_inst.less_bool))
(TOrderings.order.le_imp_less_or_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.disj @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.order_class.order.trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.order_le_imp_less_or_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_less_imp_not_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V1) @ V0))) @ cHOL.True)))))))
(TOrderings.ordering_top_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.ordering_top_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TOrderings.preorder.less_le_not_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V2) @ V3)) @ (cHOL.Not @ ((V0 @ V3) @ V2))))))))))))))
(TOrderings.wellorder_class.LeastI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V2 @ V3))))) @ (V2 @ (cOrderings.ord_class.Least @ V0)))))))))))
(TPartial_Function.admissible_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ V1) @ V0) @ ((cFun.comp @ V2) @ V3))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ (V4 @ V5)) @ (V4 @ V6))) @ ((cHOL.eq @ V5) @ V6))))))) @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ (V4 @ (V3 @ V5))) @ V5)))) @ (((cComplete_Partial_Order.ccpo.admissible @ (((cPartial_Function.img_lub @ V4) @ V3) @ V1)) @ ((cPartial_Function.img_ord @ V4) @ V0)) @ V2))))))))))))))))
(TPartial_Function.option.leq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cPartial_Function.flat_ord @ cOption.option.None) @ V0) @ V1)) @ ((c==> @ (((cPartial_Function.flat_ord @ cOption.option.None) @ V1) @ V2)) @ (((cPartial_Function.flat_ord @ cOption.option.None) @ V0) @ V2))))))))))
(TPartial_Function.option.lub_least,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ (cPartial_Function.flat_ord @ cOption.option.None)) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (((cPartial_Function.flat_ord @ cOption.option.None) @ V2) @ V1))))) @ (((cPartial_Function.flat_ord @ cOption.option.None) @ ((cPartial_Function.flat_lub @ cOption.option.None) @ V0)) @ V1))))))))
(TPartial_Function.option.lub_upper,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ (cPartial_Function.flat_ord @ cOption.option.None)) @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ (((cPartial_Function.flat_ord @ cOption.option.None) @ V1) @ ((cPartial_Function.flat_lub @ cOption.option.None) @ V0)))))))))
(TPartial_Function.tailrec.leq_refl,(call @ (^[V0]: (((cPartial_Function.flat_ord @ cHOL.undefined) @ V0) @ V0))))
(TPower.monoid_mult.power_one_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ cNat.one_nat_inst.one_nat)) @ V2)))))))))
(TPower.monoid_mult_class.power_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))))))))))
(TPower.monoid_mult_class.power_one,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ cGroups.one_class.one) @ V0)) @ cGroups.one_class.one))))
(TPower.power_class.power.power_Suc,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPower.semiring_1_class.one_power2,((cHOL.eq @ ((cPower.power_class.power @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.one_class.one))
(TPredicate.iterate_upto_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.iterate_upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TPredicate.iterate_upto_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cPredicate.iterate_upto_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V1) @ V0)))))))))))
(TPredicate.ord_pred_inst.less_pred,((c== @ cPredicate.ord_pred_inst.less_pred) @ cPredicate.ord_pred_inst.less_pred))
(TPredicate.pred.pred_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cPredicate.pred.pred_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cPredicate.pred.Pred @ V4))) @ ((c==> @ ((cHOL.eq @ V2) @ (V0 @ V4))) @ V3))))) @ V3)))))))))))
(TPredicate.pred.pred_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cPredicate.pred.pred_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cPredicate.pred.Pred @ V3))) @ ((cHOL.eq @ V2) @ (V0 @ V3)))))))))))))
(TPredicate.seq.seq_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cPredicate.seq.seq_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cPredicate.seq.seq_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))) @ V2))))))))))) @ (V1 @ V0))))))))))
(TProduct_Type.Times_subset_cancel2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cProduct_Type.Sigma @ V2) @ (^[V4]: V1))) @ ((cProduct_Type.Sigma @ V3) @ (^[V4]: V1)))) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))))))))))))
(TProduct_Type.image_split_eq_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ (^[V3]: ((cProduct_Type.Pair @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((cProduct_Type.Sigma @ ((cSet.image @ V0) @ V2)) @ (^[V3]: ((cSet.image @ V1) @ ((cLattices.inf_class.inf @ ((cSet.vimage @ V0) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))) @ V2))))))))))))
(TProduct_Type.prod.Abs_prod_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ cProduct_Type.prod)) @ (V0 @ (cProduct_Type.Abs_prod @ V2)))))) @ (V0 @ V1)))))))
(TProduct_Type.prod.Abs_prod_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cProduct_Type.prod)) @ ((c==> @ ((cSet.member @ V1) @ cProduct_Type.prod)) @ ((cHOL.eq @ ((cHOL.eq @ (cProduct_Type.Abs_prod @ V0)) @ (cProduct_Type.Abs_prod @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TProduct_Type.prod.Rep_prod_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cProduct_Type.prod)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cProduct_Type.Rep_prod @ V2))))) @ (V1 @ V0))))))))
(TProduct_Type.prod.Rep_prod_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cProduct_Type.Rep_prod @ V0)) @ (cProduct_Type.Rep_prod @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TProduct_Type.prod.arity_size_prod,(cNat.size_class @ cTYPE))
(TProduct_Type.type_definition_prod,(((cTypedef.type_definition @ cProduct_Type.Rep_prod) @ cProduct_Type.Abs_prod) @ cProduct_Type.prod))
(TProduct_Type.type_definition_unit,(((cTypedef.type_definition @ cProduct_Type.Rep_unit) @ cProduct_Type.Abs_unit) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot)))
(TProduct_Type.unit.Abs_unit_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))) @ (V0 @ (cProduct_Type.Abs_unit @ V2)))))) @ (V0 @ V1)))))))
(TProduct_Type.unit.Abs_unit_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cSet.member @ V1) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cHOL.eq @ (cProduct_Type.Abs_unit @ V0)) @ (cProduct_Type.Abs_unit @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TProduct_Type.unit.Rep_unit_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cProduct_Type.Rep_unit @ V2))))) @ (V1 @ V0))))))))
(TProduct_Type.unit.Rep_unit_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cProduct_Type.Rep_unit @ V0)) @ (cProduct_Type.Rep_unit @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TProduct_Type.unit.arity_size_unit,(cNat.size_class @ cTYPE))
(TQuickcheck_Exhaustive.cps_not_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.cps_not @ V0)) @ (^[V1]: (((cOption.option.option_case @ (V1 @ cProduct_Type.Unity)) @ (^[V2]: cOption.option.None)) @ (V0 @ (^[V2]: (cOption.option.Some @ cList.list.Nil)))))))))
(TQuickcheck_Narrowing.cfun.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Narrowing.cfun.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V2))) @ V1)))) @ V1))))))
(TQuickcheck_Narrowing.cfun.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Narrowing.cfun.Constant @ V2))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.conv.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5)))) @ ((V2 @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5)))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ ((cProduct_Type.Pair @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5)))) @ ((V2 @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5)))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Narrowing.conv_rel_def,((c== @ cQuickcheck_Narrowing.conv_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: cHOL.False))))))
(TQuickcheck_Narrowing.ffun.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Narrowing.ffun.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.ffun.Constant @ V2))) @ V1)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4))) @ V1)))))))) @ V1)))))))
(TQuickcheck_Narrowing.ffun.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Narrowing.ffun.Constant @ V2))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V0 @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V3) @ V4)))))))))) @ (V0 @ V1))))))))
(TQuickcheck_Narrowing.map_cons_def,((c== @ cQuickcheck_Narrowing.map_cons) @ (^[V0]: (^[V1]: (((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec @ (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ ((cList.map @ (^[V5]: ((cFun.comp @ V4) @ V5))) @ V3)))))) @ V1) @ V0)))))
(TQuickcheck_Random.random_bool_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_bool_inst.random_bool @ V0)) @ ((cProduct_Type.scomp @ (cRandom.range @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ (^[V1]: (cProduct_Type.Pair @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((cProduct_Type.Pair @ cHOL.False) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil))))) @ ((cProduct_Type.Pair @ cHOL.True) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil))))))))))))
(TQuickcheck_Random.random_char_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_char_inst.random_char @ V0)) @ ((cProduct_Type.scomp @ (cRandom.select @ cString.enum_char_inst.enum_char)) @ (^[V1]: (cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ (^[V2]: (cCode_Evaluation.term_of_char_inst.term_of_char @ V1))))))))))
(TQuickcheck_Random.random_list_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_list @ V0) @ V0)))))
(TQuickcheck_Random.random_pred_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_pred @ V0) @ V0)))))
(TQuickcheck_Random.random_prod_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_prod @ V0) @ V0)))))
(TQuickcheck_Random.random_term_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_term_inst.random_term @ V0)) @ ((cQuickcheck_Random.random_aux_term @ V0) @ V0)))))
(TQuickcheck_Random.random_unit_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_unit_inst.random_unit @ V0)) @ ((cQuickcheck_Random.random_aux_unit @ V0) @ V0)))))
(TRandom_Sequence.Random_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.Random_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.Random_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom_Sequence.Random_rel @ ((cProduct_Type.Pair @ V1) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V0))))))))
(TRandom_Sequence.iter_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.iter_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((cRandom_Sequence.iter_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))))))))))))))))))))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))))))))))))))))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: ((cHOL.Let @ (V4 @ V6)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cOption.option.Some @ ((cProduct_Type.Pair @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V10)))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.iter_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V5) @ (V1 @ V2))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V6) @ V7)) @ V5)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V8) @ V9)) @ V6)) @ ((cRandom_Sequence.iter_graph @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V10))) @ (V3 @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V10))))))))))))))))))))))) @ ((cRandom_Sequence.iter_graph @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V0) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V4]: ((cHOL.Let @ (V1 @ V2)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (^[V7]: (cOption.option.Some @ ((cProduct_Type.Pair @ V5) @ (V3 @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7)))))))))))))))))))))))))
(TRandom_Sequence.neg_decr_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.neg_decr_bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cLimited_Sequence.neg_decr_bind @ (((V0 @ V2) @ V3) @ V4)) @ (^[V5]: ((((V1 @ V5) @ V2) @ V3) @ V4))))))))))))
(TRandom_Sequence.pos_decr_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.pos_decr_bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (^[V4]: ((cLimited_Sequence.pos_decr_bind @ (((V0 @ V2) @ V3) @ V4)) @ (^[V5]: ((((V1 @ V5) @ V2) @ V3) @ V4))))))))))))
(TRecord.tuple_isomorphism.eq.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1)) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TRecord.tuple_isomorphism.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V1) @ V2)))))))))
(TRecord.update_accessor_noop_compE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ (V2 @ (V1 @ V3))) @ (V1 @ V3))) @ ((cHOL.eq @ ((V0 @ ((cFun.comp @ V4) @ V2)) @ V3)) @ ((V0 @ V4) @ V3)))))))))))))))
(TRings.class.comm_semiring_0.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cRings.class.comm_semiring @ V0) @ V2)) @ ((c==> @ ((cRings.class.mult_zero @ V2) @ V1)) @ (((cRings.class.comm_semiring_0 @ V0) @ V1) @ V2)))))))))))
(TRings.class.comm_semiring_1.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((c==> @ (((cRings.class.comm_semiring_0 @ V2) @ V3) @ V0)) @ ((c==> @ ((cRings.class.zero_neq_one @ V1) @ V3)) @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)))))))))))))
(TRings.class.linordered_idom.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((cGroups.class.abs_if @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V4) @ V2) @ V5) @ V1) @ V6) @ V3)) @ ((c==> @ (((((cGroups.class.sgn_if @ V7) @ V8) @ V1) @ V2) @ V3)) @ ((c==> @ ((((((cRings.class.comm_ring_1 @ V9) @ V7) @ V4) @ V2) @ V5) @ V1)) @ ((c==> @ (((((cRings.class.linordered_comm_semiring_strict @ V4) @ V6) @ V3) @ V2) @ V9)) @ ((((((((((cRings.class.linordered_idom @ V0) @ V5) @ V1) @ V2) @ V6) @ V3) @ V4) @ V7) @ V8) @ V9)))))))))))))))))))))))))))
(TRings.class.linordered_ring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cGroups.class.abs_if @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V4) @ V2) @ V5) @ V1) @ V6) @ V3)) @ ((c==> @ (((((cRings.class.linordered_semiring @ V4) @ V6) @ V3) @ V2) @ V7)) @ ((c==> @ (((((cRings.class.ring @ V4) @ V2) @ V5) @ V1) @ V7)) @ ((((((((cRings.class.linordered_ring @ V0) @ V5) @ V1) @ V2) @ V6) @ V3) @ V4) @ V7))))))))))))))))))))))
(TRings.class.ordered_comm_ring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c== @ (((((((cRings.class.ordered_comm_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.conj @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cRings.class.ordered_comm_semiring @ V0) @ V5) @ V6) @ V1) @ V4))))))))))))))))))
(TRings.class.semiring_0_cancel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.semiring_0_cancel @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((cRings.class.semiring @ V0) @ V2))))))))))
(TRings.class.semiring_1_cancel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cRings.class.semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cHOL.conj @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((cGroups.class.monoid_mult @ V2) @ V3))) @ ((cHOL.conj @ ((cRings.class.semiring @ V0) @ V3)) @ ((cRings.class.zero_neq_one @ V2) @ V1)))))))))))))
(TRings.class.semiring_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((V0 @ ((V1 @ V2) @ V3)) @ V4)) @ ((V1 @ ((V0 @ V2) @ V4)) @ ((V0 @ V3) @ V4)))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((V0 @ V2) @ ((V1 @ V3) @ V4))) @ ((V1 @ ((V0 @ V2) @ V3)) @ ((V0 @ V2) @ V4)))))))))) @ ((cRings.class.semiring_axioms @ V1) @ V0))))))))
(TRings.classrel_comm_ring_1_ring_1,(cRings.ring_1_class @ cTYPE))
(TRings.comm_semiring_0_class.intro,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_class @ cTYPE)) @ ((c==> @ (cRings.mult_zero_class @ cTYPE)) @ (cRings.comm_semiring_0_class @ cTYPE)))))
(TRings.comm_semiring_0_class.super_3,((c==> @ (cRings.comm_semiring_0_class @ cTYPE)) @ (cRings.mult_zero_class @ cTYPE)))
(TRings.comm_semiring_0_class.super_2,((c==> @ (cRings.comm_semiring_0_class @ cTYPE)) @ (cRings.comm_semiring_class @ cTYPE)))
(TRings.comm_semiring_0_class.super_1,((c==> @ (cRings.comm_semiring_0_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TRings.comm_semiring_1.dvd_0_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cRings.dvd.dvd @ V0) @ V4) @ V3)))))))))))))
(TRings.comm_semiring_1_class.intro,((c==> @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_0_class @ cTYPE)) @ ((c==> @ (cRings.dvd_class @ cTYPE)) @ ((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cRings.comm_semiring_1_class @ cTYPE))))))
(TRings.comm_semiring_1_class.super_4,((c==> @ (cRings.comm_semiring_1_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))
(TRings.comm_semiring_1_class.super_3,((c==> @ (cRings.comm_semiring_1_class @ cTYPE)) @ (cRings.dvd_class @ cTYPE)))
(TRings.comm_semiring_1_class.super_2,((c==> @ (cRings.comm_semiring_1_class @ cTYPE)) @ (cRings.comm_semiring_0_class @ cTYPE)))
(TRings.comm_semiring_1_class.super_1,((c==> @ (cRings.comm_semiring_1_class @ cTYPE)) @ (cGroups.comm_monoid_mult_class @ cTYPE)))
(TRings.comm_semiring_class.distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TRings.linordered_idom.abs_dvd_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V9) @ (V0 @ V10)) @ V11)) @ (((cRings.dvd.dvd @ V9) @ V10) @ V11))))))))))))))))))))))))))))
(TRings.linordered_idom.dvd_abs_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V9) @ V10) @ (V0 @ V11))) @ (((cRings.dvd.dvd @ V9) @ V10) @ V11))))))))))))))))))))))))))))
(TRings.linordered_idom.sgn_greater,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V3) @ (V8 @ V10))) @ ((V5 @ V3) @ V10))))))))))))))))))))))))))
(TRings.linordered_idom_class.intro,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ ((c==> @ (cGroups.sgn_if_class @ cTYPE)) @ ((c==> @ (cRings.comm_ring_1_class @ cTYPE)) @ ((c==> @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)) @ (cRings.linordered_idom_class @ cTYPE)))))))
(TRings.linordered_idom_class.super_5,((c==> @ (cRings.linordered_idom_class @ cTYPE)) @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)))
(TRings.linordered_idom_class.super_4,((c==> @ (cRings.linordered_idom_class @ cTYPE)) @ (cRings.comm_ring_1_class @ cTYPE)))
(TRings.linordered_idom_class.super_3,((c==> @ (cRings.linordered_idom_class @ cTYPE)) @ (cGroups.sgn_if_class @ cTYPE)))
(TRings.linordered_idom_class.super_2,((c==> @ (cRings.linordered_idom_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_class @ cTYPE)))
(TRings.linordered_idom_class.super_1,((c==> @ (cRings.linordered_idom_class @ cTYPE)) @ (cGroups.abs_if_class @ cTYPE)))
(TRings.linordered_ring_class.intro,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ ((c==> @ (cGroups.linordered_ab_group_add_class @ cTYPE)) @ ((c==> @ (cRings.linordered_semiring_class @ cTYPE)) @ ((c==> @ (cRings.ring_class @ cTYPE)) @ (cRings.linordered_ring_class @ cTYPE))))))
(TRings.linordered_ring_class.super_4,((c==> @ (cRings.linordered_ring_class @ cTYPE)) @ (cRings.ring_class @ cTYPE)))
(TRings.linordered_ring_class.super_3,((c==> @ (cRings.linordered_ring_class @ cTYPE)) @ (cRings.linordered_semiring_class @ cTYPE)))
(TRings.linordered_ring_class.super_2,((c==> @ (cRings.linordered_ring_class @ cTYPE)) @ (cGroups.linordered_ab_group_add_class @ cTYPE)))
(TRings.linordered_ring_class.super_1,((c==> @ (cRings.linordered_ring_class @ cTYPE)) @ (cGroups.abs_if_class @ cTYPE)))
(TRings.ordered_comm_ring_class_def,((c== @ (cRings.ordered_comm_ring_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_ring_class @ cTYPE)) @ (cRings.ordered_comm_semiring_class @ cTYPE))))
(TRings.ordered_semiring.mult_mono',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((c==> @ ((V2 @ V7) @ V8)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((c==> @ ((V2 @ V1) @ V7)) @ ((V2 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V8))))))))))))))))))))))))))
(TRings.ring_class.minus_mult_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cGroups.times_class.times @ V0) @ V1)))))))
(TRings.ring_class.minus_mult_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cGroups.times_class.times @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TRings.ring_class.mult_minus_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cGroups.times_class.times @ V0) @ V1))))))))
(TRings.semiring_0_cancel_class_def,((c== @ (cRings.semiring_0_cancel_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE))))
(TRings.semiring_1_cancel_class_def,((c== @ (cRings.semiring_1_cancel_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cGroups.monoid_mult_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.semiring_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))))
(TRings.semiring_class.distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TSMT.arity_full_exhaustive_pattern,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TSMT.arity_partial_term_of_pattern,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TSMT.pattern.pattern_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cSMT.pattern.pattern_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cSMT.pattern.Pattern)) @ ((c==> @ ((cHOL.eq @ V2) @ V0)) @ V3))) @ V3)))))))))))
(TSMT.pattern.pattern_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSMT.pattern.pattern_rec_set @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ cSMT.pattern.Pattern)) @ ((cHOL.eq @ V2) @ V0))))))))))
(TSet_Interval.INT_greaterThan_UNIV,((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ cOrderings.top_class.top) @ (^[V0]: (cSet_Interval.ord_class.greaterThan @ V0)))) @ cOrderings.bot_class.bot))
(TSet_Interval.arith_series_general,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cGroups.plus_class.plus @ V0) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ V3)) @ V1)))) @ (cSet_Interval.ord_class.lessThan @ V2)))) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ ((cNat.minus_nat_inst.minus_nat @ V2) @ cNat.one_nat_inst.one_nat))) @ V1))))))))))))
(TSet_Interval.card_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))))))
(TSet_Interval.dvd.not_Ici_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atLeast @ cRings.dvd_class.dvd) @ V0)) @ cOrderings.bot_class.bot)))))
(TSet_Interval.dvd.not_Iic_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atMost @ cRings.dvd_class.dvd) @ V0)) @ cOrderings.bot_class.bot)))))
(TSet_Interval.finite_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)))))))
(TSet_Interval.finite_same_card_bij,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))) @ (cHOL.Ex @ (^[V2]: (((cFun.bij_betw @ V2) @ V0) @ V1)))))))))))
(TSet_Interval.ord_class.atMost_def,(call @ (^[V0]: ((c== @ (cSet_Interval.ord_class.atMost @ V0)) @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet_Interval.ord_class.atMost_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cSet_Interval.ord_class.atMost @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet_Interval.setsum_restrict_set',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ (cSet.Collect @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ V3) @ V2)))))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ (V1 @ V3)) @ cGroups.zero_class.zero))) @ V0))))))))))
(TSet_Interval.single_Diff_lessThan,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ (cSet_Interval.ord_class.lessThan @ V0))) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TString.equal_char_inst.equal_char,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TSum_Type.equal_sum_inst.equal_sum,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TSum_Type.sum_map.compositionality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cSum_Type.sum_map @ V0) @ V1) @ (((cSum_Type.sum_map @ V2) @ V3) @ V4))) @ (((cSum_Type.sum_map @ ((cFun.comp @ V0) @ V2)) @ ((cFun.comp @ V1) @ V3)) @ V4)))))))))))))
(TTransfer.right_total_All_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ (cSet.Ball @ (cSet.Collect @ (cRelation.Domainp @ V0)))) @ cHOL.All)))))
(TTransfer.transfer_forall_transfer_5,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cTransfer.rev_implies)) @ cTransfer.rev_implies) @ cHOL.All) @ cTransfer.transfer_forall)))))
(TTransfer.transfer_forall_transfer_4,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cTransfer.rev_implies) @ cHOL.All) @ cTransfer.transfer_forall)))))
(TTransfer.transfer_forall_transfer_3,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.implies)) @ cHOL.implies) @ cHOL.All) @ cTransfer.transfer_forall)))))
(TTransfer.transfer_forall_transfer_2,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.implies) @ cHOL.All) @ cTransfer.transfer_forall)))))
(TTransfer.transfer_forall_transfer_1,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ cHOL.eq) @ cHOL.All) @ cTransfer.transfer_forall)))))
(TTransitive_Closure.Domain_rtrancl,(call @ (^[V0]: ((cHOL.eq @ (cRelation.Domain @ (cTransitive_Closure.rtrancl @ V0))) @ cOrderings.top_class.top))))
(TTransitive_Closure.acyclic_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cTransitive_Closure.acyclic @ ((cSet.insert @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2))) @ ((cHOL.conj @ (cTransitive_Closure.acyclic @ V2)) @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ (cTransitive_Closure.rtrancl @ V2))))))))))))
(TTransitive_Closure.acyclic_irrefl,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.acyclic @ V0)) @ (cRelation.irrefl @ (cTransitive_Closure.trancl @ V0))))))
(TTransitive_Closure.acyclic_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransitive_Closure.acyclic @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ (cTransitive_Closure.acyclic @ V1))))))))
(TTransitive_Closure.antisym_reflcl,(call @ (^[V0]: ((cHOL.eq @ (cRelation.antisym @ ((cLattices.sup_class.sup @ V0) @ cRelation.Id))) @ (cRelation.antisym @ V0)))))
(TTransitive_Closure.finite_relcomp,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ ((cRelation.relcomp @ V0) @ V1)))))))))
(TTransitive_Closure.in_rtrancl_UnI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.disj @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ V1))) @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ V2)))) @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ ((cLattices.sup_class.sup @ V1) @ V2)))))))))))
(TTransitive_Closure.irrefl_tranclI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cRelation.converse @ V0)) @ (cTransitive_Closure.rtrancl @ V0))) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V1)) @ (cTransitive_Closure.trancl @ V0)))))))))
(TTransitive_Closure.r_into_rtrancl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ V1))))))))
(TTransitive_Closure.r_into_trancl',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ V0) @ (cTransitive_Closure.trancl @ V1))))))))
(TTransitive_Closure.relpow_Suc_D2',(call @ (^[V0]: (call @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cNat.compow @ V0) @ V1))) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V5)) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V4)) @ ((cNat.compow @ V0) @ V1)))))))))))))))))
(TTransitive_Closure.relpow_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcomp @ V0) @ ((cNat.compow @ V1) @ V0))) @ ((cRelation.relcomp @ ((cNat.compow @ V1) @ V0)) @ V0)))))))
(TTransitive_Closure.relpowp_Suc_D2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNat.compow @ (cNat.Suc @ V0)) @ V1) @ V2) @ V3)) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((V1 @ V2) @ V4)) @ ((((cNat.compow @ V0) @ V1) @ V4) @ V3))))))))))))))
(TTransitive_Closure.relpowp_Suc_E2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.compow @ (cNat.Suc @ V0)) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((V1 @ V2) @ V5)) @ ((c==> @ ((((cNat.compow @ V0) @ V1) @ V5) @ V3)) @ V4))))) @ V4)))))))))))))
(TTransitive_Closure.relpowp_Suc_I2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((((cNat.compow @ V3) @ V0) @ V2) @ V4)) @ ((((cNat.compow @ (cNat.Suc @ V3)) @ V0) @ V1) @ V4))))))))))))))
(TTransitive_Closure.rtrancl.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ (call @ (^[V4]: ((V3 @ V4) @ V4)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TTransitive_Closure.rtrancl.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.rtrancl.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V0)) @ (cTransitive_Closure.rtrancl @ V1)))))))
(TTransitive_Closure.rtrancl_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ (V3 @ V0)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ (V3 @ V4)) @ (V3 @ V5))))))))) @ (V3 @ V1)))))))))))))
(TTransitive_Closure.rtrancl_reflcl,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ ((cLattices.sup_class.sup @ V0) @ cRelation.Id))) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.rtrancl_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ (cTransitive_Closure.rtrancl @ V0))) @ ((cHOL.eq @ (cTransitive_Closure.rtrancl @ V1)) @ (cTransitive_Closure.rtrancl @ V0)))))))))
(TTransitive_Closure.rtrancl_unfold,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ V0)) @ ((cLattices.sup_class.sup @ cRelation.Id) @ ((cRelation.relcomp @ (cTransitive_Closure.rtrancl @ V0)) @ V0))))))
(TTransitive_Closure.rtranclp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V4)) @ V3))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ V4)) @ ((c==> @ ((cHOL.eq @ V2) @ V6)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V4) @ V5)) @ ((c==> @ ((V0 @ V5) @ V6)) @ V3))))))))))) @ V3))))))))))))
(TTransitive_Closure.rtranclp.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.eq @ V2) @ V3))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V5)) @ ((cHOL.conj @ (((cTransitive_Closure.rtranclp @ V0) @ V3) @ V4)) @ ((V0 @ V4) @ V5)))))))))))))))))))
(TTransitive_Closure.rtranclp_idemp,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtranclp @ (cTransitive_Closure.rtranclp @ V0))) @ (cTransitive_Closure.rtranclp @ V0)))))
(TTransitive_Closure.rtranclp_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((((cNat.compow @ V3) @ V0) @ V1) @ V2)))))))))))
(TTransitive_Closure.rtranclp_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.trancl.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((V3 @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TTransitive_Closure.trancl_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cTransitive_Closure.trancl @ V4))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ V4)) @ ((V5 @ V6) @ V7))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ (cTransitive_Closure.trancl @ V4))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V8) @ V9))) @ V4)) @ ((c==> @ ((V5 @ V6) @ V7)) @ ((V5 @ V8) @ V9))))))))))))) @ ((V5 @ V2) @ V3)))))))))))))))))
(TTransitive_Closure.tranclp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V3 @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V4) @ V5)) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((V0 @ V5) @ V6)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TTransitive_Closure.tranclp.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.tranclp.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)))))))))
(TTransitive_Closure.tranclp_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V4)) @ (V3 @ V4))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V4)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ (V3 @ V4)) @ (V3 @ V5))))))))) @ (V3 @ V2)))))))))))))
(TTypedef.type_definition.Abs_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V3) @ (V1 @ V5))) @ ((c==> @ ((cSet.member @ V5) @ V2)) @ V4))))) @ V4)))))))))))))
(TTypedef.type_definition.Abs_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cSet.image @ V1) @ V2)) @ cOrderings.top_class.top)))))))))
(TTypedef.type_definition.Rep_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V3) @ (V0 @ V5))) @ V4)))) @ V4))))))))))))))
(TTypedef.type_definition.Rep_range,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cSet.image @ V0) @ cOrderings.top_class.top)) @ V2)))))))))
(TTyperep.typerep.Abs_typerep_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cTyperep.Abs_typerep @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1))) @ V1))))) @ V1))))))
(TTyperep.typerep.Rep_typerep_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cTyperep.Rep_typerep @ V2))) @ V1)))) @ V1)))))))
(TTyperep.typerep.typerep_Rep_1_def,((c== @ cTyperep.typerep.typerep_Rep_1) @ ((cList.list.list_rec @ (cDatatype.In0 @ cHOL.undefined)) @ (^[V0]: (^[V1]: (^[V2]: (cDatatype.In1 @ ((cDatatype.Scons @ (cTyperep.Rep_typerep @ V0)) @ V2))))))))
(TTyperep.typerep.typerep_rec_1_def,((c== @ cTyperep.typerep.typerep_rec_1) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cHOL.The @ (^[V4]: (((((cTyperep.typerep.typerep_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4)))))))))
(TTyperep.typerep.typerep_rec_2_def,((c== @ cTyperep.typerep.typerep_rec_2) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cHOL.The @ (^[V4]: (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4)))))))))
(TWellfounded.pred_nat_trancl_eq_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ cWellfounded.pred_nat))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TBig_Operators.comm_monoid_set.cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V3)) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V5) @ V3))))))))))))))))))
(TBig_Operators.setsum_comp_morphism,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((cGroups.plus_class.plus @ V3) @ V4))) @ ((cGroups.plus_class.plus @ (V0 @ V3)) @ (V0 @ V4)))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ ((cFun.comp @ V0) @ V1)) @ V2)) @ (V0 @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V2))))))))))))
(TBig_Operators.setsum_right_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cGroups.times_class.times @ V0) @ (V1 @ V3)))) @ V2)))))))))
(TCode_Evaluation.arity_term_of_bool,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_char,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_list,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_pred,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_prod,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_term,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_unit,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_typerep_pred,(cTyperep.typerep_class @ cTYPE))
(TCode_Evaluation.arity_typerep_term,(cTyperep.typerep_class @ cTYPE))
(TCode_Evaluation.term.term_case_def,((c== @ cCode_Evaluation.term.term_case) @ (^[V0]: (cCode_Evaluation.term.term_rec @ V0))))
(TCode_Evaluation.term.term_size_def,((c== @ cCode_Evaluation.term.term_size) @ (cCode_Evaluation.term.term_rec @ cNat.zero_nat_inst.zero_nat)))
(TCode_Numeral.Suc_natural_minus_one,(call @ (^[V0]: ((cHOL.eq @ ((cCode_Numeral.minus_natural_inst.minus_natural @ (cCode_Numeral.Suc @ V0)) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0))))
(TCode_Numeral.int_of_integer_of_int,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cInt.ring_1_class.of_int @ V0))) @ V0))))
(TCode_Numeral.int_of_integer_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TCode_Numeral.integer_of_nat.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_nat @ V0)) @ (cCode_Numeral.integer_of_int @ (cNat.semiring_1_class.of_nat @ V0))))))
(TCode_Numeral.integer_of_nat.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TCode_Numeral.integer_of_num.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_num @ V0)) @ (cCode_Numeral.integer_of_int @ (cNum.numeral_class.numeral @ V0))))))
(TCode_Numeral.integer_of_num.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_num @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TCode_Numeral.less_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cHOL.eq)) @ cInt.ord_int_inst.less_int) @ cCode_Numeral.ord_integer_inst.less_integer))
(TCode_Numeral.less_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cHOL.eq)) @ cNat.ord_nat_inst.less_nat) @ cCode_Numeral.ord_natural_inst.less_natural))
(TCode_Numeral.nat_of_integer.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_integer @ (cCode_Numeral.integer_of_int @ V0))) @ (cInt.nat @ V0)))))
(TCode_Numeral.nat_of_integer.rep_eq,(call @ (^[V0]: ((c== @ (cCode_Numeral.nat_of_integer @ V0)) @ (cInt.nat @ (cCode_Numeral.int_of_integer @ V0))))))
(TCode_Numeral.nat_of_integer_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_integer @ (cNat.semiring_1_class.of_nat @ V0))) @ V0))))
(TCode_Numeral.nat_of_natural_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ (cNat.semiring_1_class.of_nat @ V0))) @ V0))))
(TCode_Numeral.natural_of_nat_of_nat,((cHOL.eq @ cCode_Numeral.natural_of_nat) @ cNat.semiring_1_class.of_nat))
(TCode_Numeral.num_of_integer.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.num_of_integer @ (cCode_Numeral.integer_of_int @ V0))) @ (cNum.num_of_nat @ (cInt.nat @ V0))))))
(TCode_Numeral.num_of_integer.rep_eq,(call @ (^[V0]: ((c== @ (cCode_Numeral.num_of_integer @ V0)) @ (cNum.num_of_nat @ (cInt.nat @ (cCode_Numeral.int_of_integer @ V0)))))))
(TCode_Numeral.plus_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer)) @ cInt.plus_int_inst.plus_int) @ cCode_Numeral.plus_integer_inst.plus_integer))
(TCode_Numeral.plus_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cCode_Numeral.pcr_natural)) @ cNat.plus_nat_inst.plus_nat) @ cCode_Numeral.plus_natural_inst.plus_natural))
(TCode_Numeral.uminus_integer.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ (cCode_Numeral.integer_of_int @ V0))) @ (cCode_Numeral.integer_of_int @ (cInt.uminus_int_inst.uminus_int @ V0))))))
(TCode_Numeral.uminus_integer.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ V0))) @ (cInt.uminus_int_inst.uminus_int @ (cCode_Numeral.int_of_integer @ V0))))))
(TCode_Numeral.zero_integer.transfer,((cCode_Numeral.pcr_integer @ cInt.zero_int_inst.zero_int) @ cCode_Numeral.zero_integer_inst.zero_integer))
(TCode_Numeral.zero_natural.transfer,((cCode_Numeral.pcr_natural @ cNat.zero_nat_inst.zero_nat) @ cCode_Numeral.zero_natural_inst.zero_natural))
(TComplete_Lattices.INT_extend_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cSet.image @ V2) @ V0)) @ (^[V3]: (V1 @ V3)))))))))))
(TComplete_Lattices.INT_extend_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.INFI @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))))))))))
(TComplete_Lattices.INT_extend_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ (^[V3]: (V1 @ V3)))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V2]: (V1 @ V2)))))))))
(TComplete_Lattices.INT_extend_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cLattices.sup_class.sup @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.INT_extend_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ V2)))))))))))
(TComplete_Lattices.INT_extend_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.insert @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cSet.insert @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.INT_extend_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cGroups.minus_class.minus @ V0) @ (V2 @ V3)))))))))))))
(TComplete_Lattices.INT_extend_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cGroups.minus_class.minus @ cOrderings.top_class.top) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cGroups.minus_class.minus @ (V1 @ V3)) @ V2))))))))))))
(TComplete_Lattices.INT_extend_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)) @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cLattices.inf_class.inf @ V0) @ (V2 @ V3)))))))))))))
(TComplete_Lattices.INT_extend_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ V2) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ V2))))))))))))
(TComplete_Lattices.Inter_Un_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ V1))))))))
(TComplete_Lattices.UNION_empty_conv_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2)))) @ cOrderings.bot_class.bot)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.bot_class.bot)))))))))
(TComplete_Lattices.UNION_empty_conv_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.bot_class.bot)))))))))
(TComplete_Lattices.Union_Int_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.Union_Un_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.Union_empty_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ cOrderings.bot_class.bot)) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TComplete_Lattices.empty_Union_conv,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TComplete_Lattices.subset_Pow_Union,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ (cSet.Pow @ (cComplete_Lattices.Sup_class.Sup @ V0))))))
(TComplete_Partial_Order.chain_compr,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V1)) @ ((cComplete_Partial_Order.chain @ V0) @ (cSet.Collect @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V1)) @ (V2 @ V3)))))))))))))
(TComplete_Partial_Order.lfp_eq_fixp,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cHOL.eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ (cComplete_Partial_Order.ccpo_class.fixp @ V0))))))
(TDivides.ring_div.mod_diff_right_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cDivides.class.ring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ ((V6 @ V8) @ V9)) @ V10)) @ ((V2 @ ((V6 @ V8) @ ((V2 @ V9) @ V10))) @ V10))))))))))))))))))))))))))
(TDivides.ring_div_class.dvd_div_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_class.div @ V1) @ (cGroups.uminus_class.uminus @ V0))) @ (cGroups.uminus_class.uminus @ ((cDivides.div_class.div @ V1) @ V0)))))))))
(TDivides.ring_div_class.dvd_neg_div,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_class.div @ (cGroups.uminus_class.uminus @ V1)) @ V0)) @ (cGroups.uminus_class.uminus @ ((cDivides.div_class.div @ V1) @ V0)))))))))
(TDivides.ring_div_class.mod_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ ((cDivides.div_class.mod @ V0) @ V2)) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)))))))))
(TDivides.semiring_div.div_add_self1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V3 @ V6) @ V7)) @ V6)) @ ((V3 @ ((V1 @ V7) @ V6)) @ V5)))))))))))))))))))))
(TDivides.semiring_div.div_add_self2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V3 @ V7) @ V6)) @ V6)) @ ((V3 @ ((V1 @ V7) @ V6)) @ V5)))))))))))))))))))))
(TDivides.semiring_div.div_mult_swap,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((V0 @ V8) @ ((V1 @ V7) @ V6))) @ ((V1 @ ((V0 @ V8) @ V7)) @ V6)))))))))))))))))))))))
(TDivides.semiring_div.dvd_imp_mod_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V7) @ V6)) @ V4))))))))))))))))))))
(TDivides.semiring_div.mod_add_self1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ V7)) @ V6)) @ ((V2 @ V7) @ V6))))))))))))))))))))
(TDivides.semiring_div.mod_add_self2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ V7)) @ V7)) @ ((V2 @ V6) @ V7))))))))))))))))))))
(TDivides.semiring_div.mod_mult_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cHOL.eq @ ((V2 @ V6) @ V7)) @ ((V2 @ V8) @ V7))) @ ((c==> @ ((cHOL.eq @ ((V2 @ V9) @ V7)) @ ((V2 @ V10) @ V7))) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V9)) @ V7)) @ ((V2 @ ((V0 @ V8) @ V10)) @ V7))))))))))))))))))))))))))))
(TDivides.semiring_div.mult_mod_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V0 @ ((V2 @ V6) @ V7)) @ V8)) @ ((V2 @ ((V0 @ V6) @ V8)) @ ((V0 @ V7) @ V8)))))))))))))))))))))))
(TDivides.semiring_div_class.div_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.plus_class.plus @ V1) @ V2)) @ V0)) @ ((cGroups.plus_class.plus @ ((cDivides.div_class.div @ V1) @ V0)) @ ((cDivides.div_class.div @ V2) @ V0))))))))))))
(TDivides.semiring_div_class.dvd_mod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ ((cDivides.div_class.mod @ V1) @ V2)))))))))))
(TDivides.transfer_int_nat_functions_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ (cNat.semiring_1_class.of_nat @ ((cDivides.div_nat_inst.mod_nat @ V0) @ V1))))))))
(TDivides.transfer_int_nat_functions_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_int_inst.div_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ (cNat.semiring_1_class.of_nat @ ((cDivides.div_nat_inst.div_nat @ V0) @ V1))))))))
(TDivides.transfer_nat_int_functions_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ (cInt.nat @ ((cDivides.div_int_inst.mod_int @ V0) @ V1))))))))))
(TDivides.transfer_nat_int_functions_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ (cInt.nat @ ((cDivides.div_int_inst.div_int @ V0) @ V1))))))))))
(TEnum.finite_1.Abs_finite_1_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_1.finite_1_rep_set))) @ ((cHOL.eq @ (cEnum.Rep_finite_1 @ (cEnum.Abs_finite_1 @ V0))) @ V0)))))
(TEnum.finite_1.Rep_finite_1_inverse,(call @ (^[V0]: ((cHOL.eq @ (cEnum.Abs_finite_1 @ (cEnum.Rep_finite_1 @ V0))) @ V0))))
(TEnum.finite_1.finite_1_rec_set_def,((c== @ cEnum.finite_1.finite_1_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ cEnum.finite_1.a\<__caret__sub>1)) @ ((cHOL.eq @ V3) @ V0)))))))))
(TEnum.finite_1.finite_1_rep_set_def,((c== @ cEnum.finite_1.finite_1_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.eq @ V1) @ cHOL.undefined))))))
(TEnum.finite_2.Abs_finite_2_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_2.finite_2_rep_set))) @ ((cHOL.eq @ (cEnum.Rep_finite_2 @ (cEnum.Abs_finite_2 @ V0))) @ V0)))))
(TEnum.finite_2.Rep_finite_2_inverse,(call @ (^[V0]: ((cHOL.eq @ (cEnum.Abs_finite_2 @ (cEnum.Rep_finite_2 @ V0))) @ V0))))
(TEnum.finite_2.finite_2_rec_set_def,((c== @ cEnum.finite_2.finite_2_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>1)) @ ((cHOL.eq @ V4) @ V0))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_2.a\<__caret__sub>2)) @ ((cHOL.eq @ V4) @ V1)))))))))))
(TEnum.finite_2.finite_2_rep_set_def,((c== @ cEnum.finite_2.finite_2_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ cHOL.undefined))))))))
(TEnum.finite_3.Abs_finite_3_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_3.finite_3_rep_set))) @ ((cHOL.eq @ (cEnum.Rep_finite_3 @ (cEnum.Abs_finite_3 @ V0))) @ V0)))))
(TEnum.finite_3.Rep_finite_3_inverse,(call @ (^[V0]: ((cHOL.eq @ (cEnum.Abs_finite_3 @ (cEnum.Rep_finite_3 @ V0))) @ V0))))
(TEnum.finite_3.finite_3_rec_set_def,((c== @ cEnum.finite_3.finite_3_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (cInductive.complete_lattice_class.lfp @ (^[V3]: (^[V4]: (^[V5]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>1)) @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>2)) @ ((cHOL.eq @ V5) @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_3.a\<__caret__sub>3)) @ ((cHOL.eq @ V5) @ V2)))))))))))))
(TEnum.finite_3.finite_3_rep_set_def,((c== @ cEnum.finite_3.finite_3_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))))))))
(TEnum.finite_4.Abs_finite_4_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_4.finite_4_rep_set))) @ ((cHOL.eq @ (cEnum.Rep_finite_4 @ (cEnum.Abs_finite_4 @ V0))) @ V0)))))
(TEnum.finite_4.Rep_finite_4_inverse,(call @ (^[V0]: ((cHOL.eq @ (cEnum.Abs_finite_4 @ (cEnum.Rep_finite_4 @ V0))) @ V0))))
(TEnum.finite_4.finite_4_rec_set_def,((c== @ cEnum.finite_4.finite_4_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cInductive.complete_lattice_class.lfp @ (^[V4]: (^[V5]: (^[V6]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>1)) @ ((cHOL.eq @ V6) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>2)) @ ((cHOL.eq @ V6) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>3)) @ ((cHOL.eq @ V6) @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_4.a\<__caret__sub>4)) @ ((cHOL.eq @ V6) @ V3)))))))))))))))
(TEnum.finite_4.finite_4_rep_set_def,((c== @ cEnum.finite_4.finite_4_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))))))))
(TEnum.finite_5.Abs_finite_5_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cEnum.finite_5.finite_5_rep_set))) @ ((cHOL.eq @ (cEnum.Rep_finite_5 @ (cEnum.Abs_finite_5 @ V0))) @ V0)))))
(TEnum.finite_5.Rep_finite_5_inverse,(call @ (^[V0]: ((cHOL.eq @ (cEnum.Abs_finite_5 @ (cEnum.Rep_finite_5 @ V0))) @ V0))))
(TEnum.finite_5.finite_5_rec_set_def,((c== @ cEnum.finite_5.finite_5_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (cInductive.complete_lattice_class.lfp @ (^[V5]: (^[V6]: (^[V7]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>1)) @ ((cHOL.eq @ V7) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>2)) @ ((cHOL.eq @ V7) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>3)) @ ((cHOL.eq @ V7) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>4)) @ ((cHOL.eq @ V7) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cEnum.finite_5.a\<__caret__sub>5)) @ ((cHOL.eq @ V7) @ V4)))))))))))))))))
(TEnum.finite_5.finite_5_rep_set_def,((c== @ cEnum.finite_5.finite_5_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))) @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))))))))))
(TEquiv_Relations.eq_equiv_class_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))))))))))))
(TEquiv_Relations.equiv_class_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))) @ ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ V3) @ V0))))))))))))))
(TEquiv_Relations.equiv_class_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))))))))))))))
(TEquiv_Relations.equiv_imp_dvd_card,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ ((cEquiv_Relations.quotient @ V0) @ V1)) @ (^[V3]: ((cRings.dvd_class.dvd @ V2) @ (cFinite_Set.card @ V3))))) @ ((cRings.dvd_class.dvd @ V2) @ (cFinite_Set.card @ V0))))))))))))
(TEquiv_Relations.finite_equiv_class,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: V0)))) @ ((c==> @ ((cSet.member @ V2) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ (cFinite_Set.finite @ V2)))))))))))
(TEquiv_Relations.part_equivp_transp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cEquiv_Relations.part_equivp @ V0)) @ ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V0 @ V1) @ V3)))))))))))))
(TEquiv_Relations.quotient_is_empty2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))))
(TEquiv_Relations.singleton_quotient,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cEquiv_Relations.quotient @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ V1)) @ ((cSet.insert @ ((cRelation.Image @ V1) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)))))))
(TEquiv_Relations.subset_equiv_class,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V2)) @ V1)))))))))))))
(TExtraction.sumbool.sumbool_rec_def,((c== @ cExtraction.sumbool.sumbool_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cExtraction.sumbool.sumbool_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TExtraction.type_definition_sumbool,(((cTypedef.type_definition @ cExtraction.Rep_sumbool) @ cExtraction.Abs_sumbool) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set)))
(TFields.division_ring.divide_eq_imp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ ((cHOL.eq @ V9) @ ((V3 @ V10) @ V8))) @ ((cHOL.eq @ ((V1 @ V9) @ V8)) @ V10)))))))))))))))))))))))))))
(TFields.division_ring.eq_divide_imp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ ((cHOL.eq @ ((V3 @ V9) @ V8)) @ V10)) @ ((cHOL.eq @ V9) @ ((V1 @ V10) @ V8))))))))))))))))))))))))))))
(TFields.division_ring.right_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V3 @ V8) @ (V0 @ V8))) @ V2))))))))))))))))))))))
(TFields.field_class.times_divide_eq_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cFields.inverse_class.divide @ V0) @ V1)) @ V2)) @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)))))))))
(TFields.field_class.times_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)))))))))
(TFields.linordered_field.frac_less2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V10 @ V5) @ V14)) @ ((c==> @ ((V10 @ V14) @ V15)) @ ((V10 @ ((V1 @ V12) @ V15)) @ ((V1 @ V13) @ V14))))))))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_46,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ ((V2 @ V12) @ V13)) @ V5)) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V12)) @ ((V10 @ V13) @ V5))) @ ((cHOL.conj @ ((V10 @ V12) @ V5)) @ ((V10 @ V5) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_45,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V5) @ ((V2 @ V12) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V12)) @ ((V10 @ V5) @ V13))) @ ((cHOL.conj @ ((V10 @ V12) @ V5)) @ ((V10 @ V13) @ V5))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_44,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V12) @ V13)) @ V14)) @ ((cGroups.plus_class.plus @ V12) @ ((cGroups.plus_class.plus @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_43,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V12) @ V13)) @ ((cGroups.plus_class.plus @ V13) @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_42,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V12) @ ((cGroups.plus_class.plus @ V13) @ V14))) @ ((cGroups.plus_class.plus @ V13) @ ((cGroups.plus_class.plus @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_41,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V12) @ V13)) @ V14)) @ ((cGroups.times_class.times @ V12) @ ((cGroups.times_class.times @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_40,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.times_class.times @ V12) @ V13)) @ ((cGroups.times_class.times @ V13) @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_39,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.times_class.times @ V12) @ ((cGroups.times_class.times @ V13) @ V14))) @ ((cGroups.times_class.times @ V13) @ ((cGroups.times_class.times @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_38,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V12) @ (cGroups.uminus_class.uminus @ V13))) @ ((cGroups.minus_class.minus @ V12) @ V13))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_37,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V12) @ ((cGroups.minus_class.minus @ V13) @ V14))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V12) @ V13)) @ V14))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_36,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V12) @ V13)) @ V14)) @ ((cHOL.eq @ V12) @ ((cGroups.plus_class.plus @ V14) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_35,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ V12) @ ((cGroups.minus_class.minus @ V13) @ V14))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_34,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V12) @ ((cGroups.minus_class.minus @ V13) @ V14))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_33,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V12)) @ V13)) @ ((cGroups.minus_class.minus @ V13) @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_32,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V12) @ V13)) @ V14)) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_31,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V12) @ V13)) @ V14)) @ ((cGroups.minus_class.minus @ V12) @ ((cGroups.plus_class.plus @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_30,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V12) @ V13)) @ V14)) @ ((cOrderings.ord_class.less @ V12) @ ((cGroups.plus_class.plus @ V14) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_29,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V12) @ ((cGroups.minus_class.minus @ V13) @ V14))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_28,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V12) @ V13)) @ V14)) @ ((cOrderings.ord_class.less_eq @ V12) @ ((cGroups.plus_class.plus @ V14) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_27,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V12) @ ((cGroups.minus_class.minus @ V13) @ V14))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_26,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V12) @ V13)) @ V14)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V12) @ V14)) @ ((cGroups.times_class.times @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_25,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.times_class.times @ V12) @ ((cGroups.plus_class.plus @ V13) @ V14))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V12) @ V13)) @ ((cGroups.times_class.times @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_24,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.times_class.times @ V12) @ ((cGroups.minus_class.minus @ V13) @ V14))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V12) @ V13)) @ ((cGroups.times_class.times @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V12) @ V13)) @ V14)) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V12) @ V14)) @ ((cGroups.times_class.times @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V12) @ V13)) @ V14)) @ ((V2 @ V12) @ ((V2 @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V2 @ V12) @ V13)) @ ((V2 @ V13) @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V2 @ V12) @ ((V2 @ V13) @ V14))) @ ((V2 @ V13) @ ((V2 @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V4 @ ((V4 @ V12) @ V13)) @ V14)) @ ((V4 @ V12) @ ((V4 @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_18,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V4 @ V12) @ V13)) @ ((V4 @ V13) @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V4 @ V12) @ ((V4 @ V13) @ V14))) @ ((V4 @ V13) @ ((V4 @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V4 @ V12) @ (V7 @ V13))) @ ((V6 @ V12) @ V13))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V4 @ V12) @ ((V6 @ V13) @ V14))) @ ((V6 @ ((V4 @ V12) @ V13)) @ V14))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ ((V6 @ V12) @ V13)) @ V14)) @ ((cHOL.eq @ V12) @ ((V4 @ V14) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ V12) @ ((V6 @ V13) @ V14))) @ ((cHOL.eq @ ((V4 @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V6 @ V12) @ ((V6 @ V13) @ V14))) @ ((V6 @ ((V4 @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V4 @ (V7 @ V12)) @ V13)) @ ((V6 @ V13) @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V4 @ ((V6 @ V12) @ V13)) @ V14)) @ ((V6 @ ((V4 @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V6 @ ((V6 @ V12) @ V13)) @ V14)) @ ((V6 @ V12) @ ((V4 @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V2 @ ((V4 @ V12) @ V13)) @ V14)) @ ((V4 @ ((V2 @ V12) @ V14)) @ ((V2 @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V2 @ V12) @ ((V4 @ V13) @ V14))) @ ((V4 @ ((V2 @ V12) @ V13)) @ ((V2 @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V2 @ V12) @ ((V6 @ V13) @ V14))) @ ((V6 @ ((V2 @ V12) @ V13)) @ ((V2 @ V12) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V2 @ ((V6 @ V12) @ V13)) @ V14)) @ ((V6 @ ((V2 @ V12) @ V14)) @ ((V2 @ V13) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ ((V6 @ V12) @ V13)) @ V14)) @ ((V10 @ V12) @ ((V4 @ V14) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V12) @ ((V6 @ V13) @ V14))) @ ((V10 @ ((V4 @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ ((V6 @ V12) @ V13)) @ V14)) @ ((V9 @ V12) @ ((V4 @ V14) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.sign_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ V12) @ ((V6 @ V13) @ V14))) @ ((V9 @ ((V4 @ V12) @ V14)) @ V13))))))))))))))))))))))))))))))))))
(TFinite_Set.finite_Collect_less_nat,(call @ (^[V0]: (cFinite_Set.finite @ (cSet.Collect @ (^[V1]: ((cNat.ord_nat_inst.less_nat @ V1) @ V0)))))))
(TFinite_Set.folding_idem_axioms_def,(call @ (^[V0]: ((c== @ (cFinite_Set.folding_idem_axioms @ V0)) @ (cHOL.All @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V1))) @ (V0 @ V1))))))))
(TFinite_Set.pigeonhole_infinite_rel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Bex @ V1) @ (^[V4]: ((V2 @ V3) @ V4)))))) @ ((cSet.Bex @ V1) @ (^[V3]: (cHOL.Not @ (cFinite_Set.finite @ (cSet.Collect @ (^[V4]: ((cHOL.conj @ ((cSet.member @ V4) @ V0)) @ ((V2 @ V4) @ V3))))))))))))))))))
(TGroups.ab_semigroup_mult_class_def,((c== @ (cGroups.ab_semigroup_mult_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.semigroup_mult_class @ cTYPE)) @ (cGroups.class.ab_semigroup_mult_axioms @ cGroups.times_class.times))))
(TGroups.abel_semigroup.left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.abel_semigroup @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ V2) @ ((V0 @ V1) @ V3)))))))))))))
(TGroups.abel_semigroup_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (cGroups.abel_semigroup_axioms @ V0)))))
(TGroups.class.ab_semigroup_mult_def,(call @ (^[V0]: ((c== @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((cHOL.conj @ (cGroups.class.semigroup_mult @ V0)) @ (cGroups.class.ab_semigroup_mult_axioms @ V0))))))
(TGroups.class.comm_monoid_add.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((c==> @ ((cGroups.class.comm_monoid_add_axioms @ V0) @ V1)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1))))))))
(TGroups.class.monoid_add_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.monoid_add_axioms @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2))))))))))
(TGroups.comm_monoid_add_class.add_0,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TGroups.comm_monoid_add_class.intro,((c==> @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.zero_class @ cTYPE)) @ ((c==> @ ((cGroups.class.comm_monoid_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)) @ (cGroups.comm_monoid_add_class @ cTYPE)))))
(TGroups.comm_monoid_add_class.super_2,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TGroups.comm_monoid_add_class.super_1,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ (cGroups.ab_semigroup_add_class @ cTYPE)))
(TGroups.group_add.diff_minus_eq_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ (V3 @ V5))) @ ((V1 @ V4) @ V5))))))))))))))))
(TGroups.group_add_class.add_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)))))))))
(TGroups.group_add_class.minus_minus,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cGroups.uminus_class.uminus @ V0))) @ V0))))
(TGroups.group_add_class.right_minus,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ cGroups.zero_class.zero))))
(TGroups.monoid_add_class.add_0_left,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TGroups.semigroup_mult_class.axioms,(cGroups.class.semigroup_mult @ cGroups.times_class.times))
(THOL.equal_itself_inst.equal_itself,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(THilbert_Choice.GreatestM_nat_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V4)) @ V3))))) @ ((cHOL.conj @ (V0 @ ((cHilbert_Choice.GreatestM @ V2) @ V0))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ V4)) @ (V2 @ ((cHilbert_Choice.GreatestM @ V2) @ V0))))))))))))))))))
(THilbert_Choice.ex_has_greatest_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V4)) @ V3))))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ (V0 @ V4)) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (V0 @ V5)) @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ V5)) @ (V2 @ V4)))))))))))))))))))
(THilbert_Choice.some_sym_eq_trivial,(call @ (^[V0]: ((cHOL.eq @ (cHilbert_Choice.Eps @ (^[V1]: ((cHOL.eq @ V0) @ V1)))) @ V0))))
(TInductive.complete_lattice.gfp_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cInductive.complete_lattice.gfp @ V1) @ V3) @ V8)) @ (V1 @ (cSet.Collect @ (^[V9]: ((V3 @ V9) @ (V8 @ V9))))))))))))))))))))))))))
(TInductive.complete_lattice.lfp_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cInductive.complete_lattice.lfp @ V0) @ V3) @ V8)) @ (V0 @ (cSet.Collect @ (^[V9]: ((V3 @ (V8 @ V9)) @ V9)))))))))))))))))))))))))
(TInt.mult_less_cancel_right_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ V1))) @ ((cGroups.times_class.times @ V2) @ (cNum.numeral_class.numeral @ V1)))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V1)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V0)))))))))))
(TLattices.arity_boolean_algebra_fun,(cLattices.boolean_algebra_class @ cTYPE))
(TLattices.arity_bounded_lattice_fun,(cLattices.bounded_lattice_class @ cTYPE))
(TLattices.arity_distrib_lattice_fun,(cLattices.distrib_lattice_class @ cTYPE))
(TLattices.arity_semilattice_inf_fun,(cLattices.semilattice_inf_class @ cTYPE))
(TLattices.arity_semilattice_sup_fun,(cLattices.semilattice_sup_class @ cTYPE))
(TLattices.boolean_algebra.compl_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ ((V2 @ V8) @ V9))) @ ((V5 @ (V1 @ V8)) @ (V1 @ V9)))))))))))))))))))))))))
(TLattices.boolean_algebra.compl_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ ((V5 @ V8) @ V9))) @ ((V2 @ (V1 @ V8)) @ (V1 @ V9)))))))))))))))))))))))))
(TLattices.boolean_algebra_class_def,((c== @ (cLattices.boolean_algebra_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.minus_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE))) @ ((cPure.conjunction @ (cLattices.bounded_lattice_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.distrib_lattice_class @ cTYPE)) @ ((((((cLattices.class.boolean_algebra_axioms @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cLattices.inf_class.inf) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))))))
(TLattices.bounded_lattice_class_def,((c== @ (cLattices.bounded_lattice_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.lattice_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_bot_class @ cTYPE)) @ (cOrderings.order_top_class @ cTYPE)))))
(TLattices.class.boolean_algebra_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((cLattices.class.bounded_lattice @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((cLattices.class.distrib_lattice @ V2) @ V3) @ V4) @ V5)) @ ((((((cLattices.class.boolean_algebra_axioms @ V0) @ V1) @ V2) @ V5) @ V6) @ V7)))))))))))))))))))))
(TLattices.class.bounded_lattice_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (((cOrderings.class.order_bot @ V4) @ V1) @ V2)) @ (((cOrderings.class.order_top @ V1) @ V2) @ V5)))))))))))))))))
(TLattices.class.distrib_lattice_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((cLattices.class.distrib_lattice_axioms @ V0) @ V3))))))))))))
(TLattices.class.semilattice_inf_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cOrderings.class.order @ V1) @ V2)) @ ((cLattices.class.semilattice_inf_axioms @ V0) @ V1))))))))))
(TLattices.class.semilattice_sup_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cOrderings.class.order @ V1) @ V2)) @ ((cLattices.class.semilattice_sup_axioms @ V0) @ V1))))))))))
(TLattices.distrib_lattice_class_def,((c== @ (cLattices.distrib_lattice_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.lattice_class @ cTYPE)) @ ((cLattices.class.distrib_lattice_axioms @ cLattices.inf_class.inf) @ cLattices.sup_class.sup))))
(TLattices.lattice_class.inf_sup_aci_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TLattices.lattice_class.inf_sup_aci_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ V1) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TLattices.lattice_class.inf_sup_aci_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.lattice_class.inf_sup_aci_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TLattices.lattice_class.inf_sup_aci_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TLattices.lattice_class.inf_sup_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TLattices.lattice_class.inf_sup_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TLattices.lattice_class.inf_sup_aci_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V1) @ V0)))))))
(TLattices.lattice_class.inf_sup_ord_4,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TLattices.lattice_class.inf_sup_ord_3,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TLattices.lattice_class.inf_sup_ord_2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V1))))))
(TLattices.lattice_class.inf_sup_ord_1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0))))))
(TLattices.linorder_class.max.orderE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ ((cOrderings.ord_class.max @ V1) @ V0))) @ V2)) @ V2)))))))))
(TLattices.linorder_class.max.orderI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TLattices.linorder_class.min.orderE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))) @ V2)) @ V2)))))))))
(TLattices.linorder_class.min.orderI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TLattices.semilattice_inf.inf_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V3) @ V4)) @ V5)) @ ((V0 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))
(TLattices.semilattice_inf_class_def,((c== @ (cLattices.semilattice_inf_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.inf_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ ((cLattices.class.semilattice_inf_axioms @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq)))))
(TLattices.semilattice_order.absorb1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ V3))))))))))))))
(TLattices.semilattice_order.absorb2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V4) @ V3)) @ V3))))))))))))))
(TLattices.semilattice_sup.sup_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V3) @ V4)) @ V5)) @ ((V0 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))
(TLattices.semilattice_sup.sup_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V4)) @ ((V1 @ ((V0 @ V3) @ V5)) @ V4)))))))))))))))))
(TLattices.semilattice_sup_class_def,((c== @ (cLattices.semilattice_sup_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.sup_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ ((cLattices.class.semilattice_sup_axioms @ cLattices.sup_class.sup) @ cOrderings.ord_class.less_eq)))))
(TLazy_Sequence.arity_small_lazy_int,(cLazy_Sequence.small_lazy_class @ cTYPE))
(TLazy_Sequence.iterate_upto.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.iterate_upto_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.iterate_upto_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ (((V3 @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TLazy_Sequence.iterate_upto_rel_def,((c== @ cLazy_Sequence.iterate_upto_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))))))))))))))))))
(TLazy_Sequence.lazy_sequence.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V2))))) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TLazy_Sequence.lazy_sequence.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TLazy_Sequence.lazy_sequence.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TLazy_Sequence.lazy_sequence_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ V0)) @ (cLazy_Sequence.list_of_lazy_sequence @ V1))))))))
(TLazy_Sequence.small_lazy'_sumC_def,((c== @ cLazy_Sequence.small_lazy'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cLazy_Sequence.small_lazy'_graph @ V0) @ V1))))))
(TLazy_Sequence.small_lazy_class_def,((c== @ (cLazy_Sequence.small_lazy_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TLifting.pcr_Domainp_par_left_total,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ (cRelation.Domainp @ V0)) @ V1)) @ ((c==> @ (cLifting.left_total @ V2)) @ ((c==> @ ((((cTransfer.fun_rel @ V2) @ cHOL.eq) @ V3) @ V1)) @ ((cHOL.eq @ (cRelation.Domainp @ ((cRelation.relcompp @ V2) @ V0))) @ V3)))))))))))))
(TLifting.reflp_Quotient_composition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_total @ V0)) @ ((c==> @ (cRelation.reflp @ V1)) @ (cRelation.reflp @ ((cRelation.relcompp @ V0) @ ((cRelation.relcompp @ V1) @ (cRelation.conversep @ V0)))))))))))
(TLifting_Option.bi_total_option_rel,(call @ (^[V0]: ((c==> @ (cTransfer.bi_total @ V0)) @ (cTransfer.bi_total @ (cLifting_Option.option_rel @ V0))))))
(TLifting_Option.option_map_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ V1)) @ ((cTransfer.fun_rel @ (cLifting_Option.option_rel @ V0)) @ (cLifting_Option.option_rel @ V1))) @ cOption.map) @ cOption.map))))))
(TLifting_Product.bi_unique_prod_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.bi_unique @ V1)) @ (cTransfer.bi_unique @ ((cLifting_Product.prod_rel @ V0) @ V1)))))))))
(TLifting_Product.prod_case_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V1) @ V2))) @ ((cTransfer.fun_rel @ ((cLifting_Product.prod_rel @ V0) @ V1)) @ V2)) @ cProduct_Type.prod.prod_case) @ cProduct_Type.prod.prod_case))))))))
(TLimited_Sequence.neg_decr_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.neg_decr_bind @ V0) @ V1)) @ (^[V2]: (((cHOL.If @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.hit_bound) @ ((cLazy_Sequence.hb_bind @ (V0 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))) @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TLimited_Sequence.pos_decr_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLimited_Sequence.pos_decr_bind @ V0) @ V1)) @ (^[V2]: (((cHOL.If @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.bind @ (V0 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))) @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TList.card_lists_distinct_length_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ (cFinite_Set.card @ V1))) @ ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ (cNat.size_class.size @ V2)) @ V0)) @ ((cHOL.conj @ (cList.distinct @ V2)) @ ((cOrderings.ord_class.less_eq @ (cList.set @ V2)) @ V1))))))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: V2)) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V1)) @ V0)) @ cNat.one_nat_inst.one_nat)) @ (cFinite_Set.card @ V1))))))))))
(TList.complete_lattice.INF_set_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ (cList.set @ V8)) @ V9)) @ (((cList.fold @ ((cFun.comp @ V2) @ V9)) @ V8) @ V7))))))))))))))))))))))))
(TList.complete_lattice.Inf_set_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ (cList.set @ V8))) @ (((cList.fold @ V2) @ V8) @ V7))))))))))))))))))))))
(TList.complete_lattice.SUP_set_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ (cList.set @ V8)) @ V9)) @ (((cList.fold @ ((cFun.comp @ V5) @ V9)) @ V8) @ V6))))))))))))))))))))))))
(TList.complete_lattice.Sup_set_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ (cList.set @ V8))) @ (((cList.fold @ V5) @ V8) @ V6))))))))))))))))))))))
(TList.linorder.insort_insert_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ (cList.set @ V3)))) @ ((cHOL.eq @ ((((cList.linorder.insort_insert_key @ V0) @ (^[V4]: V4)) @ V2) @ V3)) @ ((((cList.linorder.insort_key @ V0) @ (^[V4]: V4)) @ V2) @ V3)))))))))))))
(TList.linorder.insort_key_left_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ (V2 @ V3)) @ (V2 @ V4)))) @ ((cHOL.eq @ ((((cList.linorder.insort_key @ V0) @ V2) @ V4) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V5))) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V4) @ V5))))))))))))))))))
(TList.linorder.sorted_insort_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((cList.linorder.sorted @ V0) @ ((((cList.linorder.insort_insert_key @ V0) @ (^[V4]: V4)) @ V3) @ V2)))))))))))))
(TList.linorder_class.insort_is_Cons,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.Ball @ (cList.set @ V0)) @ (^[V3]: ((cOrderings.ord_class.less_eq @ (V1 @ V2)) @ (V1 @ V3))))) @ ((cHOL.eq @ (((cList.linorder_class.insort_key @ V1) @ V2) @ V0)) @ ((cList.list.Cons @ V2) @ V0))))))))))
(TList.linorder_class.insort_key_def,((c== @ cList.linorder_class.insort_key) @ (^[V0]: (^[V1]: (^[V2]: (((((cList.list.list_rec @ (^[V3]: (^[V4]: ((cList.list.Cons @ V4) @ cList.list.Nil)))) @ (^[V3]: (^[V4]: (^[V5]: (^[V6]: (^[V7]: (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (V6 @ V7)) @ (V6 @ V3))) @ ((cList.list.Cons @ V7) @ ((cList.list.Cons @ V3) @ V4))) @ ((cList.list.Cons @ V3) @ ((V5 @ V6) @ V7))))))))) @ V2) @ V0) @ V1))))))
(TList.linorder_class.insort_not_Nil,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2)) @ cList.list.Nil)))))))))
(TList.linorder_class.insort_remove1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ (cList.linorder_class.sorted @ V1)) @ ((cHOL.eq @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V0) @ ((cList.remove1 @ V0) @ V1))) @ V1))))))))
(TList.linorder_class.remove1_insort,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.remove1 @ V0) @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V0) @ V1))) @ V1))))))
(TList.linorder_class.set_insort_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.set @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2))) @ ((cSet.insert @ V1) @ (cList.set @ V2))))))))))
(TList.linorder_class.sort_conv_fold,(call @ (^[V0]: ((cHOL.eq @ ((cList.linorder_class.sort_key @ (^[V1]: V1)) @ V0)) @ (((cList.fold @ (cList.linorder_class.insort_key @ (^[V1]: V1))) @ V0) @ cList.list.Nil)))))
(TList.linorder_class.sort_key_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.linorder_class.sort_key @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (((cList.linorder_class.insort_key @ V0) @ V1) @ ((cList.linorder_class.sort_key @ V0) @ V2))))))))))
(TList.linorder_class.sort_key_simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cList.linorder_class.sort_key @ V0) @ cList.list.Nil)) @ cList.list.Nil))))
(TList.linorder_class.sorted.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ ((c==> @ (V1 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.Ball @ (cList.set @ V2)) @ (^[V4]: ((cOrderings.ord_class.less_eq @ V3) @ V4)))) @ ((c==> @ (cList.linorder_class.sorted @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ ((cList.list.Cons @ V3) @ V2)))))))))) @ (V1 @ V0)))))))))
(TList.linorder_class.sorted_butlast,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cList.list.Nil))) @ ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ (cList.butlast @ V0)))))))
(TList.linorder_class.sorted_many_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.linorder_class.sorted @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cList.linorder_class.sorted @ ((cList.list.Cons @ V1) @ V2)))))))))))
(TList.linorder_class.sorted_remdups,(call @ (^[V0]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ (cList.remdups @ V0))))))
(TList.linorder_class.sorted_remove1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ ((cList.remove1 @ V1) @ V0))))))))
(TList.linorder_class.sorted_sort_id,(call @ (^[V0]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ ((cHOL.eq @ ((cList.linorder_class.sort_key @ (^[V1]: V1)) @ V0)) @ V0)))))
(TList.list.list_size_overloaded_def,((c== @ cNat.size_class.size) @ ((cList.list.list_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TList.list.size_list_inst.size_list,((c== @ cList.list.size_list_inst.size_list) @ cList.list.size_list_inst.size_list))
(TList.list_all_iff_all_interval_int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_all @ V0) @ ((cList.upto @ V1) @ V2))) @ (((cList.all_interval_int @ V0) @ V1) @ V2)))))))))
(TList.list_all_iff_all_interval_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_all @ V0) @ ((cList.upt @ V1) @ V2))) @ (((cList.all_interval_nat @ V0) @ V1) @ V2)))))))))
(TList.map_tailrec_rev_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cList.map_tailrec_rev_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ cList.list.Nil) @ V5))) @ V5)))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cList.map_tailrec_rev_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V6)) @ V7))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V6) @ ((cList.list.Cons @ (V4 @ V5)) @ V7)))))))))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TList.monoid_add.listsum_map_filter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ (cList.set @ V2))) @ ((c==> @ (cHOL.Not @ (V3 @ V5))) @ ((cHOL.eq @ (V4 @ V5)) @ V1)))))) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V4) @ ((cList.filter @ V3) @ V2)))) @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V4) @ V2))))))))))))))))
(TList.monoid_add.listsum_setsum_nth,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cList.nth @ V2) @ V3))) @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V2))))))))))))
(TList.monoid_add_class.listsum_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V2]: V0)) @ V1))) @ ((cGroups.times_class.times @ (cNat.semiring_1_class.of_nat @ (cNat.size_class.size @ V1))) @ V0)))))))
(TList.semiring_0.listsum_const_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cRings.class.semiring_0 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ (^[V6]: ((V2 @ V3) @ (V4 @ V6)))) @ V5))) @ ((V2 @ V3) @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ (^[V6]: (V4 @ V6))) @ V5))))))))))))))))))
(TList.semiring_0.listsum_mult_const,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cRings.class.semiring_0 @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ (^[V6]: ((V2 @ (V3 @ V6)) @ V4))) @ V5))) @ ((V2 @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ (^[V6]: (V3 @ V6))) @ V5))) @ V4))))))))))))))))
(TMain.arity_full_exhaustive_sumbool,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TMain.arity_partial_term_of_sumbool,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TNat.dvd.dual_order.ordering_axioms,((cOrderings.ordering @ (^[V0]: (^[V1]: ((cRings.dvd_class.dvd @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.dvd.order.strict_implies_order,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.order_class.lift_Suc_mono_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cOrderings.ord_class.less @ (V0 @ V3)) @ (V0 @ (cNat.Suc @ V3)))))) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TNat_Transfer.transfer_morphism_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat_Transfer.transfer_morphism @ V0) @ V1)) @ cHOL.True))))))
(TNitpick.arity_full_exhaustive_word,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TNitpick.arity_partial_term_of_word,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TNitpick.equal_word_inst.equal_word,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TNitpick.fun_box.Abs_fun_box_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set))) @ (V0 @ (cNitpick.Abs_fun_box @ V2)))))) @ (V0 @ V1)))))))
(TNitpick.fun_box.Abs_fun_box_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cNitpick.Abs_fun_box @ V0)) @ (cNitpick.Abs_fun_box @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TNitpick.fun_box.Rep_fun_box_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cNitpick.Rep_fun_box @ V2))))) @ (V1 @ V0))))))))
(TNitpick.fun_box.Rep_fun_box_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNitpick.Rep_fun_box @ V0)) @ (cNitpick.Rep_fun_box @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.fun_box.arity_size_fun_box,(cNat.size_class @ cTYPE))
(TNitpick.pair_box.pair_box_case_def,((c== @ cNitpick.pair_box.pair_box_case) @ (^[V0]: (cNitpick.pair_box.pair_box_rec @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2)))))))
(TNitpick.pair_box.pair_box_size_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cNitpick.pair_box.pair_box_size @ V0) @ V1)) @ (cNitpick.pair_box.pair_box_rec @ (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (V1 @ V3))) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))))
(TNum.neg_numeral.diff_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V6))) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V6) @ V5))))))))))))))))))
(TNum.neg_numeral.diff_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5)) @ (((cNum.numeral.numeral @ V4) @ V1) @ V6))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ ((cNum.plus_num_inst.plus_num @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral.diff_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V6))) @ (((cNum.numeral.numeral @ V4) @ V1) @ ((cNum.plus_num_inst.plus_num @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral.diff_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5)) @ (((cNum.numeral.numeral @ V4) @ V1) @ V6))) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ V6))))))))))))))))))
(TNum.neg_numeral.is_num_add_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6)) @ ((cHOL.eq @ ((V1 @ V5) @ V6)) @ ((V1 @ V6) @ V5))))))))))))))))))))
(TNum.neg_numeral_class.is_num.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cGroups.one_class.one)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ V2))) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V2)) @ V1))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V3))) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V2)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V3)) @ V1)))))))) @ V1)))))))))
(TNum.neg_numeral_class.is_num.simps,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.is_num @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.one_class.one)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cNum.neg_numeral_class.is_num @ V1))))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cHOL.conj @ (cNum.neg_numeral_class.is_num @ V1)) @ (cNum.neg_numeral_class.is_num @ V2)))))))))))))
(TNum.neg_numeral_class.numeral_BitM,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))) @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))) @ cGroups.one_class.one)))))
(TNum.numeral_class.numeral_plus_one,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.numeral_class.one_plus_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0))))))
(TNum.ring_1_class.mult_minus1_right,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))) @ (cGroups.uminus_class.uminus @ V0)))))
(TNum.ring_char_0.neg_numeral_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7))) @ ((cHOL.eq @ V6) @ V7))))))))))))))))))))
(TNum.ring_char_0.not_iszero_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cNum.ring_1.iszero @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)))))))))))))))))))
(TNum.semiring_char_0.numeral_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V5))) @ ((cHOL.eq @ V4) @ V5))))))))))))))))
(TNumeral_Simprocs.nat_less_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V4))) @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V3)) @ V4))))))))))))))
(TNumeral_Simprocs.nat_less_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V2)) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V1) @ V2)) @ V4))) @ ((cNat.ord_nat_inst.less_nat @ V3) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ V2)) @ V4)))))))))))))))
(TOption.option.option_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cOption.option.option_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cOption.option.None)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ (cOption.option.Some @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ (V1 @ V5))) @ V4))))) @ V4))))))))))))))
(TOption.option.option_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cOption.option.option_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cOption.option.None)) @ ((cHOL.eq @ V3) @ V0))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cOption.option.Some @ V4))) @ ((cHOL.eq @ V3) @ (V1 @ V4))))))))))))))))
(TOrderings.class.dense_linorder_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.dense_order @ V0) @ V1)) @ ((cOrderings.class.linorder @ V0) @ V1))))))))
(TOrderings.class.dense_order.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.dense_order @ V0) @ V1)) @ (cOrderings.class.dense_order_axioms @ V1)))))))
(TOrderings.class.dense_order.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.dense_order @ V0) @ V1)) @ ((cOrderings.class.order @ V0) @ V1)))))))
(TOrderings.class.order_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V1)) @ ((cHOL.eq @ V1) @ V2)))))))) @ (cOrderings.class.order_axioms @ V0)))))
(TOrderings.dense_linorder_class_def,((c== @ (cOrderings.dense_linorder_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.dense_order_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE))))
(TOrderings.dense_order_class.axioms,(cOrderings.class.dense_order_axioms @ cOrderings.ord_class.less))
(TOrderings.linorder.le_max_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ (((cOrderings.ord.max @ V0) @ V3) @ V4))) @ ((cHOL.disj @ ((V0 @ V2) @ V3)) @ ((V0 @ V2) @ V4)))))))))))))))
(TOrderings.linorder.min_le_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ (((cOrderings.ord.min @ V0) @ V2) @ V3)) @ V4)) @ ((cHOL.disj @ ((V0 @ V2) @ V4)) @ ((V0 @ V3) @ V4)))))))))))))))
(TOrderings.linorder_class.mono_invE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ V3)) @ V3))))))))))))
(TOrderings.linorder_class.split_max,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ (V0 @ V2))) @ ((cHOL.implies @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V1) @ V2))) @ (V0 @ V1)))))))))))
(TOrderings.linorder_class.split_min,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ (V0 @ V1))) @ ((cHOL.implies @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V1) @ V2))) @ (V0 @ V2)))))))))))
(TOrderings.ord_fun_inst.less_eq_fun,((c== @ cOrderings.ord_fun_inst.less_eq_fun) @ cOrderings.ord_fun_inst.less_eq_fun))
(TOrderings.order_bot_class.bot_less,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less @ cOrderings.bot_class.bot) @ V0)))))
(TOrderings.order_class.antisym_conv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.order_class.le_neq_trans,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.order_class.less_imp_neq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_class.neq_le_trans,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TOrderings.order_class.order.irrefl,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V0)))))
(TOrderings.order_class.order_axioms,((cOrderings.class.order @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.order_class.strict_monoD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.strict_mono @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TOrderings.order_class.strict_monoI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2)))))))) @ (cOrderings.order_class.strict_mono @ V0)))))
(TOrderings.order_top_class.less_top,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.top_class.top))) @ ((cOrderings.ord_class.less @ V0) @ cOrderings.top_class.top)))))
(TOrderings.preorder_class.less_asym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((c==> @ (cHOL.Not @ V2)) @ ((cOrderings.ord_class.less @ V1) @ V0))) @ V2)))))))))
(TOrderings.wellorder.not_less_Least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ ((cOrderings.ord.Least @ V0) @ (^[V4]: (V3 @ V4))))) @ (cHOL.Not @ (V3 @ V2)))))))))))))
(TOrderings.wellorder_class.Least_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((cOrderings.ord_class.less_eq @ (cOrderings.ord_class.Least @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(TPartial_Function.flat_lub_in_chain,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cComplete_Partial_Order.chain @ (cPartial_Function.flat_ord @ V0)) @ V1)) @ ((c==> @ ((cHOL.eq @ ((cPartial_Function.flat_lub @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ V0)) @ ((cSet.member @ V2) @ V1)))))))))))
(TPartial_Function.option.const_mono,(call @ (^[V0]: (call @ (^[V1]: (((cComplete_Partial_Order.monotone @ V0) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (^[V2]: V1)))))))
(TPartial_Function.option_admissible,(call @ (^[V0]: (((cComplete_Partial_Order.ccpo.admissible @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ (V1 @ V2)) @ (cOption.option.Some @ V3))) @ ((V0 @ V2) @ V3)))))))))))
(TPartial_Function.tailrec.leq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ V0) @ V1)) @ ((c==> @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ V1) @ V2)) @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ V0) @ V2))))))))))
(TPartial_Function.tailrec.lub_least,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ (cPartial_Function.flat_ord @ cHOL.undefined)) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ V2) @ V1))))) @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ ((cPartial_Function.flat_lub @ cHOL.undefined) @ V0)) @ V1))))))))
(TPartial_Function.tailrec.lub_upper,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ (cPartial_Function.flat_ord @ cHOL.undefined)) @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ V1) @ ((cPartial_Function.flat_lub @ cHOL.undefined) @ V0)))))))))
(TPower.comm_semiring_1.dvd_power_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V5)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V6) @ V7)) @ (((cRings.dvd.dvd @ V0) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V6)) @ ((((cPower.power.power @ V1) @ V0) @ V5) @ V7))))))))))))))))))))))
(TPower.comm_semiring_1.power_le_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)) @ V6)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V7) @ V5)) @ (((cRings.dvd.dvd @ V0) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V7)) @ V6)))))))))))))))))))))
(TPower.linordered_semidom.power_gt1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((V5 @ V3) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ (cNat.Suc @ V7))))))))))))))))))))))
(TPower.monoid_mult.power2_eq_square,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((V1 @ V2) @ V2))))))))))
(TPower.monoid_mult_class.power_Suc2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))) @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V1)) @ V0)))))))
(TPower.monoid_mult_class.power_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))) @ ((cPower.power_class.power @ ((cPower.power_class.power @ V0) @ V1)) @ V2)))))))))
(TPower.semiring_1_class.zero_power2,((cHOL.eq @ ((cPower.power_class.power @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.zero_class.zero))
(TPower.semiring_numeral.numeral_pow,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.pow @ V3) @ V4))) @ ((((cPower.power.power @ V0) @ V1) @ (((cNum.numeral.numeral @ V0) @ V2) @ V3)) @ (cNum.numeral_class.numeral @ V4)))))))))))))))
(TPower.semiring_numeral.numeral_sqr,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ (cNum.sqr @ V3))) @ ((V1 @ (((cNum.numeral.numeral @ V0) @ V2) @ V3)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V3)))))))))))))
(TPredicate.equal_seq_inst.equal_seq,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TPredicate.iterate_upto.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V3) @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ V3))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cPredicate.iterate_upto_rel) @ V1))))))))
(TPredicate.iterate_upto_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.iterate_upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (cPredicate.Seq @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((cPredicate.iterate_upto_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ V2)))))))))))) @ V2)))))))))
(TPredicate.iterate_upto_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate.iterate_upto_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (cPredicate.Seq @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V3 @ V4)) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))))))))) @ (cHOL.All @ (^[V6]: ((cHOL.implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ ((cPredicate.iterate_upto_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))))))))))))))))))))))
(TPredicate.iterate_upto_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.iterate_upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TPredicate.pred.pred_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TPredicate.pred.pred_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (((cPredicate.pred.pred_rec_set @ V0) @ (cPredicate.pred.Pred @ V1)) @ (V0 @ V1)))))))
(TPredicate.pred.pred_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cPredicate.pred.pred_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TPredicate.pred.pred_rep_set.intros,(call @ (^[V0]: (cPredicate.pred.pred_rep_set @ (cDatatype.Leaf @ V0)))))
(TPredicate.pred_of_set_set_fold_sup,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.pred_of_set @ (cList.set @ V0))) @ (((cList.fold @ cLattices.sup_class.sup) @ ((cList.map @ cPredicate.single) @ V0)) @ cOrderings.bot_class.bot)))))
(TPredicate_Compile.contains_pred_eq,((c== @ cPredicate_Compile.contains_pred) @ (^[V0]: (^[V1]: (cPredicate.pred.Pred @ (^[V2]: ((cPredicate_Compile.contains @ V0) @ V1)))))))
(TProduct_Type.bool.bool_rec_set_def,((c== @ cProduct_Type.bool.bool_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cHOL.True)) @ ((cHOL.eq @ V4) @ V0))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cHOL.False)) @ ((cHOL.eq @ V4) @ V1)))))))))))
(TProduct_Type.prod.Abs_prod_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cProduct_Type.prod)) @ ((cHOL.eq @ (cProduct_Type.Rep_prod @ (cProduct_Type.Abs_prod @ V0))) @ V0)))))
(TProduct_Type.prod.Rep_prod_inverse,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.Abs_prod @ (cProduct_Type.Rep_prod @ V0))) @ V0))))
(TProduct_Type.prod.prod_rec_set_def,((c== @ cProduct_Type.prod.prod_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.eq @ V3) @ ((V0 @ V4) @ V5))))))))))))))
(TProduct_Type.unit.Abs_unit_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ ((cSet.insert @ cHOL.True) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cProduct_Type.Rep_unit @ (cProduct_Type.Abs_unit @ V0))) @ V0)))))
(TProduct_Type.unit.Rep_unit_inverse,(call @ (^[V0]: ((cHOL.eq @ (cProduct_Type.Abs_unit @ (cProduct_Type.Rep_unit @ V0))) @ V0))))
(TProduct_Type.unit.unit_rec_set_def,((c== @ cProduct_Type.unit.unit_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ cProduct_Type.Unity)) @ ((cHOL.eq @ V3) @ V0)))))))))
(TQuickcheck_Exhaustive.cps_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.cps_bind @ V0) @ V1)) @ (^[V2]: (V0 @ (^[V3]: ((V1 @ V3) @ V2))))))))))
(TQuickcheck_Exhaustive.cps_plus_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.cps_plus @ V0) @ V1)) @ (^[V2]: (((cOption.option.option_case @ (V1 @ V2)) @ (^[V3]: (cOption.option.Some @ V3))) @ (V0 @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_rec @ V0) @ V1) @ (cQuickcheck_Exhaustive.unknown.Known @ V2))) @ (V1 @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.recs_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_rec @ V0) @ V1) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ V0))))))
(TQuickcheck_Exhaustive.unknown.size_4,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cQuickcheck_Exhaustive.unknown.Known @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Exhaustive.unknown.size_3,((cHOL.eq @ (cNat.size_class.size @ cQuickcheck_Exhaustive.unknown.Unknown)) @ cNat.zero_nat_inst.zero_nat))
(TQuickcheck_Exhaustive.unknown.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.unknown.unknown_size @ V0) @ (cQuickcheck_Exhaustive.unknown.Known @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Exhaustive.unknown.size_1,(call @ (^[V0]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.unknown.unknown_size @ V0) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Narrowing.cfun.Rep_cfun,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Narrowing.Rep_cfun @ V0)) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set)))))
(TQuickcheck_Narrowing.cfun.eq.simps,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Narrowing.cfun.Constant @ V0)) @ (cQuickcheck_Narrowing.cfun.Constant @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.cfun.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V1)))))))
(TQuickcheck_Narrowing.conv_sumC_def,((c== @ cQuickcheck_Narrowing.conv_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Narrowing.conv_graph @ V0) @ V1))))))
(TQuickcheck_Narrowing.eval_cfun_def,((c== @ cQuickcheck_Narrowing.eval_cfun) @ (^[V0]: ((cQuickcheck_Narrowing.cfun.cfun_rec @ (^[V1]: (^[V2]: V1))) @ V0))))
(TQuickcheck_Narrowing.eval_ffun_def,((c== @ cQuickcheck_Narrowing.eval_ffun) @ (^[V0]: (((cQuickcheck_Narrowing.ffun.ffun_rec @ (^[V1]: (^[V2]: V1))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ ((cHOL.eq @ V5) @ V1)) @ V2) @ (V4 @ V5)))))))) @ V0))))
(TQuickcheck_Narrowing.ffun.Rep_ffun,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Narrowing.Rep_ffun @ V0)) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set)))))
(TQuickcheck_Narrowing.ffun.distinct_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.ffun.Constant @ V3))))))))))))
(TQuickcheck_Narrowing.ffun.distinct_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ (((cQuickcheck_Narrowing.ffun.Update @ V1) @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.ffun.eq.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ (cQuickcheck_Narrowing.ffun.Constant @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.ffun.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.ffun.Update @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.ffun.eq.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ (((cQuickcheck_Narrowing.ffun.Update @ V1) @ V2) @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.ffun.eq.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.ffun.Constant @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.ffun.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.ffun.Constant @ V1))))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V0) @ (((cQuickcheck_Narrowing.ffun.Update @ V1) @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.non_empty_def,((c== @ cQuickcheck_Narrowing.non_empty) @ (^[V0]: (cQuickcheck_Narrowing.non_empty_sumC @ V0))))
(TQuickcheck_Narrowing.property.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (cQuickcheck_Narrowing.property.Property @ V3))) @ (V2 @ V3)))))))))))
(TQuickcheck_Narrowing.property.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ ((((V1 @ V3) @ V4) @ V5) @ (^[V6]: ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (V4 @ V6))))))))))))))))))
(TQuickcheck_Narrowing.property.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ ((((V0 @ V3) @ V4) @ V5) @ (^[V6]: ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (V4 @ V6))))))))))))))))))
(TQuickcheck_Random.arity_random_fun,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_int,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_nat,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_num,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_seq,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_set,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_sum,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.random_class_def,((c== @ (cQuickcheck_Random.random_class @ cTYPE)) @ (cTyperep.typerep_class @ cTYPE)))
(TRandom_Sequence.Random.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cRandom_Sequence.Random_rel) @ V1))))))))
(TRandom_Sequence.Random_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.Random_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V4 @ V6)) @ (^[V7]: ((cProduct_Type.scomp @ ((V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ V6)) @ (^[V8]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V7))) @ V8)))))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom_Sequence.Random_graph @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ V2)))))))))) @ V2)))))))))
(TRandom_Sequence.Random_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRandom_Sequence.Random_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (^[V5]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V3 @ V5)) @ (^[V6]: ((cProduct_Type.scomp @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ V5)) @ (^[V7]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V6))) @ V7)))))))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom_Sequence.Random_graph @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))))))
(TRandom_Sequence.Random_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.Random_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.if_random_dseq_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.if_random_dseq @ V0)) @ (((cHOL.If @ V0) @ (cRandom_Sequence.single @ cProduct_Type.Unity)) @ cRandom_Sequence.empty)))))
(TRandom_Sequence.iter_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.iter_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((cRandom_Sequence.iter_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))))))))))))))))))))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((c==> @ ((cHOL.eq @ V8) @ (V4 @ V6))) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V9) @ V10)) @ V8)) @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V11) @ V12)) @ V9)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V13))))))))))))))))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cLazy_Sequence.empty) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: ((cHOL.Let @ (V4 @ V6)) @ (cProduct_Type.prod.prod_case @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (^[V10]: (cOption.option.Some @ ((cProduct_Type.Pair @ V8) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V10)))))))))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRecord.equal_tuple_isomorphism_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TRecord.tuple_isomorphism.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V4) @ V5))) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))) @ ((cHOL.eq @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V2) @ V0)) @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V3) @ V1)))))))))))))
(TRecord.tuple_isomorphism.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TRecord.update_accessor_updator_eqE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V0 @ V3) @ V2)) @ V4)))))))))))))))
(TRelation.insert_relcomp_union_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cRelation.relcomp @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)) @ V0)) @ V2)) @ (((cFinite_Set.fold @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (^[V5]: (((cHOL.If @ ((cHOL.eq @ (cProduct_Type.snd @ V1)) @ V3)) @ ((cSet.insert @ ((cProduct_Type.Pair @ (cProduct_Type.fst @ V1)) @ V4)) @ V5)) @ V5)))))) @ V2) @ V0))))))))))
(TRings.class.comm_semiring_0.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.comm_semiring_0 @ V0) @ V1) @ V2)) @ ((cRings.class.mult_zero @ V2) @ V1)))))))))
(TRings.class.comm_semiring_0.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.comm_semiring_0 @ V0) @ V1) @ V2)) @ ((cRings.class.comm_semiring @ V0) @ V2)))))))))
(TRings.class.comm_semiring_0.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.comm_semiring_0 @ V0) @ V1) @ V2)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))))
(TRings.class.comm_semiring_1.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.zero_neq_one @ V1) @ V3)))))))))))
(TRings.class.comm_semiring_1.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cRings.class.comm_semiring_0 @ V2) @ V3) @ V0)))))))))))
(TRings.class.comm_semiring_1.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)))))))))))
(TRings.class.linordered_idom.axioms_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (((((cRings.class.linordered_comm_semiring_strict @ V6) @ V4) @ V5) @ V3) @ V9)))))))))))))))))))))))
(TRings.class.linordered_idom.axioms_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((((((cRings.class.comm_ring_1 @ V9) @ V7) @ V6) @ V3) @ V1) @ V2)))))))))))))))))))))))
(TRings.class.linordered_idom.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (((((cGroups.class.sgn_if @ V7) @ V8) @ V2) @ V3) @ V5)))))))))))))))))))))))
(TRings.class.linordered_idom.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((((((cGroups.class.ordered_ab_group_add @ V6) @ V3) @ V1) @ V2) @ V4) @ V5)))))))))))))))))))))))
(TRings.class.linordered_idom.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((((cGroups.class.abs_if @ V0) @ V2) @ V3) @ V5)))))))))))))))))))))))
(TRings.class.linordered_ring.axioms_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cRings.class.ring @ V6) @ V3) @ V1) @ V2) @ V7)))))))))))))))))))
(TRings.class.linordered_ring.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cRings.class.linordered_semiring @ V6) @ V4) @ V5) @ V3) @ V7)))))))))))))))))))
(TRings.class.linordered_ring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cGroups.class.linordered_ab_group_add @ V6) @ V3) @ V1) @ V2) @ V4) @ V5)))))))))))))))))))
(TRings.class.linordered_ring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((cGroups.class.abs_if @ V0) @ V2) @ V3) @ V5)))))))))))))))))))
(TRings.class.linordered_semidom_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V4) @ V5) @ V1) @ V2)) @ (((cRings.class.linordered_semidom_axioms @ V1) @ V3) @ V5)))))))))))))))))
(TRings.class.no_zero_divisors.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ V0))) @ (cHOL.Not @ ((cHOL.eq @ ((V1 @ V2) @ V3)) @ V0))))))))) @ ((cRings.class.no_zero_divisors @ V1) @ V0)))))))
(TRings.class.ordered_ring_abs.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ (((((((cRings.class.ordered_ring @ V1) @ V2) @ V5) @ V6) @ V7) @ V3) @ V4)) @ ((c==> @ ((((cRings.class.ordered_ring_abs_axioms @ V0) @ V2) @ V5) @ V7)) @ ((((((((cRings.class.ordered_ring_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))))
(TRings.class.ordered_semiring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V2) @ V3)) @ ((c==> @ ((cRings.class.semiring @ V0) @ V4)) @ ((c==> @ (((cRings.class.ordered_semiring_axioms @ V1) @ V2) @ V4)) @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))))
(TRings.dvd_class.dvd_class.dvd_dict,((c== @ cRings.dvd_class.dvd) @ (cRings.dvd.dvd @ cGroups.times_class.times)))
(TRings.linordered_idom.abs_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ (V0 @ V10)) @ V11)) @ ((cHOL.conj @ ((V5 @ V10) @ V11)) @ ((V5 @ (V2 @ V10)) @ V11)))))))))))))))))))))))))))))
(TRings.linordered_idom.abs_mult_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V4 @ V3) @ V10)) @ ((cHOL.eq @ ((V9 @ (V0 @ V11)) @ V10)) @ (V0 @ ((V9 @ V11) @ V10))))))))))))))))))))))))))))))
(TRings.linordered_idom.mult_sgn_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V9 @ (V8 @ V10)) @ (V0 @ V10))) @ V10)))))))))))))))))))))))))
(TRings.linordered_semidom_class_def,((c== @ (cRings.linordered_semidom_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)) @ (((cRings.class.linordered_semidom_axioms @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cOrderings.ord_class.less)))))
(TRings.no_zero_divisors_class.intro,((c==> @ (cGroups.times_class @ cTYPE)) @ ((c==> @ (cGroups.zero_class @ cTYPE)) @ ((c==> @ ((cRings.class.no_zero_divisors @ cGroups.times_class.times) @ cGroups.zero_class.zero)) @ (cRings.no_zero_divisors_class @ cTYPE)))))
(TRings.no_zero_divisors_class.super_2,((c==> @ (cRings.no_zero_divisors_class @ cTYPE)) @ (cGroups.zero_class @ cTYPE)))
(TRings.no_zero_divisors_class.super_1,((c==> @ (cRings.no_zero_divisors_class @ cTYPE)) @ (cGroups.times_class @ cTYPE)))
(TRings.ordered_ring_abs.abs_eq_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.ordered_ring_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.conj @ ((cHOL.disj @ ((V5 @ V2) @ V8)) @ ((V5 @ V8) @ V2))) @ ((cHOL.disj @ ((V5 @ V2) @ V9)) @ ((V5 @ V9) @ V2)))) @ ((cHOL.eq @ (V0 @ ((V7 @ V8) @ V9))) @ ((V7 @ (V0 @ V8)) @ (V0 @ V9))))))))))))))))))))))))))
(TRings.ordered_ring_abs_class.intro,((c==> @ (cGroups.ordered_ab_group_add_abs_class @ cTYPE)) @ ((c==> @ (cRings.ordered_ring_class @ cTYPE)) @ ((c==> @ ((((cRings.class.ordered_ring_abs_axioms @ cGroups.abs_class.abs) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cGroups.times_class.times)) @ (cRings.ordered_ring_abs_class @ cTYPE)))))
(TRings.ordered_ring_abs_class.super_2,((c==> @ (cRings.ordered_ring_abs_class @ cTYPE)) @ (cRings.ordered_ring_class @ cTYPE)))
(TRings.ordered_ring_abs_class.super_1,((c==> @ (cRings.ordered_ring_abs_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_abs_class @ cTYPE)))
(TRings.ordered_semiring_class.intro,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cRings.semiring_class @ cTYPE)) @ ((c==> @ (((cRings.class.ordered_semiring_axioms @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cGroups.times_class.times)) @ (cRings.ordered_semiring_class @ cTYPE))))))
(TRings.ordered_semiring_class.super_3,((c==> @ (cRings.ordered_semiring_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))
(TRings.ordered_semiring_class.super_2,((c==> @ (cRings.ordered_semiring_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)))
(TRings.ordered_semiring_class.super_1,((c==> @ (cRings.ordered_semiring_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TRings.ring_class.left_diff_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TRings.semiring_class.distrib_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TSMT.pattern.pattern_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TSMT.pattern.pattern_rec_set.intros,(call @ (^[V0]: (((cSMT.pattern.pattern_rec_set @ V0) @ cSMT.pattern.Pattern) @ V0))))
(TSMT.pattern.pattern_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cSMT.pattern.pattern_rep_set @ V0)) @ ((c==> @ (V1 @ cHOL.undefined)) @ (V1 @ V0))))))))
(TSMT.pattern.pattern_rep_set.intros,(cSMT.pattern.pattern_rep_set @ cHOL.undefined))
(TSet_Interval.Inf_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ V0)))))))
(TSet_Interval.atLeastAtMostSuc_conv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ (cNat.Suc @ V1))) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ (cNat.Suc @ V1))) @ ((cSet.insert @ (cNat.Suc @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)))))))))
(TSet_Interval.atLeastAtMost_insertL,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.insert @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cNat.Suc @ V0)) @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.dvd.atLeastAtMost_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.atLeast @ cRings.dvd_class.dvd) @ V0)) @ ((cSet_Interval.ord.atMost @ cRings.dvd_class.dvd) @ V1))))))))
(TSet_Interval.dvd.atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V1) @ V2))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TSet_Interval.ivl_disj_un_singleton_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_singleton_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_singleton_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_singleton_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))))))))
(TSet_Interval.ivl_disj_un_singleton_2,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cSet_Interval.ord_class.lessThan @ V0)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ (cSet_Interval.ord_class.atMost @ V0)))))
(TSet_Interval.ivl_disj_un_singleton_1,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ (cSet_Interval.ord_class.greaterThan @ V0))) @ (cSet_Interval.ord_class.atLeast @ V0)))))
(TSet_Interval.no_bot.not_Icc_eq_Iic,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet_Interval.ord.atMost @ V0) @ V4)))))))))))))))
(TSet_Interval.no_bot.not_Iic_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ V4)))))))))))))))
(TSet_Interval.no_bot.not_Iic_le_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ V4)))))))))))))))
(TSet_Interval.no_bot.not_Iic_le_Ici,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ ((cSet_Interval.ord.atLeast @ V0) @ V3)))))))))))))
(TSet_Interval.no_top.not_Icc_eq_Ici,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet_Interval.ord.atLeast @ V0) @ V4)))))))))))))))
(TSet_Interval.no_top.not_Ici_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ V4)))))))))))))))
(TSet_Interval.no_top.not_Ici_eq_Iic,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ ((cSet_Interval.ord.atMost @ V0) @ V3)))))))))))))
(TSet_Interval.no_top.not_Ici_le_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ V4)))))))))))))))
(TSet_Interval.no_top.not_Ici_le_Iic,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ ((cSet_Interval.ord.atMost @ V0) @ V3)))))))))))))
(TSet_Interval.no_top.not_Iic_eq_Ici,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ ((cSet_Interval.ord.atLeast @ V0) @ V3)))))))))))))
(TSet_Interval.ord.atLeastAtMost_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V1) @ V2)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.atLeast @ V0) @ V1)) @ ((cSet_Interval.ord.atMost @ V0) @ V2))))))))))
(TSet_Interval.ord.atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ V0) @ (((cSet_Interval.ord.atLeastAtMost @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((V1 @ V2) @ V0)) @ ((V1 @ V0) @ V3))))))))))))
(TSet_Interval.ord_class.atLeast_def,(call @ (^[V0]: ((c== @ (cSet_Interval.ord_class.atLeast @ V0)) @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TSet_Interval.ord_class.atLeast_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cSet_Interval.ord_class.atLeast @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet_Interval.setsum_multicount_gen,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V4]: ((cHOL.eq @ (cFinite_Set.card @ (cSet.Collect @ (^[V5]: ((cHOL.conj @ ((cSet.member @ V5) @ V0)) @ ((V2 @ V5) @ V4)))))) @ (V3 @ V4))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (cFinite_Set.card @ (cSet.Collect @ (^[V5]: ((cHOL.conj @ ((cSet.member @ V5) @ V1)) @ ((V2 @ V4) @ V5))))))) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1))))))))))))))
(TSet_Interval.setsum_restrict_set'',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ (cSet.Collect @ (^[V3]: ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ (V2 @ V3)))))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (((cHOL.If @ (V2 @ V3)) @ (V1 @ V3)) @ cGroups.zero_class.zero))) @ V0))))))))))
(TString.enum_char_inst.enum_ex_char,((c== @ cString.enum_char_inst.enum_ex_char) @ cString.enum_char_inst.enum_ex_char))
(TString.nibble.nibble_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: (call @ (^[V18]: ((c==> @ ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble0)) @ ((c==> @ ((cHOL.eq @ V17) @ V0)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble1)) @ ((c==> @ ((cHOL.eq @ V17) @ V1)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble2)) @ ((c==> @ ((cHOL.eq @ V17) @ V2)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble3)) @ ((c==> @ ((cHOL.eq @ V17) @ V3)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble4)) @ ((c==> @ ((cHOL.eq @ V17) @ V4)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble5)) @ ((c==> @ ((cHOL.eq @ V17) @ V5)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble6)) @ ((c==> @ ((cHOL.eq @ V17) @ V6)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble7)) @ ((c==> @ ((cHOL.eq @ V17) @ V7)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble8)) @ ((c==> @ ((cHOL.eq @ V17) @ V8)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.Nibble9)) @ ((c==> @ ((cHOL.eq @ V17) @ V9)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.NibbleA)) @ ((c==> @ ((cHOL.eq @ V17) @ V10)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.NibbleB)) @ ((c==> @ ((cHOL.eq @ V17) @ V11)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.NibbleC)) @ ((c==> @ ((cHOL.eq @ V17) @ V12)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.NibbleD)) @ ((c==> @ ((cHOL.eq @ V17) @ V13)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.NibbleE)) @ ((c==> @ ((cHOL.eq @ V17) @ V14)) @ V18))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V16) @ cString.nibble.NibbleF)) @ ((c==> @ ((cHOL.eq @ V17) @ V15)) @ V18))) @ V18))))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: (call @ (^[V16]: (call @ (^[V17]: ((cHOL.eq @ ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ V16) @ V17)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble0)) @ ((cHOL.eq @ V17) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble1)) @ ((cHOL.eq @ V17) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble2)) @ ((cHOL.eq @ V17) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble3)) @ ((cHOL.eq @ V17) @ V3))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble4)) @ ((cHOL.eq @ V17) @ V4))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble5)) @ ((cHOL.eq @ V17) @ V5))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble6)) @ ((cHOL.eq @ V17) @ V6))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble7)) @ ((cHOL.eq @ V17) @ V7))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble8)) @ ((cHOL.eq @ V17) @ V8))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.Nibble9)) @ ((cHOL.eq @ V17) @ V9))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.NibbleA)) @ ((cHOL.eq @ V17) @ V10))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.NibbleB)) @ ((cHOL.eq @ V17) @ V11))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.NibbleC)) @ ((cHOL.eq @ V17) @ V12))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.NibbleD)) @ ((cHOL.eq @ V17) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.NibbleE)) @ ((cHOL.eq @ V17) @ V14))) @ ((cHOL.conj @ ((cHOL.eq @ V16) @ cString.nibble.NibbleF)) @ ((cHOL.eq @ V17) @ V15)))))))))))))))))))))))))))))))))))))))))))))))))))))))
(TTransfer.transfer_implies_transfer_9,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cTransfer.rev_implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_8,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cTransfer.rev_implies) @ cTransfer.rev_implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_7,((((cTransfer.fun_rel @ cHOL.implies) @ ((cTransfer.fun_rel @ cHOL.eq) @ cTransfer.rev_implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_6,((((cTransfer.fun_rel @ cHOL.implies) @ ((cTransfer.fun_rel @ cTransfer.rev_implies) @ cTransfer.rev_implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_5,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_4,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.implies) @ cHOL.implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_3,((((cTransfer.fun_rel @ cTransfer.rev_implies) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_2,((((cTransfer.fun_rel @ cTransfer.rev_implies) @ ((cTransfer.fun_rel @ cHOL.implies) @ cHOL.implies)) @ cHOL.implies) @ cHOL.implies))
(TTransfer.transfer_implies_transfer_1,((((cTransfer.fun_rel @ cHOL.eq) @ ((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq)) @ cHOL.implies) @ cHOL.implies))
(TTransitive_Closure.r_into_rtranclp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)))))))))
(TTransitive_Closure.r_r_into_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.reflclp_tranclp,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cTransitive_Closure.tranclp @ V0)) @ cHOL.eq)) @ (cTransitive_Closure.rtranclp @ V0)))))
(TTransitive_Closure.relpow_code_def,((cHOL.eq @ cTransitive_Closure.relpow) @ cNat.compow))
(TTransitive_Closure.relpow_fun_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cNat.compow @ V2) @ V3))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ (V4 @ cNat.zero_nat_inst.zero_nat)) @ V0)) @ ((cHOL.conj @ ((cHOL.eq @ (V4 @ V2)) @ V1)) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V5) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ (V4 @ V5)) @ (V4 @ (cNat.Suc @ V5)))) @ V3))))))))))))))))))
(TTransitive_Closure.relpowp_Suc_D2',(call @ (^[V0]: (call @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.conj @ ((((cNat.compow @ V0) @ V1) @ V2) @ V3)) @ ((V1 @ V3) @ V4))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((V1 @ V2) @ V5)) @ ((((cNat.compow @ V0) @ V1) @ V5) @ V4))))))))))))))))
(TTransitive_Closure.relpowp_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRelation.relcompp @ V0) @ ((cNat.compow @ V1) @ V0))) @ ((cRelation.relcompp @ ((cNat.compow @ V1) @ V0)) @ V0)))))))
(TTransitive_Closure.rtrancl.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ (call @ (^[V4]: ((V3 @ V4) @ V4)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V2)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TTransitive_Closure.rtrancl_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cTransitive_Closure.rtrancl @ V4))) @ ((c==> @ ((V5 @ V0) @ V1)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ (cTransitive_Closure.rtrancl @ V4))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V8) @ V9))) @ V4)) @ ((c==> @ ((V5 @ V6) @ V7)) @ ((V5 @ V8) @ V9))))))))))))) @ ((V5 @ V2) @ V3)))))))))))))))))
(TTransitive_Closure.rtranclp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((V3 @ V4) @ V4)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V4) @ V5)) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((V0 @ V5) @ V6)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TTransitive_Closure.rtranclp.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.rtranclp.intros_1,(call @ (^[V0]: (call @ (^[V1]: (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V1))))))
(TTransitive_Closure.rtranclp_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (V3 @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V4)) @ ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ (V3 @ V4)) @ (V3 @ V5))))))))) @ (V3 @ V2)))))))))))))
(TTransitive_Closure.rtranclp_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ (cTransitive_Closure.rtranclp @ V0))) @ ((cHOL.eq @ (cTransitive_Closure.rtranclp @ V1)) @ (cTransitive_Closure.rtranclp @ V0)))))))))
(TTransitive_Closure.trancl_converse,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.trancl @ (cRelation.converse @ V0))) @ (cRelation.converse @ (cTransitive_Closure.trancl @ V0))))))
(TTransitive_Closure.tranclp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V3 @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V4) @ V5)) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((V0 @ V5) @ V6)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TTransitive_Closure.tranclp_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((V0 @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ ((V5 @ V6) @ V7))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ ((c==> @ ((V0 @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V8) @ V9))) @ ((c==> @ ((V5 @ V6) @ V7)) @ ((V5 @ V8) @ V9))))))))))))) @ ((V5 @ V3) @ V4)))))))))))))))))
(TTypedef.type_definition.Abs_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V2)) @ (V3 @ (V1 @ V5)))))) @ (V3 @ V4))))))))))))))
(TTypedef.type_definition.Abs_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V4))) @ ((cHOL.eq @ V3) @ V4))))))))))))))))
(TTypedef.type_definition.Rep_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((c==> @ (call @ (^[V5]: (V4 @ (V0 @ V5))))) @ (V4 @ V3)))))))))))))))
(TTypedef.type_definition.Rep_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V3)) @ (V0 @ V4))) @ ((cHOL.eq @ V3) @ V4))))))))))))))
(TTyperep.typerep.Abs_typerep_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1))) @ (V0 @ (cTyperep.Abs_typerep @ V2)))))) @ (V0 @ V1)))))))
(TTyperep.typerep.Abs_typerep_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1))) @ ((cHOL.eq @ ((cHOL.eq @ (cTyperep.Abs_typerep @ V0)) @ (cTyperep.Abs_typerep @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TTyperep.typerep.Rep_typerep_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cTyperep.Rep_typerep @ V2))))) @ (V1 @ V0))))))))
(TTyperep.typerep.Rep_typerep_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cTyperep.Rep_typerep @ V0)) @ (cTyperep.Rep_typerep @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TTyperep.typerep.arity_size_typerep,(cNat.size_class @ cTYPE))
(TBig_Operators.comm_monoid_set.Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V5]: (cFinite_Set.finite @ (V3 @ V5))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V5]: ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (V4 @ V5)) @ (V3 @ V5)))) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (cProduct_Type.prod.prod_case @ V4)) @ ((cProduct_Type.Sigma @ V2) @ (^[V5]: (V3 @ V5)))))))))))))))))))
(TBig_Operators.comm_monoid_set.delta,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V5]: (((cHOL.If @ ((cHOL.eq @ V5) @ V3)) @ (V4 @ V5)) @ V1))) @ V2)) @ (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ (V4 @ V3)) @ V1)))))))))))))))
(TBig_Operators.comm_monoid_set.empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V2) @ cOrderings.bot_class.bot)) @ V1)))))))))
(TBig_Operators.comm_monoid_set.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.comm_monoid @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)))))))
(TBig_Operators.linorder.Max_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V1 @ ((cBig_Operators.linorder.Max @ V0) @ V2)) @ V3)) @ ((cSet.Ball @ V2) @ (^[V4]: ((V1 @ V4) @ V3))))))))))))))))
(TBig_Operators.linorder.Min_antimono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((V0 @ ((cBig_Operators.linorder.Min @ V0) @ V3)) @ ((cBig_Operators.linorder.Min @ V0) @ V2)))))))))))))))
(TBig_Operators.linorder.Min_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V1 @ ((cBig_Operators.linorder.Min @ V0) @ V2)) @ V3)) @ ((cSet.Bex @ V2) @ (^[V4]: ((V1 @ V4) @ V3))))))))))))))))
(TBig_Operators.linorder_class.Max_Un,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cOrderings.ord_class.max @ (cBig_Operators.linorder_class.Max @ V0)) @ (cBig_Operators.linorder_class.Max @ V1))))))))))))
(TBig_Operators.linorder_class.Max_ge,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.linorder_class.Max @ V0)))))))))
(TBig_Operators.linorder_class.Max_in,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cSet.member @ (cBig_Operators.linorder_class.Max @ V0)) @ V0))))))
(TBig_Operators.linorder_class.Min_Un,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cOrderings.ord_class.min @ (cBig_Operators.linorder_class.Min @ V0)) @ (cBig_Operators.linorder_class.Min @ V1))))))))))))
(TBig_Operators.linorder_class.Min_in,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cSet.member @ (cBig_Operators.linorder_class.Min @ V0)) @ V0))))))
(TBig_Operators.linorder_class.Min_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Min @ V0)) @ V1))))))))
(TBig_Operators.linorder_class.max_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ V1) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.max_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TBig_Operators.linorder_class.max_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ V1) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V1) @ V0)))))))
(TBig_Operators.linorder_class.min_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TBig_Operators.semilattice_set.intro,(call @ (^[V0]: ((c==> @ (cLattices.semilattice @ V0)) @ (cBig_Operators.semilattice_set @ V0)))))
(TBig_Operators.semilattice_set.union,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((V0 @ ((cBig_Operators.semilattice_set.F @ V0) @ V1)) @ ((cBig_Operators.semilattice_set.F @ V0) @ V2)))))))))))))))
(TBig_Operators.setprod_mono_one_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))))
(TBig_Operators.setsum_divide_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cFields.inverse_class.divide @ (V0 @ V3)) @ V2))) @ V1)))))))))
(TBig_Operators.setsum_mono_zero_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TCode_Evaluation.term.Abs_term_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cCode_Evaluation.Abs_term @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set))) @ V1))))) @ V1))))))
(TCode_Evaluation.term.Rep_term_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cCode_Evaluation.Rep_term @ V2))) @ V1)))) @ V1)))))))
(TCode_Evaluation.term.dummy_term_def,((c== @ cCode_Evaluation.term.dummy_term) @ (cCode_Evaluation.Abs_term @ cHOL.undefined)))
(TCode_Evaluation.term.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cCode_Evaluation.term.term_case @ V2) @ V0)) @ ((cCode_Evaluation.term.term_case @ V2) @ V1))))))))))
(TCode_Evaluation.term_of_class.intro,((c==> @ (cTyperep.typerep_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TCode_Evaluation.term_of_class.super,((c==> @ (cCode_Evaluation.term_of_class @ cTYPE)) @ (cTyperep.typerep_class @ cTYPE)))
(TCode_Evaluation.term_of_itself_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_literal_def,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_literal_inst.term_of_literal @ V0)) @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ cList.list.Nil))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))) @ (cCode_Evaluation.term_of_class.term_of @ (cString.explode @ V0)))))))
(TCode_Evaluation.term_of_nibble_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_nibble_inst.term_of_nibble @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_option_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Numeral.arity_ring_div_integer,(cDivides.ring_div_class @ cTYPE))
(TCode_Numeral.equal_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cHOL.eq)) @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TCode_Numeral.equal_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cHOL.eq)) @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TCode_Numeral.int_of_integer_numeral,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TCode_Numeral.integer.int_of_integer,(call @ (^[V0]: ((cSet.member @ (cCode_Numeral.int_of_integer @ V0)) @ cOrderings.top_class.top))))
(TCode_Numeral.integer_of_natural.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cNat.semiring_1_class.of_nat) @ cNat.semiring_1_class.of_nat))
(TCode_Numeral.integer_of_natural_def,((c== @ cCode_Numeral.integer_of_natural) @ (((cFun.map_fun @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.integer_of_int) @ cNat.semiring_1_class.of_nat)))
(TCode_Numeral.less_eq_integer.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)))))))
(TCode_Numeral.less_eq_integer.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ V0) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))))))))
(TCode_Numeral.less_eq_natural.abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TCode_Numeral.less_eq_natural.rep_eq,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))))))))
(TCode_Numeral.minus_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer)) @ cInt.minus_int_inst.minus_int) @ cCode_Numeral.minus_integer_inst.minus_integer))
(TCode_Numeral.minus_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cCode_Numeral.pcr_natural)) @ cNat.minus_nat_inst.minus_nat) @ cCode_Numeral.minus_natural_inst.minus_natural))
(TCode_Numeral.nat_of_natural_numeral,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TCode_Numeral.natural.nat_of_natural,(call @ (^[V0]: ((cSet.member @ (cCode_Numeral.nat_of_natural @ V0)) @ cOrderings.top_class.top))))
(TCode_Numeral.natural.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cCode_Numeral.natural.natural_case @ V2) @ V3) @ V0)) @ (((cCode_Numeral.natural.natural_case @ V2) @ V3) @ V1))))))))))))
(TCode_Numeral.natural_of_integer.rsp,((((cTransfer.fun_rel @ cHOL.eq) @ cHOL.eq) @ cInt.nat) @ cInt.nat))
(TCode_Numeral.natural_of_integer_def,((c== @ cCode_Numeral.natural_of_integer) @ (((cFun.map_fun @ cCode_Numeral.int_of_integer) @ cCode_Numeral.natural_of_nat) @ cInt.nat)))
(TCode_Numeral.natural_zero_minus_one,((cHOL.eq @ ((cCode_Numeral.minus_natural_inst.minus_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ cCode_Numeral.one_natural_inst.one_natural)) @ cCode_Numeral.zero_natural_inst.zero_natural))
(TCode_Numeral.times_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer)) @ cInt.times_int_inst.times_int) @ cCode_Numeral.times_integer_inst.times_integer))
(TCode_Numeral.times_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cCode_Numeral.pcr_natural)) @ cNat.times_nat_inst.times_nat) @ cCode_Numeral.times_natural_inst.times_natural))
(TComplete_Lattices.True_in_image_Bex,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ cHOL.True) @ ((cSet.image @ V0) @ V1))) @ ((cSet.Bex @ V1) @ V0)))))))
(TComplete_Lattices.UN_ball_bex_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Bex @ V0) @ (^[V3]: ((cSet.Bex @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))))))))))
(TComplete_Lattices.UN_ball_bex_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Bex @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cSet.Bex @ V0) @ (^[V2]: ((cSet.Bex @ V2) @ (^[V3]: (V1 @ V3)))))))))))
(TComplete_Lattices.UN_ball_bex_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ (V1 @ V3)) @ (^[V4]: (V2 @ V4)))))))))))))
(TComplete_Lattices.UN_ball_bex_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.Ball @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (^[V2]: (V1 @ V2)))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V2) @ (^[V3]: (V1 @ V3)))))))))))
(TComplete_Lattices.UN_insert_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: ((cSet.insert @ V2) @ (V3 @ V4))))) @ ((cSet.insert @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Partial_Order.monotone_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cComplete_Partial_Order.monotone @ V0) @ V1) @ V2)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((V1 @ (V2 @ V3)) @ (V2 @ V4)))))))))))))))
(TDivides.Suc_div_eq_add3_div_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ V0)))) @ (cNum.numeral_class.numeral @ V1))) @ ((cDivides.div_nat_inst.div_nat @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TDivides.Suc_mod_eq_add3_mod_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ (cNat.Suc @ (cNat.Suc @ (cNat.Suc @ V0)))) @ (cNum.numeral_class.numeral @ V1))) @ ((cDivides.div_nat_inst.mod_nat @ ((cNat.plus_nat_inst.plus_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TDivides.ring_div_class.mod_minus_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cDivides.div_class.mod @ (cGroups.uminus_class.uminus @ ((cDivides.div_class.mod @ V0) @ V1))) @ V1)))))))
(TDivides.semiring_div.div_mult_mult1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V0 @ V6) @ V7)) @ ((V0 @ V6) @ V8))) @ ((V1 @ V7) @ V8)))))))))))))))))))))))
(TDivides.semiring_div.div_mult_mult2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V0 @ V7) @ V6)) @ ((V0 @ V8) @ V6))) @ ((V1 @ V7) @ V8)))))))))))))))))))))))
(TDivides.semiring_div.div_mult_self1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V3 @ V7) @ ((V0 @ V8) @ V6))) @ V6)) @ ((V3 @ V8) @ ((V1 @ V7) @ V6))))))))))))))))))))))))
(TDivides.semiring_div.div_mult_self2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V3 @ V7) @ ((V0 @ V6) @ V8))) @ V6)) @ ((V3 @ V8) @ ((V1 @ V7) @ V6))))))))))))))))))))))))
(TDivides.semiring_div.mod_div_decomp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((cHOL.eq @ V9) @ ((V1 @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ V10) @ ((V2 @ V6) @ V7))) @ ((c==> @ ((cHOL.eq @ V6) @ ((V3 @ ((V0 @ V9) @ V7)) @ V10))) @ V8)))))))) @ V8)))))))))))))))))))))
(TDivides.semiring_div.mod_mod_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V8) @ V7)) @ V6)) @ ((V2 @ V8) @ V6)))))))))))))))))))))))
(TDivides.semiring_div.mod_mult_mult1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ ((V0 @ V6) @ V8))) @ ((V0 @ V6) @ ((V2 @ V7) @ V8)))))))))))))))))))))))
(TDivides.semiring_div.mod_mult_mult2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ ((V0 @ V8) @ V7))) @ ((V0 @ ((V2 @ V6) @ V8)) @ V7))))))))))))))))))))))
(TDivides.semiring_div.mod_mult_self1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ ((V0 @ V7) @ V8))) @ V8)) @ ((V2 @ V6) @ V8))))))))))))))))))))))
(TDivides.semiring_div.mod_mult_self2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ ((V0 @ V7) @ V8))) @ V7)) @ ((V2 @ V6) @ V7))))))))))))))))))))))
(TDivides.semiring_div.mult_mod_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V0 @ V6) @ ((V2 @ V7) @ V8))) @ ((V2 @ ((V0 @ V6) @ V7)) @ ((V0 @ V6) @ V8)))))))))))))))))))))))
(TDivides.semiring_div_class.div_by_0,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.div @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TDivides.semiring_div_class.div_by_1,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.div @ V0) @ cGroups.one_class.one)) @ V0))))
(TDivides.semiring_div_class.div_self,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ V0) @ V0)) @ cGroups.one_class.one)))))
(TDivides.semiring_div_class.mod_by_0,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TDivides.semiring_div_class.mod_by_1,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ cGroups.one_class.one)) @ cGroups.zero_class.zero))))
(TDivides.semiring_div_class.mod_self,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ V0)) @ cGroups.zero_class.zero))))
(TDivides.semiring_numeral_div.parity,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.disj @ ((cHOL.eq @ ((V2 @ V9) @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One)))) @ V4)) @ ((cHOL.eq @ ((V2 @ V9) @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One)))) @ V5))))))))))))))))))))))))
(TEquiv_Relations.UN_equiv_class_type,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cEquiv_Relations.congruent @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V0)) @ ((cSet.member @ (V2 @ V5)) @ V4))))) @ ((cSet.member @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V3) @ (^[V5]: (V2 @ V5)))) @ V4))))))))))))))))
(TEquiv_Relations.congruent2_commuteI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cHOL.eq @ ((V2 @ V3) @ V4)) @ ((V2 @ V4) @ V3))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1)) @ ((cHOL.eq @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))) @ (((cEquiv_Relations.congruent2 @ V1) @ V1) @ V2)))))))))))
(TEquiv_Relations.eq_equiv_class_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cEquiv_Relations.quotient @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)) @ V1)) @ ((cEquiv_Relations.quotient @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)) @ V1))) @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))))))))))))
(TEquiv_Relations.part_equivp_typedef,(call @ (^[V0]: ((c==> @ (cEquiv_Relations.part_equivp @ V0)) @ (cHOL.Ex @ (^[V1]: ((cSet.member @ V1) @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((V0 @ V3) @ V3)) @ ((cHOL.eq @ V2) @ (cSet.Collect @ (V0 @ V3)))))))))))))))
(TEquiv_Relations.refl_on_comp_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRelation.refl_on @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cRelation.relcomp @ (cRelation.converse @ V1)) @ V1))))))))
(TExtraction.sumbool.sumbool_case_def,((c== @ cExtraction.sumbool.sumbool_case) @ (^[V0]: (^[V1]: ((cExtraction.sumbool.sumbool_rec @ V0) @ V1)))))
(TExtraction.sumbool.sumbool_size_def,((c== @ cExtraction.sumbool.sumbool_size) @ ((cExtraction.sumbool.sumbool_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TFields.class.field_inverse_zero_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cFields.class.field_inverse_zero_axioms @ V0) @ V5))))))))))))))))))))
(TFields.class.linordered_field.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((((((((((cRings.class.linordered_idom @ V8) @ V6) @ V7) @ V5) @ V9) @ V10) @ V4) @ V3) @ V11) @ V2)) @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11))))))))))))))))))))))))))))
(TFields.classrel_field_division_ring,(cFields.division_ring_class @ cTYPE))
(TFields.division_ring.divide_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ ((V3 @ V8) @ (V0 @ V9)))))))))))))))))))))))))
(TFields.division_ring.inverse_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ ((V3 @ V8) @ V9)) @ V2)) @ ((cHOL.eq @ (V0 @ V8)) @ V9))))))))))))))))))))))))
(TFields.division_ring_class.divide_1,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ cGroups.one_class.one)) @ V0))))
(TFields.field_inverse_zero_class_def,((c== @ (cFields.field_inverse_zero_class @ cTYPE)) @ ((cPure.conjunction @ (cFields.field_class @ cTYPE)) @ ((cFields.class.field_inverse_zero_axioms @ cFields.inverse_class.inverse) @ cGroups.zero_class.zero))))
(TFields.linordered_field.gt_half_sum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((V10 @ ((V1 @ ((V4 @ V12) @ V13)) @ ((V4 @ V3) @ V3))) @ V13))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.intro,((c==> @ (cFields.field_class @ cTYPE)) @ ((c==> @ (cRings.linordered_idom_class @ cTYPE)) @ (cFields.linordered_field_class @ cTYPE))))
(TFields.linordered_field_class.super_2,((c==> @ (cFields.linordered_field_class @ cTYPE)) @ (cRings.linordered_idom_class @ cTYPE)))
(TFields.linordered_field_class.super_1,((c==> @ (cFields.linordered_field_class @ cTYPE)) @ (cFields.field_class @ cTYPE)))
(TFinite_Set.card_eq_UNIV_imp_eq_UNIV,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ cOrderings.top_class.top)) @ ((c==> @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ cOrderings.top_class.top))) @ ((cHOL.eq @ V0) @ cOrderings.top_class.top))))))
(TFinite_Set.comp_fun_idem_axioms_def,(call @ (^[V0]: ((c== @ (cFinite_Set.comp_fun_idem_axioms @ V0)) @ (cHOL.All @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V1))) @ (V0 @ V1))))))))
(TFinite_Set.finite_cartesian_product,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1))))))))))
(TFinite_Set.finite_class.finite_UNIV,(cFinite_Set.finite @ cOrderings.top_class.top))
(TFinite_Set.finite_class.finite_code,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ cHOL.True))))
(TFinite_Set.folding.comp_fun_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.folding @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V2))) @ ((cFun.comp @ (V0 @ V2)) @ (V0 @ V1)))))))))))
(TFinite_Set.folding_idem.insert_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.folding_idem @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (((cFinite_Set.folding.F @ V0) @ V2) @ ((cSet.insert @ V3) @ V1))) @ ((V0 @ V3) @ (((cFinite_Set.folding.F @ V0) @ V2) @ V1))))))))))))))
(TFinite_Set.nat_seg_image_imp_finite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cSet.image @ V1) @ (cSet.Collect @ (^[V3]: ((cNat.ord_nat_inst.less_nat @ V3) @ V2)))))) @ (cFinite_Set.finite @ V0)))))))))
(TFun.linorder.strict_mono_imp_inj_on,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.strict_mono @ V1) @ V2)) @ ((cFun.inj_on @ V2) @ V3))))))))))))
(TFun.ordered_ab_group_add.inj_uminus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cFun.inj_on @ V3) @ V6)))))))))))))))))
(TGroups.ab_semigroup_add.add_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.ab_semigroup_add_class.intro,((c==> @ (cGroups.semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.class.ab_semigroup_add_axioms @ cGroups.plus_class.plus)) @ (cGroups.ab_semigroup_add_class @ cTYPE))))
(TGroups.ab_semigroup_add_class.super,((c==> @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ (cGroups.semigroup_add_class @ cTYPE)))
(TGroups.class.ab_semigroup_add.intro,(call @ (^[V0]: ((c==> @ (cGroups.class.semigroup_add @ V0)) @ ((c==> @ (cGroups.class.ab_semigroup_add_axioms @ V0)) @ (cGroups.class.ab_semigroup_add @ V0))))))
(TGroups.class.comm_monoid_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cGroups.class.comm_monoid_add_axioms @ V0) @ V1)))))))
(TGroups.class.comm_monoid_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ (cGroups.class.ab_semigroup_add @ V0)))))))
(TGroups.class.comm_monoid_diff.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (((cGroups.class.comm_monoid_diff_axioms @ V0) @ V1) @ V2)) @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2))))))))))
(TGroups.class.comm_monoid_mult.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((c==> @ ((cGroups.class.comm_monoid_mult_axioms @ V0) @ V1)) @ ((cGroups.class.comm_monoid_mult @ V0) @ V1))))))))
(TGroups.class.group_add_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((cHOL.eq @ ((V0 @ (V1 @ V4)) @ V4)) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((V3 @ V4) @ V5)) @ ((V0 @ V4) @ (V1 @ V5)))))))) @ ((((cGroups.class.group_add_axioms @ V3) @ V0) @ V2) @ V1))))))))))))
(TGroups.class.monoid_mult_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.monoid_mult_axioms @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V1 @ V0) @ V2)) @ V2)))) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V1 @ V2) @ V0)) @ V2))))))))))
(TGroups.comm_monoid_add_class.axioms,((cGroups.class.comm_monoid_add_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.comm_monoid_diff.diff_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ V3) @ V3)) @ V1)))))))))))
(TGroups.comm_monoid_diff_class.intro,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.minus_class @ cTYPE)) @ ((c==> @ (((cGroups.class.comm_monoid_diff_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus)) @ (cGroups.comm_monoid_diff_class @ cTYPE)))))
(TGroups.comm_monoid_diff_class.super_2,((c==> @ (cGroups.comm_monoid_diff_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TGroups.comm_monoid_diff_class.super_1,((c==> @ (cGroups.comm_monoid_diff_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TGroups.comm_monoid_mult_class.intro,((c==> @ (cGroups.ab_semigroup_mult_class @ cTYPE)) @ ((c==> @ (cGroups.one_class @ cTYPE)) @ ((c==> @ ((cGroups.class.comm_monoid_mult_axioms @ cGroups.times_class.times) @ cGroups.one_class.one)) @ (cGroups.comm_monoid_mult_class @ cTYPE)))))
(TGroups.comm_monoid_mult_class.super_2,((c==> @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ (cGroups.one_class @ cTYPE)))
(TGroups.comm_monoid_mult_class.super_1,((c==> @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ (cGroups.ab_semigroup_mult_class @ cTYPE)))
(TGroups.group_add.equation_minus_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V4) @ (V3 @ V5))) @ ((cHOL.eq @ V5) @ (V3 @ V4)))))))))))))))))
(TGroups.group_add.minus_equation_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ (V3 @ V4)) @ V5)) @ ((cHOL.eq @ (V3 @ V5)) @ V4))))))))))))))))
(TGroups.group_add_class.add_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ (cGroups.uminus_class.uminus @ V0))))))))
(TGroups.group_add_class.diff_0_right,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TGroups.group_add_class.minus_unique,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ V1)))))))
(TGroups.monoid_add_class.add_0_right,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(THilbert_Choice.Cantor_Bernstein_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V4) @ V0)) @ ((cHOL.conj @ ((cSet.Ball @ V4) @ (^[V6]: (cHOL.Not @ ((cSet.member @ V6) @ ((cSet.image @ V1) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.image @ V3) @ V4)))))))) @ ((cHOL.conj @ ((cSet.Ball @ V4) @ (^[V6]: ((cHOL.eq @ (V5 @ V6)) @ (V3 @ V6))))) @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V4)) @ (^[V6]: ((cHOL.conj @ ((cSet.member @ (V5 @ V6)) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.image @ V3) @ V4)))) @ ((cHOL.eq @ V6) @ (V1 @ (V5 @ V6))))))))))))))))))))))
(THilbert_Choice.bij_image_Collect_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.image @ V0) @ (cSet.Collect @ V1))) @ (cSet.Collect @ (^[V2]: (V1 @ (((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0) @ V2)))))))))))
(THilbert_Choice.inv_into_inv_into_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cFun.bij_betw @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cHOL.eq @ (((cHilbert_Choice.inv_into @ V2) @ ((cHilbert_Choice.inv_into @ V1) @ V0)) @ V3)) @ (V0 @ V3)))))))))))))
(TInt.linordered_idom.of_int_0_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ V3) @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V10))) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V10))))))))))))))))))))))))))
(TInt.linordered_idom.of_int_le_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V10)) @ V3)) @ ((cInt.ord_int_inst.less_eq_int @ V10) @ cInt.zero_int_inst.zero_int))))))))))))))))))))))))))
(TInt.linordered_idom.of_int_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V10)) @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V11))) @ ((cInt.ord_int_inst.less_int @ V10) @ V11))))))))))))))))))))))))))))
(TInt.ring_1_class.of_int_neg_numeral,(call @ (^[V0]: ((cHOL.eq @ (cInt.ring_1_class.of_int @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TInt.ring_char_0_class.of_int_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TLattices.arity_boolean_algebra_bool,(cLattices.boolean_algebra_class @ cTYPE))
(TLattices.boolean_algebra.compl_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V3 @ V8) @ V9)) @ ((V3 @ (V1 @ V9)) @ (V1 @ V8)))))))))))))))))))))))))
(TLattices.lattice_class.distrib_imp1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V3) @ ((cLattices.sup_class.sup @ V4) @ V5))) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V3) @ V4)) @ ((cLattices.inf_class.inf @ V3) @ V5)))))))))) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V2)))))))))))
(TLattices.lattice_class.distrib_imp2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V3) @ ((cLattices.inf_class.inf @ V4) @ V5))) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V3) @ V4)) @ ((cLattices.sup_class.sup @ V3) @ V5)))))))))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V2)))))))))))
(TLattices.lattice_class.dual_lattice,((((cLattices.class.lattice @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf))
(TLattices.linorder_class.max.absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V1) @ V0)) @ V1)))))))
(TLattices.linorder_class.max.absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V1)))))))
(TLattices.linorder_class.max.commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TLattices.linorder_class.min.absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V0)))))))
(TLattices.linorder_class.min.absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V1) @ V0)) @ V0)))))))
(TLattices.linorder_class.min.commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V1) @ V0)))))))
(TLattices.minus_bool_inst.minus_bool,((c== @ cLattices.minus_bool_inst.minus_bool) @ cLattices.minus_bool_inst.minus_bool))
(TLattices.semilattice_inf.inf_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((V1 @ ((V3 @ V6) @ V7)) @ V6)))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((V1 @ ((V3 @ V6) @ V7)) @ V7)))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((V1 @ V6) @ V7)) @ ((c==> @ ((V1 @ V6) @ V8)) @ ((V1 @ V6) @ ((V3 @ V7) @ V8))))))))))) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))))))))))))))
(TLattices.semilattice_inf.le_iff_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ V3))))))))))))))
(TLattices.semilattice_inf.le_inf_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ V3) @ ((V0 @ V4) @ V5))) @ ((cHOL.conj @ ((V1 @ V3) @ V4)) @ ((V1 @ V3) @ V5)))))))))))))))))
(TLattices.semilattice_inf.less_infI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ ((V0 @ V3) @ V5)) @ V4))))))))))))))))
(TLattices.semilattice_inf.less_infI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ ((V0 @ V5) @ V3)) @ V4))))))))))))))))
(TLattices.semilattice_order.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ ((V0 @ V4) @ V5))) @ ((c==> @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V3) @ V5)) @ V6))) @ V6))))))))))))))))))
(TLattices.semilattice_order.boundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V3) @ V5)) @ ((V1 @ V3) @ ((V0 @ V4) @ V5))))))))))))))))))
(TLattices.semilattice_sup.le_iff_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ V4))))))))))))))
(TLattices.semilattice_sup.le_sup_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ ((V0 @ V3) @ V4)) @ V5)) @ ((cHOL.conj @ ((V1 @ V3) @ V5)) @ ((V1 @ V4) @ V5)))))))))))))))))
(TLattices.semilattice_sup.less_supI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))
(TLattices.semilattice_sup.less_supI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ V3) @ ((V0 @ V5) @ V4)))))))))))))))))
(TLattices.semilattice_sup.sup_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((V1 @ V6) @ ((V3 @ V6) @ V7))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((V1 @ V7) @ ((V3 @ V6) @ V7))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((V1 @ V7) @ V6)) @ ((c==> @ ((V1 @ V8) @ V6)) @ ((V1 @ ((V3 @ V7) @ V8)) @ V6)))))))))) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))))))))))))))
(TLattices.uminus_fun_inst.uminus_fun,((c== @ cLattices.uminus_fun_inst.uminus_fun) @ cLattices.uminus_fun_inst.uminus_fun))
(TLazy_Sequence.arity_small_lazy_list,(cLazy_Sequence.small_lazy_class @ cTYPE))
(TLazy_Sequence.arity_small_lazy_prod,(cLazy_Sequence.small_lazy_class @ cTYPE))
(TLazy_Sequence.arity_small_lazy_unit,(cLazy_Sequence.small_lazy_class @ cTYPE))
(TLazy_Sequence.iterate_upto_sumC_def,((c== @ cLazy_Sequence.iterate_upto_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cLazy_Sequence.iterate_upto_graph @ V0) @ V1))))))
(TLazy_Sequence.lazy_sequence.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TLazy_Sequence.lazy_sequence.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V2))) @ V1)))) @ V1))))))
(TLazy_Sequence.lazy_sequence.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V2))))) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence_size_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_size @ V0) @ V1)) @ (cNat.Suc @ ((cList.list.list_size @ V0) @ (cLazy_Sequence.list_of_lazy_sequence @ V1)))))))))
(TLazy_Sequence.list_of_Lazy_Sequence,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ (cLazy_Sequence.Lazy_Sequence @ V0))) @ (((cOption.option.option_case @ cList.list.Nil) @ (^[V1]: ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cList.list.Cons @ V2) @ (cLazy_Sequence.list_of_lazy_sequence @ V3))))) @ V1))) @ (V0 @ cProduct_Type.Unity))))))
(TLazy_Sequence.size_lazy_sequence_eq,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ V0)) @ cNat.zero_nat_inst.zero_nat))))
(TLazy_Sequence.small_lazy'_graph_def,((c== @ cLazy_Sequence.small_lazy'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))))))))))))))))
(TLazy_Sequence.small_lazy'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))) @ V2)))))))) @ V2)))))))))
(TLazy_Sequence.small_lazy'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.small_lazy'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V2) @ V3))))))))))))))
(TLazy_Sequence.small_lazy_list.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V2)) @ V1)))) @ V1))))))
(TLazy_Sequence.small_lazy_list.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cLazy_Sequence.small_lazy_class.small_lazy @ V0)) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))) @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (cLazy_Sequence.single @ ((cList.list.Cons @ V4) @ V5))))))) @ cLazy_Sequence.empty)))) @ V2))))) @ V2)))))))))
(TLazy_Sequence.small_lazy_list.simps,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.small_lazy_class.small_lazy @ V0)) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (cLazy_Sequence.single @ ((cList.list.Cons @ V1) @ V2))))))) @ cLazy_Sequence.empty))))))
(TLifting.Quotient_rep_abs_fold_unmap,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c== @ V4) @ (V1 @ V5))) @ ((c==> @ ((V0 @ V5) @ V5)) @ ((c==> @ ((c== @ (V2 @ V4)) @ (V6 @ V4))) @ ((V0 @ (V6 @ V4)) @ V5))))))))))))))))))))
(TLifting.open_typedef_to_part_equivp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ (cSet.Collect @ (^[V3]: (V2 @ V3))))) @ (cEquiv_Relations.part_equivp @ (cLifting.invariant @ V2))))))))))
(TLifting_Option.bi_unique_option_rel,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ (cTransfer.bi_unique @ (cLifting_Option.option_rel @ V0))))))
(TLifting_Option.option_bind_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ (cLifting_Option.option_rel @ V0)) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ (cLifting_Option.option_rel @ V1))) @ (cLifting_Option.option_rel @ V1))) @ cOption.bind) @ cOption.bind))))))
(TLifting_Option.option_case_transfer,(call @ (^[V0]: (call @ (^[V1]: ((((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V1) @ V0)) @ ((cTransfer.fun_rel @ (cLifting_Option.option_rel @ V1)) @ V0))) @ cOption.option.option_case) @ cOption.option.option_case))))))
(TLifting_Product.left_total_prod_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_total @ V0)) @ ((c==> @ (cLifting.left_total @ V1)) @ (cLifting.left_total @ ((cLifting_Product.prod_rel @ V0) @ V1)))))))))
(TLifting_Set.bi_unique_set_rel_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (((cLifting_Set.set_rel @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V2) @ ((cSet.image @ V4) @ V1))) @ ((c==> @ ((cFun.inj_on @ V4) @ V1)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V5]: ((V0 @ V5) @ (V4 @ V5))))) @ V3)))))) @ V3))))))))))))
(TList.ab_group_add.listsum_subtractf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ (^[V7]: ((V2 @ (V4 @ V7)) @ (V5 @ V7)))) @ V6))) @ ((V2 @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V4) @ V6))) @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V5) @ V6))))))))))))))))))))
(TList.linorder.insort_insert_key_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((((cList.linorder.insort_insert_key @ V0) @ V2) @ V3) @ V4)) @ (((cHOL.If @ ((cSet.member @ (V2 @ V3)) @ ((cSet.image @ V2) @ (cList.set @ V4)))) @ V4) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4)))))))))))))))
(TList.linorder_class.Max.set_eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ (cList.set @ ((cList.list.Cons @ V0) @ V1)))) @ (((cList.fold @ cOrderings.ord_class.max) @ V1) @ V0)))))))
(TList.linorder_class.Min.set_eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ (cList.set @ ((cList.list.Cons @ V0) @ V1)))) @ (((cList.fold @ cOrderings.ord_class.min) @ V1) @ V0)))))))
(TList.linorder_class.distinct_insort,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.distinct @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2))) @ ((cHOL.conj @ (cHOL.Not @ ((cSet.member @ V1) @ (cList.set @ V2)))) @ (cList.distinct @ V2))))))))))
(TList.linorder_class.sorted_map_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cList.linorder_class.sorted @ ((cList.map @ V0) @ ((cList.filter @ (^[V3]: ((cHOL.eq @ (V0 @ V3)) @ (V1 @ V2)))) @ V2))))))))))
(TList.linorder_class.sorted_nth_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cList.nth @ V0) @ V1)) @ ((cList.nth @ V0) @ V2))))))))))))
(TList.linorder_class.sorted_sort_key,(call @ (^[V0]: (call @ (^[V1]: (cList.linorder_class.sorted @ ((cList.map @ V0) @ ((cList.linorder_class.sort_key @ V0) @ V1))))))))
(TList.monoid_add_class.length_concat,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.concat @ V0))) @ (cList.monoid_add_class.listsum @ ((cList.map @ cNat.size_class.size) @ V0))))))
(TList.monoid_add_class.listsum_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.list.Cons @ V0) @ V1))) @ ((cGroups.plus_class.plus @ V0) @ (cList.monoid_add_class.listsum @ V1))))))))
(TList.monoid_add_class.listsum_simps_1,((cHOL.eq @ (cList.monoid_add_class.listsum @ cList.list.Nil)) @ cGroups.zero_class.zero))
(TNat.dvd.dual_order.order_iff_strict,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.dvd.dual_order.strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0)))))))))
(TNat.dvd.order.strict_implies_not_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))))
(TNat.semiring_1_class.of_nat_aux_def,((c== @ cNat.semiring_1_class.of_nat_aux) @ (^[V0]: (^[V1]: ((((cNat.nat.nat_rec @ (^[V2]: (^[V3]: V3))) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((V3 @ V4) @ (V4 @ V5))))))) @ V1) @ V0)))))
(TNat.semiring_1_class.of_nat_in_Nats,(call @ (^[V0]: ((cSet.member @ (cNat.semiring_1_class.of_nat @ V0)) @ cNat.semiring_1_class.Nats))))
(TNat.semiring_char_0.of_nat_0_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V3) @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4))) @ ((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ V4))))))))))))))
(TNat.semiring_char_0.of_nat_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNat.semiring_1.of_nat @ V0) @ V2) @ V3) @ V4)) @ V3)) @ ((cHOL.eq @ V4) @ cNat.zero_nat_inst.zero_nat))))))))))))))
(TNitpick.fun_box.Abs_fun_box_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.fun_box.fun_box_rep_set))) @ ((cHOL.eq @ (cNitpick.Rep_fun_box @ (cNitpick.Abs_fun_box @ V0))) @ V0)))))
(TNitpick.fun_box.Rep_fun_box_inverse,(call @ (^[V0]: ((cHOL.eq @ (cNitpick.Abs_fun_box @ (cNitpick.Rep_fun_box @ V0))) @ V0))))
(TNitpick.fun_box.fun_box_rec_set_def,((c== @ cNitpick.fun_box.fun_box_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cNitpick.fun_box.FunBox @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4))))))))))))
(TNitpick.fun_box.fun_box_rep_set_def,((c== @ cNitpick.fun_box.fun_box_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.Leaf @ V2)))))))))
(TNitpick.pair_box.Abs_pair_box_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.Abs_pair_box @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set))) @ V1))))) @ V1))))))
(TNitpick.pair_box.Rep_pair_box_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cNitpick.Rep_pair_box @ V2))) @ V1)))) @ V1)))))))
(TNum.linordered_idom.abs_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10))) @ (((cNum.numeral.numeral @ V7) @ V6) @ V10))))))))))))))))))))))))))
(TNum.neg_numeral.minus_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))))))))))))))))
(TNum.neg_numeral.minus_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))))))))))))))))
(TNum.neg_numeral.minus_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ V4)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ cNum.num.One))))))))))))))
(TNum.neg_numeral_class.dbl_dec_simps_4,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))))))
(TNum.neg_numeral_class.dbl_dec_simps_3,((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ cGroups.one_class.one)) @ cGroups.one_class.one))
(TNum.neg_numeral_class.dbl_dec_simps_2,((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ cGroups.zero_class.zero)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNum.neg_numeral_class.dbl_dec_simps_1,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_dec @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit1 @ V0))))))
(TNum.neg_numeral_class.dbl_inc_simps_4,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))))))
(TNum.neg_numeral_class.dbl_inc_simps_3,((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))))
(TNum.neg_numeral_class.dbl_inc_simps_2,((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ cGroups.zero_class.zero)) @ cGroups.one_class.one))
(TNum.neg_numeral_class.dbl_inc_simps_1,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.dbl_inc @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.BitM @ V0))))))
(TNum.neg_numeral_class.is_num.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (V1 @ cGroups.one_class.one)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNum.neg_numeral_class.is_num @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cGroups.uminus_class.uminus @ V2))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cNum.neg_numeral_class.is_num @ V2)) @ ((c==> @ (V1 @ V2)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V3)) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cGroups.plus_class.plus @ V2) @ V3))))))))))) @ (V1 @ V0))))))))))
(TNum.neg_numeral_class.is_num.intros_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V1)) @ (cNum.neg_numeral_class.is_num @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TNum.neg_numeral_class.is_num.intros_2,(call @ (^[V0]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ (cNum.neg_numeral_class.is_num @ (cGroups.uminus_class.uminus @ V0))))))
(TNum.neg_numeral_class.is_num.intros_1,(cNum.neg_numeral_class.is_num @ cGroups.one_class.one))
(TNum.neg_numeral_class.minus_numeral,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TNum.neg_numeral_class.sub_num_simps_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.neg_numeral_class.dbl @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.neg_numeral_class.sub_num_simps_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.neg_numeral_class.dbl_inc @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.neg_numeral_class.sub_num_simps_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit1 @ V1))) @ (cNum.neg_numeral_class.dbl_dec @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.neg_numeral_class.sub_num_simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ (cNum.neg_numeral_class.dbl @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.neg_numeral_class.sub_num_simps_5,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit1 @ V0)) @ cNum.num.One)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.neg_numeral_class.sub_num_simps_4,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ (cNum.num.Bit0 @ V0)) @ cNum.num.One)) @ (cNum.numeral_class.numeral @ (cNum.BitM @ V0))))))
(TNum.neg_numeral_class.sub_num_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ (cNum.num.Bit1 @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.num.Bit0 @ V0))))))
(TNum.neg_numeral_class.sub_num_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ (cNum.num.Bit0 @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ (cNum.BitM @ V0))))))
(TNum.neg_numeral_class.sub_num_simps_1,((cHOL.eq @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ cNum.num.One)) @ cGroups.zero_class.zero))
(TNum.ring_1_class.eq_iff_iszero_diff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ (cNum.ring_1_class.iszero @ ((cGroups.minus_class.minus @ V0) @ V1))))))))
(TNum.ring_1_class.iszero_neg_numeral,(call @ (^[V0]: ((cHOL.eq @ (cNum.ring_1_class.iszero @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNum.ring_char_0.neg_numeral_neq_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ V0))))))))))))))))))
(TNum.ring_char_0.one_neq_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)))))))))))))))))))
(TNum.semiring_1_class.of_nat_numeral,(call @ (^[V0]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TOption.option.option_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TOption.option.option_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cOption.option.option_rec_set @ V0) @ V1) @ (cOption.option.Some @ V2)) @ (V1 @ V2)))))))))
(TOption.option.option_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cOption.option.option_rec_set @ V0) @ V1) @ cOption.option.None) @ V0))))))
(TOption.option.option_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOption.option.option_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.Leaf @ V2)))))) @ (V1 @ V0)))))))))
(TOption.option.option_rep_set.intros_2,(call @ (^[V0]: (cOption.option.option_rep_set @ (cDatatype.In1 @ (cDatatype.Leaf @ V0))))))
(TOption.option.option_rep_set.intros_1,(cOption.option.option_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TOrderings.class.linorder_axioms_def,(call @ (^[V0]: ((c== @ (cOrderings.class.linorder_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.disj @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TOrderings.class.no_bot_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V2) @ V1)))))) @ (cOrderings.class.no_bot_axioms @ V0)))))
(TOrderings.class.no_top_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (cHOL.Ex @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (cOrderings.class.no_top_axioms @ V0)))))
(TOrderings.linorder.strict_mono_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.strict_mono @ V1) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (V2 @ V3)) @ (V2 @ V4))) @ ((V1 @ V3) @ V4)))))))))))))))
(TOrderings.ord_class.ord_eq_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.ord_class.ord_le_eq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.order_bot_class.bot_least,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cOrderings.bot_class.bot) @ V0))))
(TOrderings.order_class.LeastI2_order,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cOrderings.ord_class.less_eq @ V3) @ V4))))) @ (V2 @ V3)))))) @ (V2 @ (cOrderings.ord_class.Least @ V0))))))))))))
(TOrderings.order_class.order.antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.ordering.order_iff_strict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ ((cHOL.disj @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.ordering.strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))))))))))))))
(TOrderings.ordering_top_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((V0 @ V2) @ V1)))) @ ((cOrderings.ordering_top_axioms @ V0) @ V1)))))))
(TOrderings.preorder_class.less_asym',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)))))))))
(TOrderings.preorder_class.less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.preorder_class.order_refl,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ V0))))
(TOrderings.wellorder_class.LeastI_ex,(call @ (^[V0]: ((c==> @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ (V0 @ (cOrderings.ord_class.Least @ V0))))))
(TPartial_Function.fixp_induct_option,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (^[V8]: ((V0 @ (V1 @ (V2 @ V8))) @ V7)))))) @ ((c==> @ ((c== @ V3) @ (V2 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (^[V7]: (V0 @ (V1 @ (V2 @ V7)))))))) @ ((c==> @ (call @ (^[V7]: ((cHOL.eq @ (V0 @ (V2 @ V7))) @ V7)))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((cHOL.eq @ ((V0 @ V7) @ V10)) @ (cOption.option.Some @ V11))) @ ((V4 @ V10) @ V11))))))) @ ((c==> @ ((cHOL.eq @ ((V0 @ (V1 @ V7)) @ V8)) @ (cOption.option.Some @ V9))) @ ((V4 @ V8) @ V9)))))))))) @ ((c==> @ ((cHOL.eq @ ((V0 @ V3) @ V5)) @ (cOption.option.Some @ V6))) @ ((V4 @ V5) @ V6)))))))))))))))))))))
(TPartial_Function.option.leq_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cPartial_Function.flat_ord @ cOption.option.None) @ V0) @ V1)) @ ((c==> @ (((cPartial_Function.flat_ord @ cOption.option.None) @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TPartial_Function.tailrec.const_mono,(call @ (^[V0]: (call @ (^[V1]: (((cComplete_Partial_Order.monotone @ V0) @ (cPartial_Function.flat_ord @ cHOL.undefined)) @ (^[V2]: V1)))))))
(TPartial_Function.tailrec_admissible,(call @ (^[V0]: (call @ (^[V1]: (((cComplete_Partial_Order.ccpo.admissible @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ V0))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ V0))) @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ (V2 @ V3)) @ V0))) @ ((V1 @ V3) @ (V2 @ V3))))))))))))
(TPower.linordered_idom.power2_less_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ V3))))))))))))))))))))))))))
(TPower.linordered_semidom.power_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V4 @ V6) @ V7)) @ ((c==> @ ((V4 @ V1) @ V6)) @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V8)) @ ((((cPower.power.power @ V3) @ V2) @ V7) @ V8))))))))))))))))))))))))
(TPower.monoid_mult.power_numeral_odd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V3)))) @ ((cHOL.Let @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNum.numeral_class.numeral @ V3))) @ (^[V4]: ((V1 @ ((V1 @ V2) @ V4)) @ V4))))))))))))))
(TPower.ring_1.power_neg_numeral_Bit0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V7)))) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.pow @ V6) @ (cNum.num.Bit0 @ V7))))))))))))))))))))))
(TPower.ring_1.power_neg_numeral_Bit1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V7)))) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ ((cNum.pow @ V6) @ (cNum.num.Bit1 @ V7))))))))))))))))))))))
(TPower.ring_1_class.power_minus1_odd,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)))) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))))
(TPower.ring_1_class.power_minus_Bit0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))))))))
(TPower.ring_1_class.power_minus_Bit1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cGroups.uminus_class.uminus @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V1)))) @ (cGroups.uminus_class.uminus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V1))))))))))
(TPower.ring_1_class.power_minus_even,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cGroups.uminus_class.uminus @ V0)) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cPower.power_class.power @ V0) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))))))))
(TPower.semiring_1.power_zero_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V3) @ (cNum.numeral_class.numeral @ V4))) @ V3)))))))))))))
(TPower.semiring_1_class.of_nat_power,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ (cNat.semiring_1_class.of_nat @ V0)) @ V1)))))))
(TPredicate.iterate_upto_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.iterate_upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((cPredicate.iterate_upto_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (cPredicate.Seq @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TPredicate.iterate_upto_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cPredicate.iterate_upto_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0)))))))) @ ((cPredicate.iterate_upto_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V1) @ V0))) @ (cPredicate.Seq @ (^[V4]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V2 @ V1)) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0))))))))))))))))))
(TPredicate.pred.pred_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cPredicate.pred.pred_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TPredicate.pred_of_set_set_foldr_sup,(call @ (^[V0]: ((cHOL.eq @ (cPredicate.pred_of_set @ (cList.set @ V0))) @ (((cList.foldr @ cLattices.sup_class.sup) @ ((cList.map @ cPredicate.single) @ V0)) @ cOrderings.bot_class.bot)))))
(TPredicate_Compile.contains_pred_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPredicate_Compile.contains_pred @ V0) @ V1)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (cPredicate.single @ cProduct_Type.Unity)) @ cOrderings.bot_class.bot)))))))
(TProduct_Type.split_paired_Bex_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Bex @ ((cProduct_Type.Sigma @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Bex @ V0) @ (^[V3]: ((cSet.Bex @ (V1 @ V3)) @ (^[V4]: (V2 @ ((cProduct_Type.Pair @ V3) @ V4))))))))))))))
(TQuickcheck_Exhaustive.cps_empty_def,((cHOL.eq @ cQuickcheck_Exhaustive.cps_empty) @ (^[V0]: cOption.option.None)))
(TQuickcheck_Exhaustive.unknown.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V0) @ V1) @ (cQuickcheck_Exhaustive.unknown.Known @ V2))) @ (V1 @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.cases_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V0) @ V1) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ V0))))))
(TQuickcheck_Exhaustive.unknown.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_rec @ V0) @ V1) @ (cQuickcheck_Exhaustive.unknown.Known @ V2))) @ (V1 @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.simps_6,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_rec @ V0) @ V1) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ V0))))))
(TQuickcheck_Exhaustive.unknown.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V0) @ V1) @ (cQuickcheck_Exhaustive.unknown.Known @ V2))) @ (V1 @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V0) @ V1) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ V0))))))
(TQuickcheck_Exhaustive.unknown.simps_3,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Exhaustive.unknown.Known @ V0)) @ cQuickcheck_Exhaustive.unknown.Unknown)))))
(TQuickcheck_Exhaustive.unknown.simps_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.unknown.Unknown) @ (cQuickcheck_Exhaustive.unknown.Known @ V0))))))
(TQuickcheck_Exhaustive.unknown.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.unknown.Known @ V0)) @ (cQuickcheck_Exhaustive.unknown.Known @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.unknown.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cQuickcheck_Exhaustive.unknown.Known @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TQuickcheck_Narrowing.cfun.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.cfun.Constant @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V2) @ V0)) @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V3) @ V1)))))))))))))
(TQuickcheck_Narrowing.cfun.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.cfun.Constant @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TQuickcheck_Narrowing.conv_graph_def,((c== @ cQuickcheck_Narrowing.conv_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V5) @ V6)))) @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V5)))))))))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V5) @ V6)))) @ ((cHOL.eq @ V2) @ (((cQuickcheck_Narrowing.nth @ V4) @ V5) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.conv_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.conv_rel @ V0) @ V1)) @ V2))))))))
(TQuickcheck_Narrowing.conv_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.conv_rel @ V0) @ V1)) @ cHOL.False))))))
(TQuickcheck_Narrowing.drawn_from_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.drawn_from @ V0)) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ ((cList.map @ (^[V1]: cList.list.Nil)) @ V0))) @ ((cList.map @ (^[V1]: (^[V2]: V1))) @ V0))))))
(TQuickcheck_Narrowing.equal_cfun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.equal_ffun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.ffun.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.ffun.Constant @ V6))) @ ((cHOL.eq @ (V2 @ V6)) @ (V3 @ V6)))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V1) @ (((cQuickcheck_Narrowing.ffun.Update @ V6) @ V7) @ V8))) @ ((cHOL.eq @ (((V4 @ V6) @ V7) @ V8)) @ (((V5 @ V6) @ V7) @ V8)))))))))) @ ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V2) @ V4) @ V0)) @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V3) @ V5) @ V1))))))))))))))))))
(TQuickcheck_Narrowing.ffun.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Narrowing.ffun.Constant @ V4))) @ (cHOL.Not @ (V0 @ (V1 @ V4))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.ffun.Update @ V4) @ V5) @ V6))) @ (cHOL.Not @ (V0 @ (((V2 @ V4) @ V5) @ V6))))))))))))))))))))))
(TQuickcheck_Narrowing.map_cons.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.map_cons @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2))) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ ((cList.map @ (^[V3]: ((cFun.comp @ V0) @ V3))) @ V2))))))))))
(TQuickcheck_Narrowing.property.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V0) @ V1) @ V2) @ (cQuickcheck_Narrowing.property.Property @ V3))) @ (V2 @ V3)))))))))))
(TQuickcheck_Narrowing.property.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ (((V1 @ V3) @ V4) @ V5)))))))))))))))
(TQuickcheck_Narrowing.property.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ (((V0 @ V3) @ V4) @ V5)))))))))))))))
(TQuickcheck_Narrowing.property.simps_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (cQuickcheck_Narrowing.property.Property @ V3))) @ (V2 @ V3)))))))))))
(TQuickcheck_Narrowing.property.simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ ((((V1 @ V3) @ V4) @ V5) @ (^[V6]: ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (V4 @ V6))))))))))))))))))
(TQuickcheck_Narrowing.property.simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ ((((V0 @ V3) @ V4) @ V5) @ (^[V6]: ((((cQuickcheck_Narrowing.property.property_rec @ V0) @ V1) @ V2) @ (V4 @ V6))))))))))))))))))
(TQuickcheck_Narrowing.property.simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V0) @ V1) @ V2) @ (cQuickcheck_Narrowing.property.Property @ V3))) @ (V2 @ V3)))))))))))
(TQuickcheck_Narrowing.property.simps_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ (((V1 @ V3) @ V4) @ V5)))))))))))))))
(TQuickcheck_Narrowing.property.simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ (((V0 @ V3) @ V4) @ V5)))))))))))))))
(TQuickcheck_Narrowing.property.simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (((cQuickcheck_Narrowing.property.Existential @ V1) @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.property.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.property.Property @ V3))))))))))))
(TQuickcheck_Narrowing.property.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (((cQuickcheck_Narrowing.property.Universal @ V1) @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.property.simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.property.Property @ V3))))))))))))
(TQuickcheck_Narrowing.property.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))))))))))))))))
(TQuickcheck_Narrowing.property.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))))))))))))))))
(TQuickcheck_Narrowing.property.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (cQuickcheck_Narrowing.property.Property @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.property.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.property.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.property.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Narrowing.property.property_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Universal @ V5) @ V6) @ V7))) @ (V0 @ (((V1 @ V5) @ V6) @ V7)))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Existential @ V5) @ V6) @ V7))) @ (V0 @ (((V2 @ V5) @ V6) @ V7)))))))))) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cQuickcheck_Narrowing.property.Property @ V5))) @ (V0 @ (V3 @ V5)))))))))))))))))))
(TQuickcheck_Random.arity_random_bool,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_char,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_list,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_pred,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_prod,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_term,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_unit,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.random_itself_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cTYPE) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))))))
(TQuickcheck_Random.random_nibble_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_nibble_inst.random_nibble @ V0)) @ ((cQuickcheck_Random.random_aux_nibble @ V0) @ V0)))))
(TQuickcheck_Random.random_option_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_option @ V0) @ V0)))))
(TRandom_Sequence.Random_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.Random_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom_Sequence.Random_graph @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V4 @ V6)) @ (^[V7]: ((cProduct_Type.scomp @ ((V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ V6)) @ (^[V8]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V7))) @ V8)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.Random_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom_Sequence.Random_graph @ ((cProduct_Type.Pair @ V1) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ V1) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((cRandom_Sequence.Random_graph @ ((cProduct_Type.Pair @ V1) @ V0)) @ (^[V3]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V1 @ V3)) @ (^[V4]: ((cProduct_Type.scomp @ ((V2 @ ((cProduct_Type.Pair @ V1) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V4))) @ V5)))))))))))))))))
(TRandom_Sequence.not_random_dseq_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.not_random_dseq @ V0)) @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.Let @ (((V0 @ V1) @ V2) @ V3)) @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cProduct_Type.Pair @ (cLimited_Sequence.not_seq @ V4)) @ V5))))))))))))
(TRecord.arity_type_tuple_isomorphism,(cHOL.type_class @ cTYPE))
(TRecord.random_tuple_isomorphism_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cRecord.random_aux_tuple_isomorphism @ V0) @ V0)))))
(TRecord.update_accessor_accessor_eqE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (V1 @ V2)) @ V5)))))))))))))))
(TRings.class.linordered_semiring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ (((((cRings.class.ordered_semiring @ V0) @ V3) @ V1) @ V2) @ V4))))))))))))))
(TRings.class.ordered_comm_ring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ (((((cRings.class.ordered_comm_semiring @ V0) @ V5) @ V6) @ V1) @ V4)) @ (((((((cRings.class.ordered_comm_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6))))))))))))))))))
(TRings.class.ordered_ring_abs.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.ordered_ring_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((cRings.class.ordered_ring_abs_axioms @ V0) @ V2) @ V5) @ V7)))))))))))))))))))
(TRings.class.ordered_ring_abs.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.ordered_ring_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((((cRings.class.ordered_ring @ V1) @ V2) @ V5) @ V6) @ V7) @ V3) @ V4)))))))))))))))))))
(TRings.class.ordered_ring_abs.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.ordered_ring_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)))))))))))))))))))
(TRings.class.ordered_semiring.axioms_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cRings.class.ordered_semiring_axioms @ V1) @ V2) @ V4)))))))))))))
(TRings.class.ordered_semiring.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cRings.class.semiring @ V0) @ V4)))))))))))))
(TRings.class.ordered_semiring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V2) @ V3)))))))))))))
(TRings.class.ordered_semiring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))))))))
(TRings.class.semiring_0_cancel.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cRings.class.semiring @ V0) @ V2)) @ (((cRings.class.semiring_0_cancel @ V0) @ V1) @ V2))))))))))
(TRings.class.semiring_1_cancel.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cGroups.class.monoid_mult @ V2) @ V3)) @ ((c==> @ ((cRings.class.semiring @ V0) @ V3)) @ ((c==> @ ((cRings.class.zero_neq_one @ V2) @ V1)) @ ((((cRings.class.semiring_1_cancel @ V0) @ V1) @ V2) @ V3))))))))))))))
(TRings.classrel_linordered_idom_idom,(cRings.idom_class @ cTYPE))
(TRings.comm_semiring_1.dvd_mult_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ ((V0 @ V4) @ V5)) @ V6)) @ (((cRings.dvd.dvd @ V0) @ V4) @ V6))))))))))))))))))
(TRings.comm_semiring_1.dvd_triv_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cRings.dvd.dvd @ V0) @ V4) @ ((V0 @ V4) @ V5))))))))))))))))
(TRings.comm_semiring_1.mult_dvd_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ (((cRings.dvd.dvd @ V0) @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V7))))))))))))))))))))))
(TRings.comm_semiring_1_class.dvd_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2)))))))))))
(TRings.comm_semiring_1_class.one_dvd,(call @ (^[V0]: ((cRings.dvd_class.dvd @ cGroups.one_class.one) @ V0))))
(TRings.linordered_idom.abs_mult_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V5 @ (V0 @ V10)) @ V11)) @ ((c==> @ ((V5 @ (V0 @ V12)) @ V13)) @ ((V5 @ ((V9 @ (V0 @ V10)) @ (V0 @ V12))) @ ((V9 @ V11) @ V13))))))))))))))))))))))))))))))))))
(TRings.linordered_idom.abs_mult_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V9 @ (V0 @ V10)) @ (V0 @ V10))) @ ((V9 @ V10) @ V10))))))))))))))))))))))))))
(TRings.linordered_idom.dvd_if_abs_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((cHOL.eq @ (V0 @ V10)) @ (V0 @ V11))) @ (((cRings.dvd.dvd @ V9) @ V10) @ V11))))))))))))))))))))))))))))
(TRings.linordered_idom_class.abs_one,((cHOL.eq @ (cGroups.abs_class.abs @ cGroups.one_class.one)) @ cGroups.one_class.one))
(TRings.linordered_idom_class.abs_sgn,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ ((cGroups.times_class.times @ V0) @ (cGroups.sgn_class.sgn @ V0))))))
(TRings.linordered_idom_class.sgn_0_0,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.sgn_class.sgn @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TRings.linordered_idom_class.sgn_neg,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ (cGroups.sgn_class.sgn @ V0)) @ (cGroups.uminus_class.uminus @ cGroups.one_class.one))))))
(TRings.linordered_idom_class.sgn_pos,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ (cGroups.sgn_class.sgn @ V0)) @ cGroups.one_class.one)))))
(TRings.linordered_idom_class.sgn_sgn,(call @ (^[V0]: ((cHOL.eq @ (cGroups.sgn_class.sgn @ (cGroups.sgn_class.sgn @ V0))) @ (cGroups.sgn_class.sgn @ V0)))))
(TRings.linordered_semiring_class_def,((c== @ (cRings.linordered_semiring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ (cRings.ordered_semiring_class @ cTYPE))))
(TRings.no_zero_divisors_class.axioms,((cRings.class.no_zero_divisors @ cGroups.times_class.times) @ cGroups.zero_class.zero))
(TRings.ordered_comm_ring_class.intro,((c==> @ (cRings.comm_ring_class @ cTYPE)) @ ((c==> @ (cRings.ordered_comm_semiring_class @ cTYPE)) @ (cRings.ordered_comm_ring_class @ cTYPE))))
(TRings.ordered_comm_ring_class.super_2,((c==> @ (cRings.ordered_comm_ring_class @ cTYPE)) @ (cRings.ordered_comm_semiring_class @ cTYPE)))
(TRings.ordered_comm_ring_class.super_1,((c==> @ (cRings.ordered_comm_ring_class @ cTYPE)) @ (cRings.comm_ring_class @ cTYPE)))
(TRings.ordered_ring_abs_class.axioms,((((cRings.class.ordered_ring_abs_axioms @ cGroups.abs_class.abs) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cGroups.times_class.times))
(TRings.ordered_semiring_class.axioms,(((cRings.class.ordered_semiring_axioms @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cGroups.times_class.times))
(TRings.ring_class.minus_mult_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cGroups.times_class.times @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TRings.ring_class.right_diff_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TRings.semiring_0_cancel_class.intro,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cRings.semiring_class @ cTYPE)) @ (cRings.semiring_0_cancel_class @ cTYPE))))
(TRings.semiring_0_cancel_class.super_2,((c==> @ (cRings.semiring_0_cancel_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))
(TRings.semiring_0_cancel_class.super_1,((c==> @ (cRings.semiring_0_cancel_class @ cTYPE)) @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)))
(TRings.semiring_1_cancel_class.intro,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.monoid_mult_class @ cTYPE)) @ ((c==> @ (cRings.semiring_class @ cTYPE)) @ ((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cRings.semiring_1_cancel_class @ cTYPE))))))
(TRings.semiring_1_cancel_class.super_4,((c==> @ (cRings.semiring_1_cancel_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))
(TRings.semiring_1_cancel_class.super_3,((c==> @ (cRings.semiring_1_cancel_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))
(TRings.semiring_1_cancel_class.super_2,((c==> @ (cRings.semiring_1_cancel_class @ cTYPE)) @ (cGroups.monoid_mult_class @ cTYPE)))
(TRings.semiring_1_cancel_class.super_1,((c==> @ (cRings.semiring_1_cancel_class @ cTYPE)) @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)))
(TSMT.pattern.narrowing_pattern.simps,((cHOL.eq @ cSMT.narrowing_pattern_inst.narrowing_pattern) @ (cQuickcheck_Narrowing.cons @ cSMT.pattern.Pattern)))
(TSMT.pattern.pattern_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cSMT.pattern.pattern_rep_set @ V0)) @ ((c==> @ (V1 @ cHOL.undefined)) @ (V1 @ V0))))))))
(TSet_Interval.atLeastLessThan_add_Un,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))))
(TSet_Interval.atLeastLessThan_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))))
(TSet_Interval.card_atLeastAtMost_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ (cInt.nat @ ((cInt.plus_int_inst.plus_int @ ((cInt.minus_int_inst.minus_int @ V1) @ V0)) @ cInt.one_int_inst.one_int))))))))
(TSet_Interval.card_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)))))))
(TSet_Interval.dvd.Icc_subset_Ici_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ ((cSet_Interval.ord.atLeast @ cRings.dvd_class.dvd) @ V2))) @ ((cHOL.disj @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))) @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))
(TSet_Interval.dvd.Icc_subset_Iic_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ ((cSet_Interval.ord.atMost @ cRings.dvd_class.dvd) @ V2))) @ ((cHOL.disj @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))) @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))
(TSet_Interval.ex_bij_betw_finite_nat,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: (((cFun.bij_betw @ V1) @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ (cFinite_Set.card @ V0)))))))))
(TSet_Interval.ex_bij_betw_nat_finite,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: (((cFun.bij_betw @ V1) @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ (cFinite_Set.card @ V0))) @ V0)))))))
(TSet_Interval.finite_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)))))))
(TSet_Interval.greaterThan_subset_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.greaterThan @ V0)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet_Interval.no_bot.not_Ici_eq_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ cOrderings.top_class.top))))))))))
(TSet_Interval.no_bot.not_UNIV_eq_Ici,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ cOrderings.top_class.top) @ ((cSet_Interval.ord.atLeast @ V0) @ V2)))))))))))
(TSet_Interval.no_bot.not_UNIV_le_Ici,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ ((cSet_Interval.ord.atLeast @ V0) @ V2)))))))))))
(TSet_Interval.no_top.not_Icc_eq_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ cOrderings.top_class.top))))))))))))
(TSet_Interval.no_top.not_Iic_eq_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ cOrderings.top_class.top))))))))))
(TSet_Interval.no_top.not_UNIV_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ cOrderings.top_class.top) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)))))))))))))
(TSet_Interval.no_top.not_UNIV_eq_Iic,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ cOrderings.top_class.top) @ ((cSet_Interval.ord.atMost @ V0) @ V2)))))))))))
(TSet_Interval.no_top.not_UNIV_le_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)))))))))))))
(TSet_Interval.no_top.not_UNIV_le_Iic,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ ((cSet_Interval.ord.atMost @ V0) @ V2)))))))))))
(TSet_Interval.ord_class.lessThan_def,(call @ (^[V0]: ((c== @ (cSet_Interval.ord_class.lessThan @ V0)) @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TSet_Interval.ord_class.lessThan_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cSet_Interval.ord_class.lessThan @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V1)))))))
(TSet_Interval.order.not_Ici_eq_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ cOrderings.bot_class.bot))))))))))
(TSet_Interval.order.not_Iic_eq_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ cOrderings.bot_class.bot))))))))))
(TSet_Interval.order_class.Icc_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ V3))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))) @ ((cHOL.conj @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V2) @ V3))))))))))))))
(TSet_Interval.setsum_setsum_restrict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V5]: ((V2 @ V4) @ V5))) @ (cSet.Collect @ (^[V5]: ((cHOL.conj @ ((cSet.member @ V5) @ V1)) @ ((V3 @ V4) @ V5))))))) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V5]: ((V2 @ V5) @ V4))) @ (cSet.Collect @ (^[V5]: ((cHOL.conj @ ((cSet.member @ V5) @ V0)) @ ((V3 @ V5) @ V4))))))) @ V1)))))))))))))
(TSet_Interval.setsum_shift_lb_Suc0_0,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ cNat.zero_nat_inst.zero_nat) @ V1)))))))))
(TString.enum_char_inst.enum_all_char,((c== @ cString.enum_char_inst.enum_all_char) @ cString.enum_char_inst.enum_all_char))
(TString.enum_nibble_inst.enum_nibble,((c== @ cString.enum_nibble_inst.enum_nibble) @ cString.enum_nibble_inst.enum_nibble))
(TString.nibble.nibble_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TString.nibble.nibble_rec_set.intros_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleF) @ V15))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleE) @ V14))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleD) @ V13))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleC) @ V12))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleB) @ V11))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.NibbleA) @ V10))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble9) @ V9))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble8) @ V8))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble7) @ V7))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble6) @ V6))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble5) @ V5))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble4) @ V4))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble3) @ V3))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble2) @ V2))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble1) @ V1))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: (call @ (^[V15]: ((((((((((((((((((cString.nibble.nibble_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11) @ V12) @ V13) @ V14) @ V15) @ cString.nibble.Nibble0) @ V0))))))))))))))))))))))))))))))))))
(TString.nibble.nibble_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cString.nibble.nibble_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ (V1 @ V0)))))))))))))))))))))))
(TString.nibble.nibble_rep_set.intros_16,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_15,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_14,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_13,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_12,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_11,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_10,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_9,(cString.nibble.nibble_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_8,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_7,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_6,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_5,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_4,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_3,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_2,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined))))))
(TString.nibble.nibble_rep_set.intros_1,(cString.nibble.nibble_rep_set @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined))))))
(TString.nibble_of_nat_of_char_div_16,(call @ (^[V0]: ((cHOL.eq @ (cString.nibble_of_nat @ ((cDivides.div_nat_inst.div_nat @ (cString.nat_of_char @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ (cNum.num.Bit0 @ cNum.num.One)))))))) @ ((cString.char.char_case @ (^[V1]: (^[V2]: V1))) @ V0)))))
(TSum_Type.sum.size_sum_inst.size_sum,((c== @ cSum_Type.sum.size_sum_inst.size_sum) @ cSum_Type.sum.size_sum_inst.size_sum))
(TTransitive_Closure.acyclic_converse,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.acyclic @ (cRelation.converse @ V0))) @ (cTransitive_Closure.acyclic @ V0)))))
(TTransitive_Closure.converse_tranclE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ V3))))) @ V3))))))))))))
(TTransitive_Closure.irrefl_trancl_rD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.All @ (^[V3]: (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V3)) @ (cTransitive_Closure.trancl @ V0)))))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V2)))))))))))
(TTransitive_Closure.relpowp_code_def,((cHOL.eq @ cTransitive_Closure.relpowp) @ cNat.compow))
(TTransitive_Closure.relpowp_fun_conv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cNat.compow @ V0) @ V1) @ V2) @ V3)) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ (V4 @ cNat.zero_nat_inst.zero_nat)) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ (V4 @ V0)) @ V3)) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V5) @ V0)) @ ((V1 @ (V4 @ V5)) @ (V4 @ (cNat.Suc @ V5))))))))))))))))))))
(TTransitive_Closure.rtrancl_converse,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ (cRelation.converse @ V0))) @ (cRelation.converse @ (cTransitive_Closure.rtrancl @ V0))))))
(TTransitive_Closure.rtranclp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((V3 @ V4) @ V4)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V4) @ V5)) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((V0 @ V5) @ V6)) @ ((V3 @ V4) @ V6))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TTransitive_Closure.rtranclp_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((V5 @ V1) @ V2)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ ((c==> @ ((V0 @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V8) @ V9))) @ ((c==> @ ((V5 @ V6) @ V7)) @ ((V5 @ V8) @ V9))))))))))))) @ ((V5 @ V3) @ V4)))))))))))))))))
(TTransitive_Closure.rtranclp_reflclp,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtranclp @ ((cLattices.sup_class.sup @ V0) @ cHOL.eq))) @ (cTransitive_Closure.rtranclp @ V0)))))
(TTransitive_Closure.trancl_converseD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ (cRelation.converse @ V2)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ (cTransitive_Closure.trancl @ V2)))))))))))
(TTransitive_Closure.trancl_converseI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cRelation.converse @ (cTransitive_Closure.trancl @ V2)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ (cRelation.converse @ V2)))))))))))
(TTransitive_Closure.tranclp_converse,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.tranclp @ (cRelation.conversep @ V0))) @ (cRelation.conversep @ (cTransitive_Closure.tranclp @ V0))))))
(TTypedef.type_definition.Abs_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((cHOL.eq @ (V0 @ (V1 @ V3))) @ V3))))))))))))
(TTypedef.type_definition.Rep_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTypedef.type_definition @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (V1 @ (V0 @ V3))) @ V3)))))))))))
(TTyperep.typerep.Abs_typerep_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cTyperep.typerep.typerep_rep_set_1))) @ ((cHOL.eq @ (cTyperep.Rep_typerep @ (cTyperep.Abs_typerep @ V0))) @ V0)))))
(TTyperep.typerep.Rep_typerep_inverse,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.Abs_typerep @ (cTyperep.Rep_typerep @ V0))) @ V0))))
(TTyperep.typerep.typerep_rec_set_def,((c== @ cTyperep.typerep.typerep_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (cInductive.complete_lattice_class.lfp @ (^[V3]: (^[V4]: (^[V5]: (^[V6]: (^[V7]: (^[V8]: ((cHOL.disj @ (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: ((cHOL.conj @ (cHOL.Not @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V7) @ ((cTyperep.typerep.Typerep @ V11) @ V9))) @ ((cHOL.conj @ ((cHOL.eq @ V8) @ (((V0 @ V11) @ V9) @ V10))) @ (((((V3 @ cHOL.True) @ V9) @ V10) @ cHOL.undefined) @ cHOL.undefined))))))))))) @ ((cHOL.disj @ ((cHOL.conj @ V4) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cList.list.Nil)) @ ((cHOL.eq @ V6) @ V1)))) @ (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: (cHOL.Ex @ (^[V12]: ((cHOL.conj @ V4) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ ((cList.list.Cons @ V9) @ V11))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ ((((V2 @ V9) @ V11) @ V10) @ V12))) @ ((cHOL.conj @ (((((V3 @ cHOL.False) @ cHOL.undefined) @ cHOL.undefined) @ V9) @ V10)) @ (((((V3 @ cHOL.True) @ V11) @ V12) @ cHOL.undefined) @ cHOL.undefined)))))))))))))))))))))))))))
(TTyperep.typerep.typerep_rep_set_def,((c== @ cTyperep.typerep.typerep_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ (cHOL.Not @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cDatatype.Scons @ (cDatatype.Leaf @ V4)) @ V3))) @ ((V0 @ cHOL.True) @ V3)))))))) @ ((cHOL.disj @ ((cHOL.conj @ V1) @ ((cHOL.eq @ V2) @ (cDatatype.In0 @ cHOL.undefined)))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ V1) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (cDatatype.In1 @ ((cDatatype.Scons @ V3) @ V4)))) @ ((cHOL.conj @ ((V0 @ cHOL.False) @ V3)) @ ((V0 @ cHOL.True) @ V4))))))))))))))))
(TBig_Operators.card_cartesian_product,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1)))) @ ((cNat.times_nat_inst.times_nat @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ V1))))))))
(TBig_Operators.comm_monoid_set.axioms,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((cGroups.comm_monoid @ V0) @ V1)))))))
(TBig_Operators.comm_monoid_set.delta',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V5]: (((cHOL.If @ ((cHOL.eq @ V3) @ V5)) @ (V4 @ V5)) @ V1))) @ V2)) @ (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ (V4 @ V3)) @ V1)))))))))))))))
(TBig_Operators.comm_monoid_set.insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V3) @ V2))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cSet.insert @ V3) @ V2))) @ ((V0 @ (V4 @ V3)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)))))))))))))))))
(TBig_Operators.comm_monoid_set.remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)) @ ((V0 @ (V4 @ V3)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))))))))))))))))))
(TBig_Operators.lattice.inf_Sup_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ ((cSet.member @ V5) @ V4)) @ ((cHOL.eq @ ((V0 @ V5) @ ((cBig_Operators.semilattice_sup.Sup_fin @ V3) @ V4))) @ V5)))))))))))))))))
(TBig_Operators.lattice.sup_Inf_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ ((cSet.member @ V5) @ V4)) @ ((cHOL.eq @ ((V3 @ V5) @ ((cBig_Operators.semilattice_inf.Inf_fin @ V0) @ V4))) @ V5)))))))))))))))))
(TBig_Operators.linorder.Max_singleton,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.linorder.Max @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ V2)))))))))
(TBig_Operators.linorder.Min_singleton,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.linorder.Min @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ V2)))))))))
(TBig_Operators.linorder_class.Max_def,((cHOL.eq @ cBig_Operators.linorder_class.Max) @ (cBig_Operators.semilattice_set.F @ cOrderings.ord_class.max)))
(TBig_Operators.linorder_class.Max_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ V0)) @ V1)))))))))
(TBig_Operators.linorder_class.Min_def,((cHOL.eq @ cBig_Operators.linorder_class.Min) @ (cBig_Operators.semilattice_set.F @ cOrderings.ord_class.min)))
(TBig_Operators.linorder_class.Min_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ V0)) @ V1)))))))))
(TBig_Operators.semilattice_set.axioms,(call @ (^[V0]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ (cLattices.semilattice @ V0)))))
(TBig_Operators.semilattice_set.closed,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cSet.member @ ((V0 @ V2) @ V3)) @ ((cSet.insert @ V2) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))))))) @ ((cSet.member @ ((cBig_Operators.semilattice_set.F @ V0) @ V1)) @ V1))))))))))
(TBig_Operators.semilattice_set.insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cSet.insert @ V2) @ V1))) @ ((V0 @ V2) @ ((cBig_Operators.semilattice_set.F @ V0) @ V1)))))))))))))
(TBig_Operators.semilattice_set.remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V2) @ ((V0 @ V2) @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))))))))))))))
(TBig_Operators.semilattice_set.subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cHOL.eq @ ((V0 @ ((cBig_Operators.semilattice_set.F @ V0) @ V2)) @ ((cBig_Operators.semilattice_set.F @ V0) @ V1))) @ ((cBig_Operators.semilattice_set.F @ V0) @ V1)))))))))))))
(TBig_Operators.setprod_mono_one_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1))))))))))))
(TBig_Operators.setsum_mono_zero_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1))))))))))))
(TBig_Operators.setsum_strict_mono_ex1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ (V2 @ V3))))) @ ((c==> @ ((cSet.Bex @ V0) @ (^[V3]: ((cOrderings.ord_class.less @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cOrderings.ord_class.less @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TCode_Evaluation.arity_term_of_itself,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_nibble,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_option,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.term.Abs_term_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set))) @ (V0 @ (cCode_Evaluation.Abs_term @ V2)))))) @ (V0 @ V1)))))))
(TCode_Evaluation.term.Abs_term_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cCode_Evaluation.Abs_term @ V0)) @ (cCode_Evaluation.Abs_term @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TCode_Evaluation.term.Rep_term_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cCode_Evaluation.Rep_term @ V2))))) @ (V1 @ V0))))))))
(TCode_Evaluation.term.Rep_term_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cCode_Evaluation.Rep_term @ V0)) @ (cCode_Evaluation.Rep_term @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TCode_Evaluation.term.arity_size_term,(cNat.size_class @ cTYPE))
(TCode_Evaluation.term_of_integer_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_natural_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_typerep_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_typerep_inst.term_of_typerep @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.type_definition_term,(((cTypedef.type_definition @ cCode_Evaluation.Rep_term) @ cCode_Evaluation.Abs_term) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set)))
(TCode_Numeral.integer.id_abs_transfer,((((cTransfer.fun_rel @ cHOL.eq) @ cCode_Numeral.pcr_integer) @ (^[V0]: V0)) @ cCode_Numeral.integer_of_int))
(TCode_Numeral.integer_of_nat.transfer,((((cTransfer.fun_rel @ cHOL.eq) @ cCode_Numeral.pcr_integer) @ cNat.semiring_1_class.of_nat) @ cCode_Numeral.integer_of_nat))
(TCode_Numeral.integer_of_num.transfer,((((cTransfer.fun_rel @ cHOL.eq) @ cCode_Numeral.pcr_integer) @ cNum.numeral_class.numeral) @ cCode_Numeral.integer_of_num))
(TCode_Numeral.nat_of_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cHOL.eq) @ cInt.nat) @ cCode_Numeral.nat_of_integer))
(TCode_Numeral.natural.id_abs_transfer,((((cTransfer.fun_rel @ cHOL.eq) @ cCode_Numeral.pcr_natural) @ (^[V0]: V0)) @ cCode_Numeral.natural_of_nat))
(TCode_Numeral.natural.natural_rec_def,((c== @ cCode_Numeral.natural.natural_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TCode_Numeral.num_of_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cHOL.eq) @ ((cFun.comp @ cNum.num_of_nat) @ cInt.nat)) @ cCode_Numeral.num_of_integer))
(TCode_Numeral.type_definition_integer,(((cTypedef.type_definition @ cCode_Numeral.int_of_integer) @ cCode_Numeral.integer_of_int) @ cOrderings.top_class.top))
(TCode_Numeral.type_definition_natural,(((cTypedef.type_definition @ cCode_Numeral.nat_of_natural) @ cCode_Numeral.natural_of_nat) @ cOrderings.top_class.top))
(TCode_Numeral.uminus_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_integer) @ cInt.uminus_int_inst.uminus_int) @ cCode_Numeral.uminus_integer_inst.uminus_integer))
(TComplete_Lattices.INT_insert_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: ((cSet.insert @ V2) @ (V3 @ V4))))) @ ((cSet.insert @ V2) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Partial_Order.ccpo.fixp_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.fixp @ V0) @ V1) @ V3)) @ (V0 @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V3)))))))))))))
(TDivides.mod_2_not_eq_zero_eq_one_int,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cInt.zero_int_inst.zero_int))) @ ((cHOL.eq @ ((cDivides.div_int_inst.mod_int @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cInt.one_int_inst.one_int)))))
(TDivides.mod_2_not_eq_zero_eq_one_nat,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cNat.zero_nat_inst.zero_nat))) @ ((cHOL.eq @ ((cDivides.div_nat_inst.mod_nat @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cNat.one_nat_inst.one_nat)))))
(TDivides.ring_div_class.mod_diff_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ V1)) @ ((cDivides.div_class.mod @ V2) @ V1))) @ ((c==> @ ((cHOL.eq @ ((cDivides.div_class.mod @ V3) @ V1)) @ ((cDivides.div_class.mod @ V4) @ V1))) @ ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ V0) @ V3)) @ V1)) @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ V2) @ V4)) @ V1)))))))))))))))
(TDivides.semiring_div.dvd_div_eq_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V7) @ V6)) @ V8)) @ ((cHOL.eq @ V7) @ ((V0 @ V8) @ V6)))))))))))))))))))))))))
(TDivides.semiring_div.dvd_eq_mod_eq_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V7) @ V6)) @ V4))))))))))))))))))))
(TDivides.semiring_div.dvd_mod_imp_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ ((V2 @ V7) @ V8))) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)) @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)))))))))))))))))))))))
(TDivides.semiring_div.mod_add_left_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ V7)) @ V8)) @ ((V2 @ ((V3 @ ((V2 @ V6) @ V8)) @ V7)) @ V8))))))))))))))))))))))
(TDivides.semiring_div.mod_div_trivial,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ ((V2 @ V6) @ V7)) @ V7)) @ V4)))))))))))))))))))
(TDivides.semiring_div.mod_mod_trivial,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V6) @ V7)) @ V7)) @ ((V2 @ V6) @ V7))))))))))))))))))))
(TDivides.semiring_div_class.div_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cPower.power_class.power @ ((cDivides.div_class.div @ V1) @ V0)) @ V2)) @ ((cDivides.div_class.div @ ((cPower.power_class.power @ V1) @ V2)) @ ((cPower.power_class.power @ V0) @ V2)))))))))))
(TDivides.semiring_div_class.power_mod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cPower.power_class.power @ ((cDivides.div_class.mod @ V0) @ V1)) @ V2)) @ V1)) @ ((cDivides.div_class.mod @ ((cPower.power_class.power @ V0) @ V2)) @ V1)))))))))
(TEnum.enum_option_inst.enum_ex_option,((c== @ cEnum.enum_option_inst.enum_ex_option) @ cEnum.enum_option_inst.enum_ex_option))
(TEnum.finite_1.finite_1_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cEnum.finite_1.finite_1_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cEnum.finite_1.a\<__caret__sub>1)) @ ((c==> @ ((cHOL.eq @ V2) @ V0)) @ V3))) @ V3)))))))))))
(TEnum.finite_1.finite_1_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cEnum.finite_1.finite_1_rec_set @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ cEnum.finite_1.a\<__caret__sub>1)) @ ((cHOL.eq @ V2) @ V0))))))))))
(TEnum.finite_2.finite_2_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cEnum.finite_2.finite_2_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cEnum.finite_2.a\<__caret__sub>1)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cEnum.finite_2.a\<__caret__sub>2)) @ ((c==> @ ((cHOL.eq @ V3) @ V1)) @ V4))) @ V4))))))))))))))
(TEnum.finite_2.finite_2_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cEnum.finite_2.finite_2_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cEnum.finite_2.a\<__caret__sub>1)) @ ((cHOL.eq @ V3) @ V0))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cEnum.finite_2.a\<__caret__sub>2)) @ ((cHOL.eq @ V3) @ V1)))))))))))))
(TEnum.finite_3.finite_3_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cEnum.finite_3.finite_3_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cEnum.finite_3.a\<__caret__sub>1)) @ ((c==> @ ((cHOL.eq @ V4) @ V0)) @ V5))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cEnum.finite_3.a\<__caret__sub>2)) @ ((c==> @ ((cHOL.eq @ V4) @ V1)) @ V5))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cEnum.finite_3.a\<__caret__sub>3)) @ ((c==> @ ((cHOL.eq @ V4) @ V2)) @ V5))) @ V5)))))))))))))))))
(TEnum.finite_3.finite_3_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((((cEnum.finite_3.finite_3_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_3.a\<__caret__sub>1)) @ ((cHOL.eq @ V4) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_3.a\<__caret__sub>2)) @ ((cHOL.eq @ V4) @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cEnum.finite_3.a\<__caret__sub>3)) @ ((cHOL.eq @ V4) @ V2))))))))))))))))
(TEnum.finite_4.finite_4_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cEnum.finite_4.finite_4_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>1)) @ ((c==> @ ((cHOL.eq @ V5) @ V0)) @ V6))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>2)) @ ((c==> @ ((cHOL.eq @ V5) @ V1)) @ V6))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>3)) @ ((c==> @ ((cHOL.eq @ V5) @ V2)) @ V6))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>4)) @ ((c==> @ ((cHOL.eq @ V5) @ V3)) @ V6))) @ V6))))))))))))))))))))
(TEnum.finite_4.finite_4_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((((cEnum.finite_4.finite_4_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>1)) @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>2)) @ ((cHOL.eq @ V5) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>3)) @ ((cHOL.eq @ V5) @ V2))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cEnum.finite_4.a\<__caret__sub>4)) @ ((cHOL.eq @ V5) @ V3)))))))))))))))))))
(TEnum.finite_5.finite_5_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>1)) @ ((c==> @ ((cHOL.eq @ V6) @ V0)) @ V7))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>2)) @ ((c==> @ ((cHOL.eq @ V6) @ V1)) @ V7))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>3)) @ ((c==> @ ((cHOL.eq @ V6) @ V2)) @ V7))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>4)) @ ((c==> @ ((cHOL.eq @ V6) @ V3)) @ V7))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>5)) @ ((c==> @ ((cHOL.eq @ V6) @ V4)) @ V7))) @ V7)))))))))))))))))))))))
(TEnum.finite_5.finite_5_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>1)) @ ((cHOL.eq @ V6) @ V0))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>2)) @ ((cHOL.eq @ V6) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>3)) @ ((cHOL.eq @ V6) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>4)) @ ((cHOL.eq @ V6) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cEnum.finite_5.a\<__caret__sub>5)) @ ((cHOL.eq @ V6) @ V4))))))))))))))))))))))
(TEnum.ord_finite_1_inst.less_finite_1,((c== @ cEnum.ord_finite_1_inst.less_finite_1) @ cEnum.ord_finite_1_inst.less_finite_1))
(TEnum.ord_finite_2_inst.less_finite_2,((c== @ cEnum.ord_finite_2_inst.less_finite_2) @ cEnum.ord_finite_2_inst.less_finite_2))
(TEnum.ord_finite_3_inst.less_finite_3,((c== @ cEnum.ord_finite_3_inst.less_finite_3) @ cEnum.ord_finite_3_inst.less_finite_3))
(TEquiv_Relations.UN_UN_split_split_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((((V2 @ V3) @ V4) @ V5) @ V6)))))))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: ((cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: ((((V2 @ V5) @ V6) @ V7) @ V8)))) @ V4)))) @ V3)))))))))))))
(TEquiv_Relations.UN_equiv_class_type2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cEquiv_Relations.equiv @ V2) @ V3)) @ ((c==> @ (((cEquiv_Relations.congruent2 @ V1) @ V3) @ V4)) @ ((c==> @ ((cSet.member @ V5) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ ((cSet.member @ V6) @ ((cEquiv_Relations.quotient @ V2) @ V3))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cSet.member @ V8) @ V0)) @ ((c==> @ ((cSet.member @ V9) @ V2)) @ ((cSet.member @ ((V4 @ V8) @ V9)) @ V7)))))))) @ ((cSet.member @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V5) @ (^[V8]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V6) @ (^[V9]: ((V4 @ V8) @ V9)))))) @ V7))))))))))))))))))))))))
(TExtraction.sumbool.Abs_sumbool_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cExtraction.Abs_sumbool @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set))) @ V1))))) @ V1))))))
(TExtraction.sumbool.Rep_sumbool_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cExtraction.Rep_sumbool @ V2))) @ V1)))) @ V1)))))))
(TFields.class.linordered_field.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((((((((((cRings.class.linordered_idom @ V8) @ V6) @ V7) @ V5) @ V9) @ V10) @ V4) @ V3) @ V11) @ V2)))))))))))))))))))))))))))
(TFields.class.linordered_field.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))))))))))
(TFields.division_ring_class.inverse_1,((cHOL.eq @ (cFields.inverse_class.inverse @ cGroups.one_class.one)) @ cGroups.one_class.one))
(TFields.field_class.add_divide_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ V0))))))))))
(TFields.field_class.divide_add_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.times_class.times @ V0) @ V2))) @ V0))))))))))
(TFinite_Set.comp_fun_commute.fold_rec,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V3) @ V1)) @ ((V0 @ V2) @ (((cFinite_Set.fold @ V0) @ V3) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))))))))
(TFinite_Set.comp_fun_commute_Pow_fold,(cFinite_Set.comp_fun_commute @ (^[V0]: (^[V1]: ((cLattices.sup_class.sup @ V1) @ ((cSet.image @ (cSet.insert @ V0)) @ V1))))))
(TFinite_Set.finite_Collect_bounded_ex,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (V0 @ V2))))) @ ((cHOL.eq @ (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ (V0 @ V3)) @ ((V1 @ V2) @ V3)))))))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ (V0 @ V2)) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V3]: ((V1 @ V3) @ V2))))))))))))))
(TFinite_Set.finite_conv_nat_seg_image,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cSet.image @ V2) @ (cSet.Collect @ (^[V3]: ((cNat.ord_nat_inst.less_nat @ V3) @ V1)))))))))))))
(TFinite_Set.finite_imp_inj_to_nat_seg,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ ((cSet.image @ V1) @ V0)) @ (cSet.Collect @ (^[V3]: ((cNat.ord_nat_inst.less_nat @ V3) @ V2))))) @ ((cFun.inj_on @ V1) @ V0))))))))))
(TFinite_Set.finite_set_of_finite_funs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ (cFinite_Set.finite @ (cSet.Collect @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.conj @ ((cHOL.implies @ ((cSet.member @ V4) @ V0)) @ ((cSet.member @ (V3 @ V4)) @ V1))) @ ((cHOL.implies @ (cHOL.Not @ ((cSet.member @ V4) @ V0))) @ ((cHOL.eq @ (V3 @ V4)) @ V2)))))))))))))))))
(TFinite_Set.folding_idem_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V1))) @ (V0 @ V1))))) @ (cFinite_Set.folding_idem_axioms @ V0)))))
(TFunDef.is_measure.is_measure_trivial,(call @ (^[V0]: (cFunDef.is_measure @ V0))))
(TGroups.ab_group_add.diff_eq_0_iff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ V1)) @ ((cHOL.eq @ V4) @ V5))))))))))))))))
(TGroups.ab_semigroup_add_class.add_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TGroups.ab_semigroup_add_class.add_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TGroups.ab_semigroup_add_class.add_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TGroups.ab_semigroup_add_class.axioms,(cGroups.class.ab_semigroup_add_axioms @ cGroups.plus_class.plus))
(TGroups.ab_semigroup_mult_class.intro,((c==> @ (cGroups.semigroup_mult_class @ cTYPE)) @ ((c==> @ (cGroups.class.ab_semigroup_mult_axioms @ cGroups.times_class.times)) @ (cGroups.ab_semigroup_mult_class @ cTYPE))))
(TGroups.ab_semigroup_mult_class.super,((c==> @ (cGroups.ab_semigroup_mult_class @ cTYPE)) @ (cGroups.semigroup_mult_class @ cTYPE)))
(TGroups.class.ab_group_add_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cGroups.class.ab_group_add_axioms @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V0 @ (V3 @ V4)) @ V4)) @ V1)))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V0 @ V4) @ (V3 @ V5))))))))))))))))))
(TGroups.class.ab_semigroup_add.axioms_2,(call @ (^[V0]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ (cGroups.class.ab_semigroup_add_axioms @ V0)))))
(TGroups.class.ab_semigroup_add.axioms_1,(call @ (^[V0]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ (cGroups.class.semigroup_add @ V0)))))
(TGroups.class.ab_semigroup_mult.intro,(call @ (^[V0]: ((c==> @ (cGroups.class.semigroup_mult @ V0)) @ ((c==> @ (cGroups.class.ab_semigroup_mult_axioms @ V0)) @ (cGroups.class.ab_semigroup_mult @ V0))))))
(TGroups.class.comm_monoid_diff.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ (((cGroups.class.comm_monoid_diff_axioms @ V0) @ V1) @ V2)))))))))
(TGroups.class.comm_monoid_diff.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))))
(TGroups.class.comm_monoid_mult.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cGroups.class.comm_monoid_mult_axioms @ V0) @ V1)))))))
(TGroups.class.comm_monoid_mult.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ (cGroups.class.ab_semigroup_mult @ V0)))))))
(TGroups.class.monoid_add_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))) @ ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))) @ ((cGroups.class.monoid_add_axioms @ V0) @ V1))))))))
(TGroups.comm_monoid_diff_class.axioms,(((cGroups.class.comm_monoid_diff_axioms @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus))
(TGroups.comm_monoid_mult_class.axioms,((cGroups.class.comm_monoid_mult_axioms @ cGroups.times_class.times) @ cGroups.one_class.one))
(TGroups.comm_monoid_mult_class.mult_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.one_class.one) @ V0)) @ V0))))
(TGroups.group_add.eq_neg_iff_add_eq_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V4) @ (V3 @ V5))) @ ((cHOL.eq @ ((V1 @ V4) @ V5)) @ V2))))))))))))))))
(TGroups.group_add.neg_equal_iff_equal,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ (V3 @ V4)) @ (V3 @ V5))) @ ((cHOL.eq @ V4) @ V5))))))))))))))))
(TGroups.group_add_class.diff_diff_eq2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TGroups.group_add_class.equals_zero_I,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ V1)))))))
(TGroups.group_add_class.minus_diff_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cGroups.minus_class.minus @ V1) @ V0)))))))
(TGroups.monoid_mult_class.mult_1_left,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.one_class.one) @ V0)) @ V0))))
(TGroups.semigroup_add_class.add.assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TGroups.semigroup_add_class.add_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(THilbert_Choice.Ex_inj_on_UNION_Sigma,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cFun.inj_on @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3))))) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3))))) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3))))))))))))
(THilbert_Choice.image_inv_into_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cSet.image @ V0) @ V1)) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((cHOL.eq @ ((cSet.image @ V0) @ ((cSet.image @ ((cHilbert_Choice.inv_into @ V1) @ V0)) @ V3))) @ V3))))))))))))
(THilbert_Choice.inv_into_image_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cHOL.eq @ ((cSet.image @ ((cHilbert_Choice.inv_into @ V1) @ V0)) @ ((cSet.image @ V0) @ V2))) @ V2))))))))))
(TLattices.boolean_algebra_class.intro,((c==> @ (cGroups.minus_class @ cTYPE)) @ ((c==> @ (cGroups.uminus_class @ cTYPE)) @ ((c==> @ (cLattices.bounded_lattice_class @ cTYPE)) @ ((c==> @ (cLattices.distrib_lattice_class @ cTYPE)) @ ((c==> @ ((((((cLattices.class.boolean_algebra_axioms @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cLattices.inf_class.inf) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top)) @ (cLattices.boolean_algebra_class @ cTYPE)))))))
(TLattices.boolean_algebra_class.super_4,((c==> @ (cLattices.boolean_algebra_class @ cTYPE)) @ (cLattices.distrib_lattice_class @ cTYPE)))
(TLattices.boolean_algebra_class.super_3,((c==> @ (cLattices.boolean_algebra_class @ cTYPE)) @ (cLattices.bounded_lattice_class @ cTYPE)))
(TLattices.boolean_algebra_class.super_2,((c==> @ (cLattices.boolean_algebra_class @ cTYPE)) @ (cGroups.uminus_class @ cTYPE)))
(TLattices.boolean_algebra_class.super_1,((c==> @ (cLattices.boolean_algebra_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TLattices.bounded_lattice_class.intro,((c==> @ (cLattices.lattice_class @ cTYPE)) @ ((c==> @ (cOrderings.order_bot_class @ cTYPE)) @ ((c==> @ (cOrderings.order_top_class @ cTYPE)) @ (cLattices.bounded_lattice_class @ cTYPE)))))
(TLattices.bounded_lattice_class.super_3,((c==> @ (cLattices.bounded_lattice_class @ cTYPE)) @ (cOrderings.order_top_class @ cTYPE)))
(TLattices.bounded_lattice_class.super_2,((c==> @ (cLattices.bounded_lattice_class @ cTYPE)) @ (cOrderings.order_bot_class @ cTYPE)))
(TLattices.bounded_lattice_class.super_1,((c==> @ (cLattices.bounded_lattice_class @ cTYPE)) @ (cLattices.lattice_class @ cTYPE)))
(TLattices.class.boolean_algebra.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((((cLattices.class.boolean_algebra_axioms @ V6) @ V7) @ V0) @ V3) @ V4) @ V5)) @ ((((((((cLattices.class.boolean_algebra @ V6) @ V7) @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))))))))
(TLattices.class.bounded_lattice.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cOrderings.class.order_bot @ V4) @ V1) @ V2)) @ ((c==> @ (((cOrderings.class.order_top @ V1) @ V2) @ V5)) @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))))
(TLattices.class.distrib_lattice.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cLattices.class.distrib_lattice_axioms @ V0) @ V3)) @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3))))))))))))
(TLattices.class.semilattice_inf.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cLattices.class.semilattice_inf_axioms @ V2) @ V0)) @ (((cLattices.class.semilattice_inf @ V2) @ V0) @ V1))))))))))
(TLattices.class.semilattice_sup.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cLattices.class.semilattice_sup_axioms @ V2) @ V0)) @ (((cLattices.class.semilattice_sup @ V2) @ V0) @ V1))))))))))
(TLattices.distrib_lattice_class.intro,((c==> @ (cLattices.lattice_class @ cTYPE)) @ ((c==> @ ((cLattices.class.distrib_lattice_axioms @ cLattices.inf_class.inf) @ cLattices.sup_class.sup)) @ (cLattices.distrib_lattice_class @ cTYPE))))
(TLattices.distrib_lattice_class.super,((c==> @ (cLattices.distrib_lattice_class @ cTYPE)) @ (cLattices.lattice_class @ cTYPE)))
(TLattices.linorder_class.max.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.linorder_class.max.boundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V2)) @ V1))))))))))
(TLattices.linorder_class.min.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.linorder_class.min.boundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2)))))))))))
(TLattices.semilattice_inf.inf_absorb1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ V3))))))))))))))
(TLattices.semilattice_inf.inf_absorb2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V4) @ V3)) @ V3))))))))))))))
(TLattices.semilattice_inf.inf_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))))))))))
(TLattices.semilattice_inf_class.intro,((c==> @ (cLattices.inf_class @ cTYPE)) @ ((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ ((cLattices.class.semilattice_inf_axioms @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq)) @ (cLattices.semilattice_inf_class @ cTYPE)))))
(TLattices.semilattice_inf_class.super_2,((c==> @ (cLattices.semilattice_inf_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TLattices.semilattice_inf_class.super_1,((c==> @ (cLattices.semilattice_inf_class @ cTYPE)) @ (cLattices.inf_class @ cTYPE)))
(TLattices.semilattice_neutr_order_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cLattices.semilattice_neutr_order @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cLattices.semilattice_neutr @ V0) @ V1)) @ (((cLattices.semilattice_order @ V0) @ V2) @ V3))))))))))))
(TLattices.semilattice_order.order_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ V3) @ ((V0 @ V3) @ V4)))))))))))))))
(TLattices.semilattice_sup.sup_absorb1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V4) @ V3)) @ V4))))))))))))))
(TLattices.semilattice_sup.sup_absorb2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ V4))))))))))))))
(TLattices.semilattice_sup.sup_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))))))))))
(TLattices.semilattice_sup_class.intro,((c==> @ (cLattices.sup_class @ cTYPE)) @ ((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ ((cLattices.class.semilattice_sup_axioms @ cLattices.sup_class.sup) @ cOrderings.ord_class.less_eq)) @ (cLattices.semilattice_sup_class @ cTYPE)))))
(TLattices.semilattice_sup_class.super_2,((c==> @ (cLattices.semilattice_sup_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TLattices.semilattice_sup_class.super_1,((c==> @ (cLattices.semilattice_sup_class @ cTYPE)) @ (cLattices.sup_class @ cTYPE)))
(TLazy_Sequence.iterate_upto_graph_def,((c== @ cLazy_Sequence.iterate_upto_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))) @ (cHOL.induct_forall @ (^[V7]: ((cHOL.induct_implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))))))))))))))))
(TLazy_Sequence.iterate_upto_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.iterate_upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ V2)))))))))))) @ V2)))))))))
(TLazy_Sequence.iterate_upto_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.iterate_upto_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V3))))))))))))))))))
(TLazy_Sequence.lazy_sequence.eq.simps,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TLazy_Sequence.lazy_sequence.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1)))))))
(TLazy_Sequence.small_lazy'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ V1))) @ ((cLazy_Sequence.small_lazy'_rel @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))) @ ((cProduct_Type.Pair @ V0) @ V1))))))))
(TLazy_Sequence.small_lazy_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cLazy_Sequence.small_lazy_class @ cTYPE)))
(TLazy_Sequence.small_lazy_class.super,((c==> @ (cLazy_Sequence.small_lazy_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TLazy_Sequence.small_lazy_list.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V2)) @ (V0 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TLazy_Sequence.small_lazy_list.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cLazy_Sequence.small_lazy_class.small_lazy @ V0)) @ V1)) @ ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy_list_rel) @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))) @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (cLazy_Sequence.single @ ((cList.list.Cons @ V4) @ V5))))))) @ cLazy_Sequence.empty)))) @ ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy_list_rel) @ V3)) @ V2)))))) @ V2))))))))))
(TLazy_Sequence.small_lazy_list.psimps,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy_list_rel) @ V0)) @ ((cHOL.eq @ (cLazy_Sequence.small_lazy_class.small_lazy @ V0)) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (cLazy_Sequence.single @ ((cList.list.Cons @ V1) @ V2))))))) @ cLazy_Sequence.empty)))))))
(TLifting.functional_converse_relation,(call @ (^[V0]: ((c==> @ (cLifting.left_unique @ V0)) @ ((c==> @ (cTransfer.right_total @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.Ex1 @ (^[V2]: ((V0 @ V2) @ V1))))))))))
(TLifting_Option.left_total_option_rel,(call @ (^[V0]: ((c==> @ (cLifting.left_total @ V0)) @ (cLifting.left_total @ (cLifting_Option.option_rel @ V0))))))
(TLifting_Product.left_unique_prod_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLifting.left_unique @ V0)) @ ((c==> @ (cLifting.left_unique @ V1)) @ (cLifting.left_unique @ ((cLifting_Product.prod_rel @ V0) @ V1)))))))))
(TLifting_Product.right_total_prod_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_total @ V0)) @ ((c==> @ (cTransfer.right_total @ V1)) @ (cTransfer.right_total @ ((cLifting_Product.prod_rel @ V0) @ V1)))))))))
(TList.ab_group_add.uminus_listsum_map,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V4) @ V5)))) @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ ((cFun.comp @ V3) @ V4)) @ V5)))))))))))))))))
(TList.linorder.distinct_insort_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cList.distinct @ V2)) @ (cList.distinct @ ((((cList.linorder.insort_insert_key @ V0) @ V3) @ V4) @ V2)))))))))))))))
(TList.linorder.insort_insert_key_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cSet.member @ (V2 @ V3)) @ ((cSet.image @ V2) @ (cList.set @ V4)))) @ ((cHOL.eq @ ((((cList.linorder.insort_insert_key @ V0) @ V2) @ V3) @ V4)) @ V4))))))))))))))
(TList.linorder.sorted_equals_nth_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted @ V0) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ (cNat.size_class.size @ V2))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V4) @ V3)) @ ((V0 @ ((cList.nth @ V2) @ V4)) @ ((cList.nth @ V2) @ V3)))))))))))))))))
(TList.linorder.sorted_list_of_set_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cList.linorder.sorted_list_of_set @ V0)) @ ((cFinite_Set.folding.F @ ((cList.linorder.insort_key @ V0) @ (^[V2]: V2))) @ cList.list.Nil))))))))
(TList.linorder_class.foldr_max_sorted,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ V0))) @ ((cHOL.eq @ (((cList.foldr @ cOrderings.ord_class.max) @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cList.list.Nil)) @ V1) @ ((cOrderings.ord_class.max @ ((cList.nth @ V0) @ cNat.zero_nat_inst.zero_nat)) @ V1)))))))))
(TList.linorder_class.insort_key.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cList.linorder_class.insort_key @ V0) @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2))) @ ((cList.list.Cons @ V1) @ ((cList.list.Cons @ V2) @ V3))) @ ((cList.list.Cons @ V2) @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V3)))))))))))))
(TList.linorder_class.insort_key.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cList.linorder_class.insort_key @ V0) @ V1) @ cList.list.Nil)) @ ((cList.list.Cons @ V1) @ cList.list.Nil)))))))
(TList.linorder_class.insort_left_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.linorder_class.insort_key @ (^[V3]: V3)) @ V0) @ (((cList.linorder_class.insort_key @ (^[V3]: V3)) @ V1) @ V2))) @ (((cList.linorder_class.insort_key @ (^[V3]: V3)) @ V1) @ (((cList.linorder_class.insort_key @ (^[V3]: V3)) @ V0) @ V2))))))))))
(TList.linorder_class.sorted_dropWhile,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ ((cList.dropWhile @ V1) @ V0))))))))
(TList.linorder_class.sorted_nth_monoI,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cList.nth @ V0) @ V1)) @ ((cList.nth @ V0) @ V2))))))))) @ (cList.linorder_class.sorted @ V0)))))
(TList.linorder_class.sorted_takeWhile,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ ((cList.takeWhile @ V1) @ V0))))))))
(TList.listrel_subset_rtrancl_listrel1,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cList.listrel @ V0)) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V0))))))
(TList.monoid_add.length_product_lists,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (cNat.size_class.size @ (cList.product_lists @ V2))) @ (((cList.foldr @ cNat.times_nat_inst.times_nat) @ ((cList.map @ cNat.size_class.size) @ V2)) @ cNat.one_nat_inst.one_nat))))))))))
(TList.monoid_add_class.listsum_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.append @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cList.monoid_add_class.listsum @ V0)) @ (cList.monoid_add_class.listsum @ V1))))))))
(TList.setsum_set_upt_conv_listsum_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ (cList.set @ ((cList.upt @ V1) @ V2)))) @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ ((cList.upt @ V1) @ V2)))))))))))
(TList.transfer_nat_int_list_functions_2,((cHOL.eq @ cList.list.Nil) @ (cList.return_list @ cList.list.Nil)))
(TList.transfer_nat_int_list_functions_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.append @ V0) @ V1)) @ (cList.return_list @ ((cList.append @ (cList.embed_list @ V0)) @ (cList.embed_list @ V1)))))))))
(TMain.sumbool.narrowing_sumbool.simps,((cHOL.eq @ cMain.narrowing_sumbool_inst.narrowing_sumbool) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cExtraction.sumbool.Left)) @ (cQuickcheck_Narrowing.cons @ cExtraction.sumbool.Right))))
(TMap.restrict_complement_singleton_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMap.restrict_map @ V0) @ (cGroups.uminus_class.uminus @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ (((cFun.fun_upd @ V0) @ V1) @ cOption.option.None)))))))
(TNat.arity_comm_semiring_1_cancel_nat,(cRings.comm_semiring_1_cancel_class @ cTYPE))
(TNat.class.semiring_char_0_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cNat.class.semiring_char_0_axioms @ V0) @ V1) @ V2)) @ ((cFun.inj_on @ (((cNat.semiring_1.of_nat @ V0) @ V1) @ V2)) @ cOrderings.top_class.top)))))))))
(TNat.linordered_idom_class.abs_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TNat.linordered_semidom.of_nat_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6)) @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V7))) @ ((cNat.ord_nat_inst.less_eq_nat @ V6) @ V7))))))))))))))))))))
(TNat.semiring_char_0_class.inj_of_nat,((cFun.inj_on @ cNat.semiring_1_class.of_nat) @ cOrderings.top_class.top))
(TNitpick.pair_box.Abs_pair_box_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set))) @ (V0 @ (cNitpick.Abs_pair_box @ V2)))))) @ (V0 @ V1)))))))
(TNitpick.pair_box.Abs_pair_box_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cNitpick.Abs_pair_box @ V0)) @ (cNitpick.Abs_pair_box @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TNitpick.pair_box.Rep_pair_box_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cNitpick.Rep_pair_box @ V2))))) @ (V1 @ V0))))))))
(TNitpick.pair_box.Rep_pair_box_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNitpick.Rep_pair_box @ V0)) @ (cNitpick.Rep_pair_box @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNitpick.pair_box.arity_size_pair_box,(cNat.size_class @ cTYPE))
(TNitpick.partial_term_of_fun_box_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TNitpick.random_word_inst.random_word,((c== @ cNitpick.random_word_inst.random_word) @ cNitpick.random_word_inst.random_word))
(TNum.linordered_idom.sub_non_negative,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ V3) @ (((((cNum.neg_numeral.sub @ V1) @ V6) @ V7) @ V10) @ V11))) @ ((cNum.ord_num_inst.less_eq_num @ V11) @ V10))))))))))))))))))))))))))))
(TNum.linordered_idom.sub_non_positive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ (((((cNum.neg_numeral.sub @ V1) @ V6) @ V7) @ V10) @ V11)) @ V3)) @ ((cNum.ord_num_inst.less_eq_num @ V10) @ V11))))))))))))))))))))))))))))
(TNum.neg_numeral.diff_numeral_special_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5)) @ V4)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ ((cNum.plus_num_inst.plus_num @ V5) @ cNum.num.One)))))))))))))))))
(TNum.neg_numeral.diff_numeral_special_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5)) @ V4)) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ cNum.num.One))))))))))))))))
(TNum.neg_numeral.diff_numeral_special_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))) @ (((cNum.numeral.numeral @ V4) @ V1) @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V5)))))))))))))))))
(TNum.neg_numeral.diff_numeral_special_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ (((cNum.numeral.numeral @ V4) @ V1) @ V5))) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ cNum.num.One) @ V5))))))))))))))))
(TNum.neg_numeral_class.is_num.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (V1 @ cGroups.one_class.one)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (cNum.neg_numeral_class.is_num @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cGroups.uminus_class.uminus @ V2))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cNum.neg_numeral_class.is_num @ V2)) @ ((c==> @ (V1 @ V2)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V3)) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cGroups.plus_class.plus @ V2) @ V3))))))))))) @ (V1 @ V0))))))))))
(TNum.neg_numeral_class.is_num_numeral,(call @ (^[V0]: (cNum.neg_numeral_class.is_num @ (cNum.numeral_class.numeral @ V0)))))
(TNum.numeral.one_plus_numeral_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.class.numeral @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ (((cNum.numeral.numeral @ V1) @ V0) @ V2))) @ ((V0 @ (((cNum.numeral.numeral @ V1) @ V0) @ V2)) @ V1))))))))))
(TNum.ring_1_class.not_iszero_Numeral1,(cHOL.Not @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ cNum.num.One))))
(TNum.ring_char_0.eq_neg_numeral_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ V3))))))))))))))))))
(TNum.ring_char_0.eq_neg_numeral_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)))))))))))))))))))
(TNum.ring_char_0.eq_neg_numeral_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ V0))))))))))))))))))
(TNum.ring_char_0.eq_neg_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)))))))))))))))))))
(TNum.ring_char_0.eq_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V7)))))))))))))))))))))
(TNum.ring_char_0.eq_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7)))))))))))))))))))))
(TNum.ring_char_0.eq_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7))) @ ((cHOL.eq @ V6) @ V7))))))))))))))))))))
(TNum.ring_char_0.neg_numeral_neq_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ V3))))))))))))))))))
(TNum.ring_char_0.zero_neq_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)))))))))))))))))))
(TNum.semiring_char_0.eq_numeral_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)))))))))))))))
(TNum.semiring_char_0.eq_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)) @ V3))))))))))))))
(TNum.semiring_char_0.eq_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ (((cNum.numeral.numeral @ V0) @ V2) @ V4))) @ ((cHOL.eq @ cNum.num.One) @ V4))))))))))))))
(TNum.semiring_char_0.eq_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)) @ V0)) @ ((cHOL.eq @ V4) @ cNum.num.One))))))))))))))
(TNum.semiring_char_0.eq_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V5))) @ ((cHOL.eq @ V4) @ V5))))))))))))))))
(TNum.semiring_char_0.numeral_neq_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)) @ V3))))))))))))))
(TNum.semiring_char_0.zero_neq_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)))))))))))))))
(TNumeral_Simprocs.nat_mult_eq_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TNumeral_Simprocs.nat_mult_le_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2))))))))))
(TOption.option.option_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOption.option.option_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.Leaf @ V2)))))) @ (V1 @ V0)))))))))
(TOrderings.class.dense_linorder.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.dense_order @ V0) @ V1)) @ ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cOrderings.class.dense_linorder @ V0) @ V1))))))))
(TOrderings.class.order_bot_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.order_bot_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((V1 @ V0) @ V2)))))))))
(TOrderings.class.order_top_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.order_top_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TOrderings.class.wellorder_axioms_def,(call @ (^[V0]: ((c== @ (cOrderings.class.wellorder_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ (cHOL.All @ (^[V3]: ((cHOL.implies @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))))))
(TOrderings.dense_linorder_class.intro,((c==> @ (cOrderings.dense_order_class @ cTYPE)) @ ((c==> @ (cOrderings.linorder_class @ cTYPE)) @ (cOrderings.dense_linorder_class @ cTYPE))))
(TOrderings.dense_linorder_class.super_2,((c==> @ (cOrderings.dense_linorder_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE)))
(TOrderings.dense_linorder_class.super_1,((c==> @ (cOrderings.dense_linorder_class @ cTYPE)) @ (cOrderings.dense_order_class @ cTYPE)))
(TOrderings.linorder.less_max_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V2) @ (((cOrderings.ord.max @ V0) @ V3) @ V4))) @ ((cHOL.disj @ ((V1 @ V2) @ V3)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.linorder.max_less_iff_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ (((cOrderings.ord.max @ V0) @ V2) @ V3)) @ V4)) @ ((cHOL.conj @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))))))))
(TOrderings.linorder.min_less_iff_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ V2) @ (((cOrderings.ord.min @ V0) @ V3) @ V4))) @ ((cHOL.conj @ ((V1 @ V2) @ V3)) @ ((V1 @ V2) @ V4)))))))))))))))
(TOrderings.linorder.min_less_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((V1 @ (((cOrderings.ord.min @ V0) @ V2) @ V3)) @ V4)) @ ((cHOL.disj @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))))))))
(TOrderings.linorder_class.less_linear,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.linorder_class.max_of_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ (V0 @ V1)) @ (V0 @ V2))) @ (V0 @ ((cOrderings.ord_class.max @ V1) @ V2)))))))))))
(TOrderings.linorder_class.min_of_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ (V0 @ V1)) @ (V0 @ V2))) @ (V0 @ ((cOrderings.ord_class.min @ V1) @ V2)))))))))))
(TOrderings.no_bot_class.no_bot_axioms,((cOrderings.class.no_bot @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.no_top_class.no_top_axioms,((cOrderings.class.no_top @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.ord_bool_inst.less_eq_bool,((c== @ cOrderings.ord_bool_inst.less_eq_bool) @ cOrderings.ord_bool_inst.less_eq_bool))
(TOrderings.order_bot_class.bot_unique,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TOrderings.order_class.Least_equality,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cHOL.eq @ (cOrderings.ord_class.Least @ V0)) @ V1))))))))
(TOrderings.order_top_class.top_unique,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ V0)) @ ((cHOL.eq @ V0) @ cOrderings.top_class.top)))))
(TOrderings.preorder.less_imp_not_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.preorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ (cHOL.Not @ ((V1 @ V3) @ V2))) @ cHOL.True))))))))))))
(TOrderings.preorder_class.less_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TOrderings.preorder_class.less_irrefl,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V0)))))
(TOrderings.preorder_class.order_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.wellorder_class.LeastI2_ex,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Ex @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))) @ (V1 @ (cOrderings.ord_class.Least @ V0)))))))))
(TPartial_Function.fixp_induct_tailrec,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (call @ (^[V8]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ V0))) @ (cPartial_Function.flat_ord @ V0)) @ (^[V9]: ((V1 @ (V2 @ (V3 @ V9))) @ V8)))))) @ ((c==> @ ((c== @ V4) @ (V3 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ V0))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ V0))) @ (^[V8]: (V1 @ (V2 @ (V3 @ V8)))))))) @ ((c==> @ (call @ (^[V8]: ((cHOL.eq @ (V1 @ (V3 @ V8))) @ V8)))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((cHOL.eq @ ((V1 @ V8) @ V11)) @ V12)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V12) @ V0))) @ ((V5 @ V11) @ V12)))))))) @ ((c==> @ ((cHOL.eq @ ((V1 @ (V2 @ V8)) @ V9)) @ V10)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V10) @ V0))) @ ((V5 @ V9) @ V10))))))))))) @ ((c==> @ ((cHOL.eq @ ((V1 @ V4) @ V6)) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V7) @ V0))) @ ((V5 @ V6) @ V7))))))))))))))))))))))))
(TPartial_Function.flat_interpretation,(call @ (^[V0]: ((cPartial_Function.partial_function_definitions @ (cPartial_Function.flat_ord @ V0)) @ (cPartial_Function.flat_lub @ V0)))))
(TPartial_Function.option.fixp_rule_uc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (^[V5]: ((V0 @ (V1 @ (V2 @ V5))) @ V4)))))) @ ((c==> @ ((c== @ V3) @ (V2 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (^[V4]: (V0 @ (V1 @ (V2 @ V4)))))))) @ ((c==> @ (call @ (^[V4]: ((cHOL.eq @ (V2 @ (V0 @ V4))) @ V4)))) @ ((cHOL.eq @ V3) @ (V1 @ V3))))))))))))))
(TPartial_Function.tailrec.leq_antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ V0) @ V1)) @ ((c==> @ (((cPartial_Function.flat_ord @ cHOL.undefined) @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TPower.comm_semiring_1.dvd_power_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V4) @ V5)) @ (((cRings.dvd.dvd @ V0) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V6)) @ ((((cPower.power.power @ V1) @ V0) @ V5) @ V6)))))))))))))))))))
(TPower.linordered_idom.zero_le_power2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ V3) @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))))))))))))))))
(TPower.monoid_mult.funpow_times_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((cNat.compow @ (V2 @ V3)) @ (V1 @ V3))) @ (V1 @ ((((cPower.power.power @ V0) @ V1) @ V3) @ (V2 @ V3))))))))))))))
(TPower.monoid_mult.power_numeral_even,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V3)))) @ ((cHOL.Let @ ((((cPower.power.power @ V0) @ V1) @ V2) @ (cNum.numeral_class.numeral @ V3))) @ (^[V4]: ((V1 @ V4) @ V4))))))))))))))
(TPower.monoid_mult_class.power_odd_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ ((cPower.power_class.power @ V0) @ V1)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TPower.ring_1_class.power_minus1_even,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ cGroups.one_class.one))))
(TPower.semiring_numeral.power_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ (((cNum.numeral.numeral @ V0) @ V2) @ V3)) @ (cNum.numeral_class.numeral @ V4))) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.pow @ V3) @ V4)))))))))))))))
(TPredicate.equal_pred_inst.equal_pred,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TPredicate.iterate_upto_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPredicate.iterate_upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((cPredicate.iterate_upto_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (cPredicate.Seq @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cPredicate.seq.Empty) @ ((cPredicate.seq.Insert @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TPredicate.minus_pred_inst.minus_pred,((c== @ cPredicate.minus_pred_inst.minus_pred) @ cPredicate.minus_pred_inst.minus_pred))
(TPredicate.ord_pred_inst.less_eq_pred,((c== @ cPredicate.ord_pred_inst.less_eq_pred) @ cPredicate.ord_pred_inst.less_eq_pred))
(TPredicate.seq.size_seq_inst.size_seq,((c== @ cPredicate.seq.size_seq_inst.size_seq) @ cPredicate.seq.size_seq_inst.size_seq))
(TPredicate_Compile.contains_pred_notI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cPredicate_Compile.contains @ V0) @ V1))) @ ((cPredicate.eval @ (cPredicate.not_pred @ ((cPredicate_Compile.contains_pred @ V0) @ V1))) @ cProduct_Type.Unity)))))))
(TProduct_Type.bool.bool_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cProduct_Type.bool.bool_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cHOL.True)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cHOL.False)) @ ((c==> @ ((cHOL.eq @ V3) @ V1)) @ V4))) @ V4))))))))))))))
(TProduct_Type.bool.bool_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cProduct_Type.bool.bool_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cHOL.True)) @ ((cHOL.eq @ V3) @ V0))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cHOL.False)) @ ((cHOL.eq @ V3) @ V1)))))))))))))
(TProduct_Type.prod.prod_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cProduct_Type.prod.prod_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V2) @ ((V0 @ V4) @ V5))) @ V3))))))) @ V3)))))))))))
(TProduct_Type.prod.prod_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cProduct_Type.prod.prod_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.eq @ V2) @ ((V0 @ V3) @ V4)))))))))))))))
(TProduct_Type.split_paired_Ball_Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.Ball @ ((cProduct_Type.Sigma @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ (V1 @ V3)) @ (^[V4]: (V2 @ ((cProduct_Type.Pair @ V3) @ V4))))))))))))))
(TProduct_Type.unit.unit_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cProduct_Type.unit.unit_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cProduct_Type.Unity)) @ ((c==> @ ((cHOL.eq @ V2) @ V0)) @ V3))) @ V3)))))))))))
(TProduct_Type.unit.unit_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cProduct_Type.unit.unit_rec_set @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ cProduct_Type.Unity)) @ ((cHOL.eq @ V2) @ V0))))))))))
(TQuickcheck_Exhaustive.cps_single_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.cps_single @ V0)) @ (^[V1]: (V1 @ V0))))))
(TQuickcheck_Exhaustive.unknown.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Exhaustive.unknown.Known @ V2))))) @ (V0 @ V1))))))))
(TQuickcheck_Exhaustive.unknown.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.unknown.Known @ V0)) @ (cQuickcheck_Exhaustive.unknown.Known @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.unknown.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Exhaustive.unknown.Known @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TQuickcheck_Exhaustive.unknown.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ (V0 @ V1))) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V3) @ (cQuickcheck_Exhaustive.unknown.Known @ V4))) @ (V0 @ (V2 @ V4))))))))))))))))
(TQuickcheck_Narrowing.arity_type_cfun,(cHOL.type_class @ cTYPE))
(TQuickcheck_Narrowing.arity_type_ffun,(cHOL.type_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero_def,((c== @ cQuickcheck_Narrowing.around_zero) @ (^[V0]: (cQuickcheck_Narrowing.around_zero_sumC @ V0))))
(TQuickcheck_Narrowing.conv_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.conv_rel @ V0) @ V1)) @ ((V2 @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.eval_cfun.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.eval_cfun @ (cQuickcheck_Narrowing.cfun.Constant @ V0)) @ V1)) @ V0))))))
(TQuickcheck_Narrowing.eval_ffun.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cQuickcheck_Narrowing.eval_ffun @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ V3)) @ (((cHOL.If @ ((cHOL.eq @ V3) @ V0)) @ V1) @ ((cQuickcheck_Narrowing.eval_ffun @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.eval_ffun.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.eval_ffun @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ V1)) @ V0))))))
(TQuickcheck_Narrowing.ffun.Update_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cQuickcheck_Narrowing.ffun.Update @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.Abs_ffun @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V0))) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V1))) @ (cQuickcheck_Narrowing.Rep_ffun @ V2)))))))))))))
(TQuickcheck_Narrowing.non_empty.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ V1)))) @ V1))))))
(TQuickcheck_Narrowing.non_empty.elims_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cQuickcheck_Narrowing.non_empty @ V0))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ ((c==> @ (cHOL.Not @ (cHOL.Not @ (cList.null @ V2)))) @ V1))))) @ V1)))))))
(TQuickcheck_Narrowing.non_empty.elims_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.non_empty @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ ((c==> @ (cHOL.Not @ (cList.null @ V2))) @ V1))))) @ V1)))))))
(TQuickcheck_Narrowing.non_empty.elims_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cQuickcheck_Narrowing.non_empty @ V0)) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ ((c==> @ ((cHOL.eq @ V1) @ (cHOL.Not @ (cList.null @ V3)))) @ V2))))) @ V2)))))))))
(TQuickcheck_Narrowing.non_empty.simps,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.non_empty @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0))) @ (cHOL.Not @ (cList.null @ V0))))))
(TQuickcheck_Narrowing.property.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (V0 @ (V3 @ V5))))) @ (V0 @ (((cQuickcheck_Narrowing.property.Universal @ V2) @ V3) @ V4)))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (V0 @ (V3 @ V5))))) @ (V0 @ (((cQuickcheck_Narrowing.property.Existential @ V2) @ V3) @ V4)))))))))) @ ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Narrowing.property.Property @ V2))))) @ (V0 @ V1)))))))))
(TQuickcheck_Narrowing.property.inject_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (cQuickcheck_Narrowing.property.Property @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.property.inject_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.property.inject_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.property.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Narrowing.property.property_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Universal @ V5) @ V6) @ V7))) @ (cHOL.Not @ (V0 @ (((V1 @ V5) @ V6) @ V7))))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Existential @ V5) @ V6) @ V7))) @ (cHOL.Not @ (V0 @ (((V2 @ V5) @ V6) @ V7))))))))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cQuickcheck_Narrowing.property.Property @ V5))) @ (cHOL.Not @ (V0 @ (V3 @ V5)))))))))))))))))))))
(TQuickcheck_Narrowing.property.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Narrowing.property.property_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Universal @ V5) @ V6) @ V7))) @ (V0 @ (((V1 @ V5) @ V6) @ V7)))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Existential @ V5) @ V6) @ V7))) @ (V0 @ (((V2 @ V5) @ V6) @ V7)))))))))) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cQuickcheck_Narrowing.property.Property @ V5))) @ (V0 @ (V3 @ V5)))))))))))))))))))
(TQuickcheck_Narrowing.random_cfun_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Narrowing.random_aux_cfun @ V0) @ V0)))))
(TQuickcheck_Narrowing.random_ffun_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Narrowing.random_aux_ffun @ V0) @ V0)))))
(TQuickcheck_Random.random_aux_num_def,((c== @ cQuickcheck_Random.random_aux_num) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cNum.num.One) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (V2 @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNum.num.Bit0) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V5)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (V2 @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNum.num.Bit1) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V5)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cNum.num.One) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_seq_def,((c== @ cQuickcheck_Random.random_aux_seq) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cPredicate.seq.Empty) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.seq.Insert) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil)))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (V2 @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.seq.Join) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cPredicate.seq.Empty) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.seq.Insert) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ cList.list.Nil))))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_set_def,((c== @ cQuickcheck_Random.random_aux_set) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ cList.list.Nil))))) @ (^[V1]: (^[V2]: (^[V3]: (cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V4]: ((cProduct_Type.scomp @ (V2 @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V5)))))))) @ cList.list.Nil)))))))) @ V0))))
(TQuickcheck_Random.random_aux_sum_def,((c== @ cQuickcheck_Random.random_aux_sum) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inl) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inr) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil)))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inl) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inr) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil)))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_class.intro,((c==> @ (cTyperep.typerep_class @ cTYPE)) @ (cQuickcheck_Random.random_class @ cTYPE)))
(TQuickcheck_Random.random_class.super,((c==> @ (cQuickcheck_Random.random_class @ cTYPE)) @ (cTyperep.typerep_class @ cTYPE)))
(TQuickcheck_Random.random_integer_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_integer_inst.random_integer @ V0)) @ ((cProduct_Type.scomp @ (cRandom.range @ ((cCode_Numeral.plus_natural_inst.plus_natural @ ((cCode_Numeral.times_natural_inst.times_natural @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)) @ cCode_Numeral.one_natural_inst.one_natural))) @ (^[V1]: (cProduct_Type.Pair @ ((cHOL.Let @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V0) @ V1)) @ (cCode_Numeral.integer_of_natural @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ V0))) @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ (cCode_Numeral.integer_of_natural @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ V1))))) @ (^[V2]: ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V2))))))))))))
(TQuickcheck_Random.random_literal_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_literal_inst.random_literal @ V0)) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ (cString.STR @ cList.list.Nil)) @ (^[V1]: (cCode_Evaluation.term_of_literal_inst.term_of_literal @ (cString.STR @ cList.list.Nil)))))))))
(TQuickcheck_Random.random_natural_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_natural_inst.random_natural @ V0)) @ ((cProduct_Type.scomp @ (cRandom.range @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (^[V1]: (cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ (^[V2]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V1))))))))))
(TQuickcheck_Random.random_typerep_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_typerep_inst.random_typerep @ V0)) @ ((cQuickcheck_Random.random_aux_typerep @ ((cOrderings.ord_class.max @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ V0)))))
(TRandom_Sequence.Random_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRandom_Sequence.Random_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cRandom_Sequence.Random_graph @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_eq_natural @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (cProduct_Type.Pair @ cLimited_Sequence.empty)) @ ((cProduct_Type.scomp @ (V4 @ V6)) @ (^[V7]: ((cProduct_Type.scomp @ ((V3 @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ V6)) @ (^[V8]: (cProduct_Type.Pair @ ((cLimited_Sequence.union @ (cLimited_Sequence.single @ (cProduct_Type.fst @ V7))) @ V8)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TRandom_Sequence.neg_iterate_upto_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRandom_Sequence.neg_iterate_upto @ V0) @ V1) @ V2)) @ (^[V3]: (^[V4]: (^[V5]: (((cLimited_Sequence.neg_iterate_upto @ V0) @ V1) @ V2))))))))))))
(TRandom_Sequence.pos_iterate_upto_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRandom_Sequence.pos_iterate_upto @ V0) @ V1) @ V2)) @ (^[V3]: (^[V4]: (^[V5]: (((cLimited_Sequence.pos_iterate_upto @ V0) @ V1) @ V2))))))))))))
(TRecord.arity_equal_tuple_isomorphism,(cHOL.equal_class @ cTYPE))
(TRecord.typerep_tuple_isomorphism_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))))
(TRelation.comp_fun_commute_Image_fold,(call @ (^[V0]: (cFinite_Set.comp_fun_commute @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (^[V3]: (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ ((cSet.insert @ V2) @ V3)) @ V3)))))))))
(TRings.class.comm_semiring_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRings.class.comm_semiring_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V1 @ ((V0 @ V2) @ V3)) @ V4)) @ ((V0 @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))))))))
(TRings.class.linordered_semidom.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V4) @ V5) @ V1) @ V2)) @ ((c==> @ (((cRings.class.linordered_semidom_axioms @ V1) @ V3) @ V5)) @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))))
(TRings.class.ordered_comm_ring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cRings.class.ordered_comm_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (((((cRings.class.ordered_comm_semiring @ V0) @ V5) @ V6) @ V1) @ V4)))))))))))))))))
(TRings.class.ordered_comm_ring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cRings.class.ordered_comm_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))))
(TRings.class.semiring_0_cancel.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.semiring_0_cancel @ V0) @ V1) @ V2)) @ ((cRings.class.semiring @ V0) @ V2)))))))))
(TRings.class.semiring_0_cancel.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.semiring_0_cancel @ V0) @ V1) @ V2)) @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)))))))))
(TRings.class.semiring_1_cancel.axioms_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.zero_neq_one @ V2) @ V1)))))))))))
(TRings.class.semiring_1_cancel.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.semiring @ V0) @ V3)))))))))))
(TRings.class.semiring_1_cancel.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.monoid_mult @ V2) @ V3)))))))))))
(TRings.class.semiring_1_cancel.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)))))))))))
(TRings.comm_semiring_1.dvd_0_left_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cRings.dvd.dvd @ V0) @ V3) @ V4)) @ ((cHOL.eq @ V4) @ V3))))))))))))))
(TRings.comm_semiring_1.dvd_mult_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ ((V0 @ V4) @ V5)) @ V6)) @ (((cRings.dvd.dvd @ V0) @ V5) @ V6))))))))))))))))))
(TRings.comm_semiring_1.dvd_triv_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (((cRings.dvd.dvd @ V0) @ V4) @ ((V0 @ V5) @ V4))))))))))))))))
(TRings.comm_semiring_1_class.dvd_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.times_class.times @ V2) @ V1))))))))))
(TRings.comm_semiring_1_class.dvd_refl,(call @ (^[V0]: ((cRings.dvd_class.dvd @ V0) @ V0))))
(TRings.linordered_idom_class.abs_mult,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cGroups.times_class.times @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))))))))
(TRings.linordered_idom_class.sgn_less,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.sgn_class.sgn @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TRings.linordered_ring.zero_le_square,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((V4 @ V3) @ ((V7 @ V8) @ V8))))))))))))))))))))))
(TRings.linordered_semidom.less_1_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((c==> @ ((V5 @ V3) @ V7)) @ ((V5 @ V3) @ ((V2 @ V6) @ V7))))))))))))))))))))))
(TRings.linordered_semidom.zero_le_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V1) @ V3)))))))))))))))
(TRings.linordered_semidom_class.intro,((c==> @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ ((c==> @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)) @ ((c==> @ (((cRings.class.linordered_semidom_axioms @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cOrderings.ord_class.less)) @ (cRings.linordered_semidom_class @ cTYPE)))))
(TRings.linordered_semidom_class.super_2,((c==> @ (cRings.linordered_semidom_class @ cTYPE)) @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)))
(TRings.linordered_semidom_class.super_1,((c==> @ (cRings.linordered_semidom_class @ cTYPE)) @ (cRings.comm_semiring_1_cancel_class @ cTYPE)))
(TRings.mult_zero_class.mult_zero_left,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TRings.no_zero_divisors.divisors_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.class.no_zero_divisors @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ V1)) @ ((cHOL.eq @ V3) @ V1)))))))))))))
(TRings.ordered_ring.split_mult_pos_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((cHOL.disj @ ((cHOL.conj @ ((V2 @ V1) @ V7)) @ ((V2 @ V1) @ V8))) @ ((cHOL.conj @ ((V2 @ V7) @ V1)) @ ((V2 @ V8) @ V1)))) @ ((V2 @ V1) @ ((V4 @ V7) @ V8)))))))))))))))))))))))
(TRings.ordered_ring_class.le_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V1)) @ V4))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V3)) @ V1)) @ V2)) @ V4)))))))))))))
(TRings.ordered_ring_class.le_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V1)) @ V4))) @ ((cOrderings.ord_class.less_eq @ V2) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V3) @ V0)) @ V1)) @ V4))))))))))))))
(TRings.semiring.combine_common_factor,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cRings.class.semiring @ V0) @ V1)) @ ((cHOL.eq @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V0 @ ((V1 @ V4) @ V3)) @ V5))) @ ((V0 @ ((V1 @ ((V0 @ V2) @ V4)) @ V3)) @ V5))))))))))))))))
(TRings.semiring_class.semiring_axioms,((cRings.class.semiring @ cGroups.plus_class.plus) @ cGroups.times_class.times))
(TSMT.equal_pattern_inst.equal_pattern,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TSet_Interval.Inf_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ V0)))))))
(TSet_Interval.Sup_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ V1)))))))
(TSet_Interval.atLeast_Suc_greaterThan,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ (cNat.Suc @ V0))) @ (cSet_Interval.ord_class.greaterThan @ V0)))))
(TSet_Interval.dvd.atLeastLessThan_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((((cSet_Interval.ord.atLeastLessThan @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.atLeast @ cRings.dvd_class.dvd) @ V0)) @ ((cSet_Interval.ord.lessThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1))))))))
(TSet_Interval.dvd.atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((((cSet_Interval.ord.atLeastLessThan @ cRings.dvd_class.dvd) @ (^[V3]: (^[V4]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V3) @ V4)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V4) @ V3)))))) @ V1) @ V2))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TSet_Interval.dvd.atLeastatMost_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TSet_Interval.finite_M_bounded_by_nat,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ (V0 @ V2)) @ ((cNat.ord_nat_inst.less_nat @ V2) @ V1))))))))))
(TSet_Interval.image_Suc_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cNat.Suc) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))))))))
(TSet_Interval.image_add_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ (^[V3]: ((cNat.plus_nat_inst.plus_nat @ V3) @ V0))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0))))))))))
(TSet_Interval.ord.atLeastLessThan_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V2) @ V3)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ ((cSet_Interval.ord.lessThan @ V1) @ V3))))))))))))
(TSet_Interval.ord.atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cSet.member @ V0) @ ((((cSet_Interval.ord.atLeastLessThan @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((V1 @ V3) @ V0)) @ ((V2 @ V0) @ V4))))))))))))))
(TSet_Interval.setsum_atMost_Suc_shift,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V0 @ V2))) @ (cSet_Interval.ord_class.atMost @ (cNat.Suc @ V1)))) @ ((cGroups.plus_class.plus @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V0 @ (cNat.Suc @ V2)))) @ (cSet_Interval.ord_class.atMost @ V1)))))))))
(TString.char.char_size_overloaded_def,((c== @ cString.char.size_char_inst.size_char) @ (cString.char.char_rec @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat)))))
(TString.char.size_char_inst.size_char,((c== @ cString.char.size_char_inst.size_char) @ cString.char.size_char_inst.size_char))
(TString.enum_char_product_enum_nibble,((cHOL.eq @ cString.enum_char_inst.enum_char) @ ((cList.map @ (cProduct_Type.prod.prod_case @ cString.char.Char)) @ ((cList.product @ cString.enum_nibble_inst.enum_nibble) @ cString.enum_nibble_inst.enum_nibble))))
(TString.nibble.nibble_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cString.nibble.nibble_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))) @ (V1 @ V0)))))))))))))))))))))))
(TSum_Type.sum.sum_size_overloaded_def,((c== @ cNat.size_class.size) @ ((cSum_Type.sum.sum_rec @ (^[V0]: cNat.zero_nat_inst.zero_nat)) @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TTransitive_Closure.acyclicP_converse,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.acyclic @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (((cRelation.conversep @ V0) @ V1) @ V2))))))) @ (cTransitive_Closure.acyclic @ (cSet.Collect @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2))))))))))
(TTransitive_Closure.converse_rtranclE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ V3))))) @ V3))))))))))))
(TTransitive_Closure.converse_tranclpE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((V0 @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V4)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V4) @ V2)) @ V3))))) @ V3))))))))))))
(TTransitive_Closure.r_comp_rtrancl_eq,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcomp @ V0) @ (cTransitive_Closure.rtrancl @ V0))) @ ((cRelation.relcomp @ (cTransitive_Closure.rtrancl @ V0)) @ V0)))))
(TTransitive_Closure.relpowp_relpow_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ V0) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ V1))))) @ (^[V2]: (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ ((cNat.compow @ V0) @ V1))))))))))
(TTransitive_Closure.rtrancl_Un_subset,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (cTransitive_Closure.rtrancl @ V0)) @ (cTransitive_Closure.rtrancl @ V1))) @ (cTransitive_Closure.rtrancl @ ((cLattices.sup_class.sup @ V0) @ V1))))))))
(TTransitive_Closure.rtrancl_converseD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ (cRelation.converse @ V2)))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ (cTransitive_Closure.rtrancl @ V2))))))))))
(TTransitive_Closure.rtrancl_converseI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V0)) @ (cTransitive_Closure.rtrancl @ (cRelation.converse @ V2)))))))))))
(TTransitive_Closure.rtrancl_r_diff_Id,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ ((cGroups.minus_class.minus @ V0) @ cRelation.Id))) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.trancl_Int_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ ((cLattices.inf_class.inf @ (cTransitive_Closure.trancl @ V0)) @ V1)) @ V0)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cTransitive_Closure.trancl @ V0)) @ V1))))))))
(TTransitive_Closure.tranclp_converseD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.tranclp @ (cRelation.conversep @ V0)) @ V1) @ V2)) @ (((cRelation.conversep @ (cTransitive_Closure.tranclp @ V0)) @ V1) @ V2)))))))))
(TTransitive_Closure.tranclp_converseI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRelation.conversep @ (cTransitive_Closure.tranclp @ V0)) @ V1) @ V2)) @ (((cTransitive_Closure.tranclp @ (cRelation.conversep @ V0)) @ V1) @ V2)))))))))
(TTransitive_Closure.tranclp_trancl_eq,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.tranclp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cTransitive_Closure.trancl @ V0))))))))
(TTyperep.typerep_class.typerep_of_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep_of @ V0)) @ (cTyperep.typerep_class.typerep @ cTYPE)))))
(TTyperep.typerep_fun_inst.typerep_fun,((c== @ cTyperep.typerep_fun_inst.typerep_fun) @ cTyperep.typerep_fun_inst.typerep_fun))
(TTyperep.typerep_int_inst.typerep_int,((c== @ cTyperep.typerep_int_inst.typerep_int) @ cTyperep.typerep_int_inst.typerep_int))
(TTyperep.typerep_nat_inst.typerep_nat,((c== @ cTyperep.typerep_nat_inst.typerep_nat) @ cTyperep.typerep_nat_inst.typerep_nat))
(TTyperep.typerep_num_inst.typerep_num,((c== @ cTyperep.typerep_num_inst.typerep_num) @ cTyperep.typerep_num_inst.typerep_num))
(TTyperep.typerep_set_inst.typerep_set,((c== @ cTyperep.typerep_set_inst.typerep_set) @ cTyperep.typerep_set_inst.typerep_set))
(TTyperep.typerep_sum_inst.typerep_sum,((c== @ cTyperep.typerep_sum_inst.typerep_sum) @ cTyperep.typerep_sum_inst.typerep_sum))
(TWellfounded.wf_iff_acyclic_if_finite,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cWellfounded.wf @ V0)) @ (cTransitive_Closure.acyclic @ V0))))))
(TBig_Operators.comm_monoid_set.distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V5]: ((V0 @ (V2 @ V5)) @ (V3 @ V5)))) @ V4)) @ ((V0 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V2) @ V4)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V3) @ V4)))))))))))))))
(TBig_Operators.comm_monoid_set.eq_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V2) @ V3)) @ (((cFinite_Set.fold @ ((cFun.comp @ V0) @ V2)) @ V1) @ V3))))))))))))
(TBig_Operators.comm_monoid_set.neutral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: ((cHOL.eq @ (V3 @ V4)) @ V1)))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V3) @ V2)) @ V1))))))))))))
(TBig_Operators.comm_monoid_set.reindex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ V3)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cSet.image @ V2) @ V3))) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ ((cFun.comp @ V4) @ V2)) @ V3)))))))))))))))
(TBig_Operators.comm_monoid_set.related,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((V2 @ V1) @ V1)) @ ((c==> @ (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: (cHOL.All @ (^[V8]: (cHOL.All @ (^[V9]: ((cHOL.implies @ ((cHOL.conj @ ((V2 @ V6) @ V8)) @ ((V2 @ V7) @ V9))) @ ((V2 @ ((V0 @ V6) @ V7)) @ ((V0 @ V8) @ V9)))))))))))) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V6]: ((V2 @ (V4 @ V6)) @ (V5 @ V6))))) @ ((V2 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V3)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V5) @ V3))))))))))))))))))))
(TBig_Operators.linorder_class.Max_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Max @ V0)) @ (cBig_Operators.linorder_class.Max @ V1))))))))))
(TBig_Operators.linorder_class.dual_Max,((cHOL.eq @ (cBig_Operators.linorder.Max @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0))))) @ cBig_Operators.linorder_class.Min))
(TBig_Operators.linorder_class.dual_Min,((cHOL.eq @ (cBig_Operators.linorder.Min @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0))))) @ cBig_Operators.linorder_class.Max))
(TBig_Operators.linorder_class.dual_max,((cHOL.eq @ (cOrderings.ord.max @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0))))) @ cOrderings.ord_class.min))
(TBig_Operators.linorder_class.dual_min,((cHOL.eq @ (cOrderings.ord.min @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0))))) @ cOrderings.ord_class.max))
(TBig_Operators.linorder_class.le_maxI1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TBig_Operators.linorder_class.le_maxI2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TBig_Operators.semilattice_set.eq_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cSet.insert @ V2) @ V1))) @ (((cFinite_Set.fold @ V0) @ V2) @ V1)))))))))))
(TBig_Operators.semilattice_set.in_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.member @ V2) @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ ((cBig_Operators.semilattice_set.F @ V0) @ V1))) @ ((cBig_Operators.semilattice_set.F @ V0) @ V1))))))))))))
(TBig_Operators.setsum_nonneg_leq_bound,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (V1 @ V4)))))) @ ((c==> @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (V1 @ V4))) @ V0)) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V2))))))))))))))
(TCode_Evaluation.arity_term_of_integer,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_literal,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_natural,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_typerep,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.term.Abs_term_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cCode_Evaluation.term.term_rep_set))) @ ((cHOL.eq @ (cCode_Evaluation.Rep_term @ (cCode_Evaluation.Abs_term @ V0))) @ V0)))))
(TCode_Evaluation.term.Rep_term_inverse,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.Abs_term @ (cCode_Evaluation.Rep_term @ V0))) @ V0))))
(TCode_Evaluation.term.term_rec_set_def,((c== @ cCode_Evaluation.term.term_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ cCode_Evaluation.term.dummy_term)) @ ((cHOL.eq @ V3) @ V0)))))))))
(TCode_Evaluation.term.term_rep_set_def,((c== @ cCode_Evaluation.term.term_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.eq @ V1) @ cHOL.undefined))))))
(TCode_Evaluation.term_of_finite_1_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_finite_1_inst.term_of_finite_1 @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_finite_2_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_finite_2_inst.term_of_finite_2 @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_finite_3_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_finite_3_inst.term_of_finite_3 @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_finite_4_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_finite_4_inst.term_of_finite_4 @ V0)) @ cHOL.undefined))))
(TCode_Evaluation.term_of_finite_5_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_finite_5_inst.term_of_finite_5 @ V0)) @ cHOL.undefined))))
(TCode_Numeral.arity_semiring_1_natural,(cRings.semiring_1_class @ cTYPE))
(TCode_Numeral.integer_of_int_eq_of_int,((cHOL.eq @ cCode_Numeral.integer_of_int) @ cInt.ring_1_class.of_int))
(TCode_Numeral.integer_of_nat_eq_of_nat,((cHOL.eq @ cCode_Numeral.integer_of_nat) @ cNat.semiring_1_class.of_nat))
(TCode_Numeral.less_eq_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cHOL.eq)) @ cInt.ord_int_inst.less_eq_int) @ cCode_Numeral.ord_integer_inst.less_eq_integer))
(TCode_Numeral.less_eq_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ ((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cHOL.eq)) @ cNat.ord_nat_inst.less_eq_nat) @ cCode_Numeral.ord_natural_inst.less_eq_natural))
(TCode_Numeral.natural.natural_case_def,((c== @ cCode_Numeral.natural.natural_case) @ (^[V0]: (^[V1]: ((cCode_Numeral.natural.natural_rec @ V0) @ (^[V2]: (^[V3]: (V1 @ V2))))))))
(TCode_Numeral.natural.natural_size_def,((c== @ cCode_Numeral.natural.natural_size) @ ((cCode_Numeral.natural.natural_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))
(TComplete_Partial_Order.admissible_all,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V4]: ((V2 @ V4) @ V3)))))) @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V3]: (cHOL.All @ (^[V4]: ((V2 @ V3) @ V4)))))))))))))
(TComplete_Partial_Order.ccpo_class_def,((c== @ (cComplete_Partial_Order.ccpo_class @ cTYPE)) @ ((cPure.conjunction @ (cComplete_Lattices.Sup_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ ((cComplete_Partial_Order.class.ccpo_axioms @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq)))))
(TComplete_Partial_Order.class.ccpo_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cOrderings.class.order @ V1) @ V2)) @ ((cComplete_Partial_Order.class.ccpo_axioms @ V0) @ V1))))))))))
(TDivides.class.semiring_div_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cDivides.class.semiring_div_axioms @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.eq @ ((V3 @ ((V0 @ ((V1 @ V5) @ V6)) @ V6)) @ ((V2 @ V5) @ V6))) @ V5)))))) @ (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V1 @ V5) @ V4)) @ V4))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V1 @ V4) @ V5)) @ V4)))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V3 @ V6) @ ((V0 @ V7) @ V5))) @ V5)) @ ((V3 @ V7) @ ((V1 @ V6) @ V5))))))))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V0 @ V5) @ V6)) @ ((V0 @ V5) @ V7))) @ ((V1 @ V6) @ V7))))))))))))))))))))))))
(TDivides.ring_div_class.mod_minus_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ V1)) @ ((cDivides.div_class.mod @ V2) @ V1))) @ ((cHOL.eq @ ((cDivides.div_class.mod @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cDivides.div_class.mod @ (cGroups.uminus_class.uminus @ V2)) @ V1))))))))))
(TDivides.semiring_div.div_mod_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V3 @ ((V3 @ ((V0 @ ((V1 @ V6) @ V7)) @ V7)) @ ((V2 @ V6) @ V7))) @ V8)) @ ((V3 @ V6) @ V8))))))))))))))))))))))
(TDivides.semiring_div.mod_add_right_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V3 @ V6) @ V7)) @ V8)) @ ((V2 @ ((V3 @ V6) @ ((V2 @ V7) @ V8))) @ V8))))))))))))))))))))))
(TDivides.semiring_div.mod_div_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V3 @ ((V0 @ ((V1 @ V6) @ V7)) @ V7)) @ ((V2 @ V6) @ V7))) @ V6)))))))))))))))))))
(TDivides.semiring_div.mod_mult_left_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ V8)) @ ((V2 @ ((V0 @ ((V2 @ V6) @ V8)) @ V7)) @ V8))))))))))))))))))))))
(TDivides.semiring_div_class.mod_add_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ ((cDivides.div_class.mod @ V0) @ V2)) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)))))))))
(TDivides.semiring_numeral_div.discrete,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ ((V8 @ V9) @ V10)) @ ((V7 @ ((V3 @ V9) @ V5)) @ V10))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.div_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V4) @ V9)) @ ((c==> @ ((V8 @ V9) @ V10)) @ ((cHOL.eq @ ((V1 @ V9) @ V10)) @ V4)))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.mod_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V4) @ V9)) @ ((c==> @ ((V8 @ V9) @ V10)) @ ((cHOL.eq @ ((V2 @ V9) @ V10)) @ V9)))))))))))))))))))))))))))
(TEnum.enum_class.card_UNIV_length_enum,((cHOL.eq @ (cFinite_Set.card @ cOrderings.top_class.top)) @ (cNat.size_class.size @ cEnum.enum_class.enum)))
(TEnum.enum_finite_1_inst.enum_finite_1,((c== @ cEnum.enum_finite_1_inst.enum_finite_1) @ cEnum.enum_finite_1_inst.enum_finite_1))
(TEnum.enum_finite_2_inst.enum_finite_2,((c== @ cEnum.enum_finite_2_inst.enum_finite_2) @ cEnum.enum_finite_2_inst.enum_finite_2))
(TEnum.enum_finite_3_inst.enum_finite_3,((c== @ cEnum.enum_finite_3_inst.enum_finite_3) @ cEnum.enum_finite_3_inst.enum_finite_3))
(TEnum.enum_finite_4_inst.enum_finite_4,((c== @ cEnum.enum_finite_4_inst.enum_finite_4) @ cEnum.enum_finite_4_inst.enum_finite_4))
(TEnum.enum_finite_5_inst.enum_finite_5,((c== @ cEnum.enum_finite_5_inst.enum_finite_5) @ cEnum.enum_finite_5_inst.enum_finite_5))
(TEnum.enum_option_inst.enum_all_option,((c== @ cEnum.enum_option_inst.enum_all_option) @ cEnum.enum_option_inst.enum_all_option))
(TEnum.finite_1.finite_1_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TEnum.finite_1.finite_1_rec_set.intros,(call @ (^[V0]: (((cEnum.finite_1.finite_1_rec_set @ V0) @ cEnum.finite_1.a\<__caret__sub>1) @ V0))))
(TEnum.finite_1.finite_1_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_1.finite_1_rep_set @ V0)) @ ((c==> @ (V1 @ cHOL.undefined)) @ (V1 @ V0))))))))
(TEnum.finite_1.finite_1_rep_set.intros,(cEnum.finite_1.finite_1_rep_set @ cHOL.undefined))
(TEnum.finite_2.finite_2_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TEnum.finite_2.finite_2_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((((cEnum.finite_2.finite_2_rec_set @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>2) @ V1))))))
(TEnum.finite_2.finite_2_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cEnum.finite_2.finite_2_rec_set @ V0) @ V1) @ cEnum.finite_2.a\<__caret__sub>1) @ V0))))))
(TEnum.finite_2.finite_2_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_2.finite_2_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (V1 @ (cDatatype.In1 @ cHOL.undefined))) @ (V1 @ V0)))))))))
(TEnum.finite_2.finite_2_rep_set.intros_2,(cEnum.finite_2.finite_2_rep_set @ (cDatatype.In1 @ cHOL.undefined)))
(TEnum.finite_2.finite_2_rep_set.intros_1,(cEnum.finite_2.finite_2_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TEnum.finite_3.finite_3_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TEnum.finite_3.finite_3_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cEnum.finite_3.finite_3_rec_set @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>3) @ V2))))))))
(TEnum.finite_3.finite_3_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cEnum.finite_3.finite_3_rec_set @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>2) @ V1))))))))
(TEnum.finite_3.finite_3_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cEnum.finite_3.finite_3_rec_set @ V0) @ V1) @ V2) @ cEnum.finite_3.a\<__caret__sub>1) @ V0))))))))
(TEnum.finite_3.finite_3_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_3.finite_3_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))) @ (V1 @ V0))))))))))
(TEnum.finite_3.finite_3_rep_set.intros_3,(cEnum.finite_3.finite_3_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))
(TEnum.finite_3.finite_3_rep_set.intros_2,(cEnum.finite_3.finite_3_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))
(TEnum.finite_3.finite_3_rep_set.intros_1,(cEnum.finite_3.finite_3_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TEnum.finite_4.finite_4_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TEnum.finite_4.finite_4_rec_set.intros_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((((((cEnum.finite_4.finite_4_rec_set @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>4) @ V3))))))))))
(TEnum.finite_4.finite_4_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((((((cEnum.finite_4.finite_4_rec_set @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>3) @ V2))))))))))
(TEnum.finite_4.finite_4_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((((((cEnum.finite_4.finite_4_rec_set @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>2) @ V1))))))))))
(TEnum.finite_4.finite_4_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((((((cEnum.finite_4.finite_4_rec_set @ V0) @ V1) @ V2) @ V3) @ cEnum.finite_4.a\<__caret__sub>1) @ V0))))))))))
(TEnum.finite_4.finite_4_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_4.finite_4_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))) @ (V1 @ V0)))))))))))
(TEnum.finite_4.finite_4_rep_set.intros_4,(cEnum.finite_4.finite_4_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))
(TEnum.finite_4.finite_4_rep_set.intros_3,(cEnum.finite_4.finite_4_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))
(TEnum.finite_4.finite_4_rep_set.intros_2,(cEnum.finite_4.finite_4_rep_set @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined))))
(TEnum.finite_4.finite_4_rep_set.intros_1,(cEnum.finite_4.finite_4_rep_set @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined))))
(TEnum.finite_5.finite_5_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TEnum.finite_5.finite_5_rec_set.intros_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>5) @ V4))))))))))))
(TEnum.finite_5.finite_5_rec_set.intros_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>4) @ V3))))))))))))
(TEnum.finite_5.finite_5_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>3) @ V2))))))))))))
(TEnum.finite_5.finite_5_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>2) @ V1))))))))))))
(TEnum.finite_5.finite_5_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((((cEnum.finite_5.finite_5_rec_set @ V0) @ V1) @ V2) @ V3) @ V4) @ cEnum.finite_5.a\<__caret__sub>1) @ V0))))))))))))
(TEnum.finite_5.finite_5_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_5.finite_5_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))) @ (V1 @ V0))))))))))))
(TEnum.finite_5.finite_5_rep_set.intros_5,(cEnum.finite_5.finite_5_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))
(TEnum.finite_5.finite_5_rep_set.intros_4,(cEnum.finite_5.finite_5_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))))
(TEnum.finite_5.finite_5_rep_set.intros_3,(cEnum.finite_5.finite_5_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))
(TEnum.finite_5.finite_5_rep_set.intros_2,(cEnum.finite_5.finite_5_rep_set @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined))))
(TEnum.finite_5.finite_5_rep_set.intros_1,(cEnum.finite_5.finite_5_rep_set @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined))))
(TEquiv_Relations.UN_equiv_class_inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cEquiv_Relations.congruent @ V1) @ V2)) @ ((c==> @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V3) @ (^[V5]: (V2 @ V5)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V4) @ (^[V5]: (V2 @ V5))))) @ ((c==> @ ((cSet.member @ V3) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ ((cSet.member @ V4) @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ V5) @ V0)) @ ((c==> @ ((cSet.member @ V6) @ V0)) @ ((c==> @ ((cHOL.eq @ (V2 @ V5)) @ (V2 @ V6))) @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ V1))))))))) @ ((cHOL.eq @ V3) @ V4))))))))))))))))))
(TEquiv_Relations.sym_trans_comp_subset,(call @ (^[V0]: ((c==> @ (cRelation.sym @ V0)) @ ((c==> @ (cRelation.trans @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ (cRelation.converse @ V0)) @ V0)) @ V0))))))
(TExtraction.sumbool.Abs_sumbool_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set))) @ (V0 @ (cExtraction.Abs_sumbool @ V2)))))) @ (V0 @ V1)))))))
(TExtraction.sumbool.Abs_sumbool_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cExtraction.Abs_sumbool @ V0)) @ (cExtraction.Abs_sumbool @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TExtraction.sumbool.Rep_sumbool_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cExtraction.Rep_sumbool @ V2))))) @ (V1 @ V0))))))))
(TExtraction.sumbool.Rep_sumbool_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cExtraction.Rep_sumbool @ V0)) @ (cExtraction.Rep_sumbool @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TExtraction.sumbool.arity_size_sumbool,(cNat.size_class @ cTYPE))
(TFields.class.division_ring_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cFields.class.division_ring_axioms @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ V4))) @ ((cHOL.eq @ ((V3 @ (V0 @ V5)) @ V5)) @ V2))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ V4))) @ ((cHOL.eq @ ((V3 @ V5) @ (V0 @ V5))) @ V2))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.eq @ ((V1 @ V5) @ V6)) @ ((V3 @ V5) @ (V0 @ V6)))))))))))))))))))))
(TFields.class.field_inverse_zero.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cFields.class.field_inverse_zero_axioms @ V0) @ V5)) @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7))))))))))))))))))))
(TFields.division_ring.divide_zero_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V5) @ V8)) @ V5)))))))))))))))))))))
(TFields.division_ring.right_inverse_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V9) @ V8)) @ V2)) @ ((cHOL.eq @ V9) @ V8)))))))))))))))))))))))))
(TFields.field_class.diff_divide_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cFields.inverse_class.divide @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ V0))))))))))
(TFields.field_class.divide_diff_eq_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cFields.inverse_class.divide @ ((cGroups.minus_class.minus @ V1) @ ((cGroups.times_class.times @ V0) @ V2))) @ V0))))))))))
(TFields.field_inverse_zero_class.intro,((c==> @ (cFields.field_class @ cTYPE)) @ ((c==> @ ((cFields.class.field_inverse_zero_axioms @ cFields.inverse_class.inverse) @ cGroups.zero_class.zero)) @ (cFields.field_inverse_zero_class @ cTYPE))))
(TFields.field_inverse_zero_class.super,((c==> @ (cFields.field_inverse_zero_class @ cTYPE)) @ (cFields.field_class @ cTYPE)))
(TFields.linordered_field.less_half_sum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((V10 @ V12) @ ((V1 @ ((V4 @ V12) @ V13)) @ ((V4 @ V3) @ V3))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.frac_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V3)) @ ((cFields.inverse_class.divide @ V1) @ V2)))))))))))))))
(TFinite_Set.comp_fun_idem_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V1))) @ (V0 @ V1))))) @ (cFinite_Set.comp_fun_idem_axioms @ V0)))))
(TFinite_Set.finite_cartesian_productD1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1)))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ (cFinite_Set.finite @ V0))))))))
(TFinite_Set.finite_cartesian_productD2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ ((cProduct_Type.Sigma @ V0) @ (^[V2]: V1)))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ (cFinite_Set.finite @ V1))))))))
(TFinite_Set.finite_class.finite_axioms,(cFinite_Set.class.finite @ cTYPE))
(TFinite_Set.folding_idem.comp_fun_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.folding_idem @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V1))) @ (V0 @ V1))))))))
(TGroups.ab_group_add.minus_add_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (V3 @ ((V0 @ V4) @ V5))) @ ((V0 @ (V3 @ V4)) @ (V3 @ V5)))))))))))))))))
(TGroups.ab_group_add_class.diff_add_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TGroups.ab_semigroup_mult.mult_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.ab_semigroup_mult_class.axioms,(cGroups.class.ab_semigroup_mult_axioms @ cGroups.times_class.times))
(TGroups.add_mono_thms_linordered_field_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V2) @ V3))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.add_mono_thms_linordered_field_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V2) @ V3))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.add_mono_thms_linordered_field_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.add_mono_thms_linordered_field_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V2) @ V3))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.add_mono_thms_linordered_field_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V2) @ V3))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.cancel_semigroup_add_class_def,((c== @ (cGroups.cancel_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.semigroup_add_class @ cTYPE)) @ (cGroups.class.cancel_semigroup_add_axioms @ cGroups.plus_class.plus))))
(TGroups.class.ab_semigroup_mult.axioms_2,(call @ (^[V0]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ (cGroups.class.ab_semigroup_mult_axioms @ V0)))))
(TGroups.class.ab_semigroup_mult.axioms_1,(call @ (^[V0]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ (cGroups.class.semigroup_mult @ V0)))))
(TGroups.class.cancel_semigroup_add_def,(call @ (^[V0]: ((c== @ (cGroups.class.cancel_semigroup_add @ V0)) @ ((cHOL.conj @ (cGroups.class.semigroup_add @ V0)) @ (cGroups.class.cancel_semigroup_add_axioms @ V0))))))
(TGroups.class.monoid_mult_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))) @ ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V2) @ V1)) @ V2)))) @ ((cGroups.class.monoid_mult_axioms @ V1) @ V0))))))))
(TGroups.class.ordered_ab_group_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V4) @ V5))))))))))))))))
(TGroups.comm_monoid_diff.diff_add_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ V3) @ ((V0 @ V3) @ V4))) @ V1)))))))))))))
(TGroups.comm_monoid_diff.diff_diff_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V3) @ V4)) @ V5)) @ ((V2 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))
(TGroups.group_add_class.right_minus_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ V1)))))))
(TGroups.monoid_mult_class.mult_1_right,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.one_class.one)) @ V0))))
(TGroups.ordered_ab_group_add_class_def,((c== @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_group_add_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE))))
(THilbert_Choice.wf_linord_ex_has_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.trancl @ V0))) @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V4)) @ (cTransitive_Closure.rtrancl @ V0))))))))) @ ((c==> @ (V1 @ V2)) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ (V1 @ V4)) @ (cHOL.All @ (^[V5]: ((cHOL.implies @ (V1 @ V5)) @ ((cSet.member @ ((cProduct_Type.Pair @ (V3 @ V4)) @ (V3 @ V5))) @ (cTransitive_Closure.rtrancl @ V0))))))))))))))))))))
(TInt.linordered_idom.of_int_0_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V3) @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V10))) @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V10))))))))))))))))))))))))))
(TInt.linordered_idom.of_int_less_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ (((((cInt.ring_1.of_int @ V7) @ V6) @ V3) @ V1) @ V10)) @ V3)) @ ((cInt.ord_int_inst.less_int @ V10) @ cInt.zero_int_inst.zero_int))))))))))))))))))))))))))
(TInt.ring_char_0_class.of_int_0_eq_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cInt.ring_1_class.of_int @ V0))) @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)))))
(TInt.ring_char_0_class.of_int_eq_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cInt.ring_1_class.of_int @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)))))
(TLattices.boolean_algebra.compl_bot_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ V6)) @ V7)))))))))))))))))))
(TLattices.boolean_algebra.compl_top_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ V7)) @ V6)))))))))))))))))))
(TLattices.boolean_algebra.compl_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ ((V2 @ V8) @ V9)) @ V6)) @ ((c==> @ ((cHOL.eq @ ((V5 @ V8) @ V9)) @ V7)) @ ((cHOL.eq @ (V1 @ V8)) @ V9)))))))))))))))))))))))))
(TLattices.boolean_algebra.double_compl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ (V1 @ V8))) @ V8)))))))))))))))))))))
(TLattices.boolean_algebra_class.axioms,((((((cLattices.class.boolean_algebra_axioms @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cLattices.inf_class.inf) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))
(TLattices.class.boolean_algebra.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cLattices.class.boolean_algebra_axioms @ V0) @ V1) @ V2) @ V5) @ V6) @ V7)))))))))))))))))))
(TLattices.class.boolean_algebra.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((cLattices.class.distrib_lattice @ V2) @ V3) @ V4) @ V5)))))))))))))))))))
(TLattices.class.boolean_algebra.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cLattices.class.bounded_lattice @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TLattices.class.bounded_lattice.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((cOrderings.class.order_top @ V1) @ V2) @ V5)))))))))))))))
(TLattices.class.bounded_lattice.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((cOrderings.class.order_bot @ V4) @ V1) @ V2)))))))))))))))
(TLattices.class.bounded_lattice.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)))))))))))))))
(TLattices.class.distrib_lattice.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cLattices.class.distrib_lattice_axioms @ V0) @ V3)))))))))))
(TLattices.class.distrib_lattice.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)))))))))))
(TLattices.class.semilattice_inf.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cLattices.class.semilattice_inf_axioms @ V0) @ V1)))))))))
(TLattices.class.semilattice_inf.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cOrderings.class.order @ V1) @ V2)))))))))
(TLattices.class.semilattice_sup.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cLattices.class.semilattice_sup_axioms @ V0) @ V1)))))))))
(TLattices.class.semilattice_sup.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cOrderings.class.order @ V1) @ V2)))))))))
(TLattices.distrib_lattice_class.axioms,((cLattices.class.distrib_lattice_axioms @ cLattices.inf_class.inf) @ cLattices.sup_class.sup))
(TLattices.lattice_class.distrib_inf_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V2))) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.lattice_class.distrib_sup_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TLattices.lattice_class.inf_sup_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ V0))))))
(TLattices.lattice_class.lattice_axioms,((((cLattices.class.lattice @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup))
(TLattices.lattice_class.sup_inf_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ V0))))))
(TLattices.linorder_class.max.left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TLattices.linorder_class.max.order_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ ((cOrderings.ord_class.max @ V1) @ V0))))))))
(TLattices.linorder_class.min.left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.min @ V0) @ V1)))))))
(TLattices.linorder_class.min.order_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))))))))
(TLattices.semilattice_inf.inf_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V3) @ V5)) @ ((V1 @ V3) @ ((V0 @ V4) @ V5))))))))))))))))))
(TLattices.semilattice_inf_class.axioms,((cLattices.class.semilattice_inf_axioms @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq))
(TLattices.semilattice_order.cobounded1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((V1 @ ((V0 @ V3) @ V4)) @ V3)))))))))))))
(TLattices.semilattice_order.cobounded2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((V1 @ ((V0 @ V3) @ V4)) @ V4)))))))))))))
(TLattices.semilattice_order_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cLattices.semilattice_order_axioms @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V1 @ V3) @ V4)) @ ((cHOL.eq @ V3) @ ((V0 @ V3) @ V4)))))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V2 @ V3) @ V4)) @ ((cHOL.conj @ ((V1 @ V3) @ V4)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4)))))))))))))))))
(TLattices.semilattice_sup_class.axioms,((cLattices.class.semilattice_sup_axioms @ cLattices.sup_class.sup) @ cOrderings.ord_class.less_eq))
(TLattices.uminus_bool_inst.uminus_bool,((c== @ cLattices.uminus_bool_inst.uminus_bool) @ cLattices.uminus_bool_inst.uminus_bool))
(TLazy_Sequence.equal_lazy_sequence_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TLazy_Sequence.iterate_upto_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.iterate_upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.iterate_upto_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cLazy_Sequence.iterate_upto_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V1) @ V0)))))))))))
(TLazy_Sequence.lazy_sequence.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V2) @ V0)) @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V3) @ V1)))))))))))))
(TLazy_Sequence.lazy_sequence.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TLazy_Sequence.lazy_sequence_size_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_size @ V0) @ V1)) @ (((cOption.option.option_case @ cNat.one_nat_inst.one_nat) @ (^[V2]: ((cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (cNat.Suc @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V3)) @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_size @ V0) @ V4)))))) @ V2))) @ (cLazy_Sequence.yield @ V1))))))))
(TLazy_Sequence.small_lazy'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V1) @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cInt.plus_int_inst.plus_int @ V2) @ cInt.one_int_inst.one_int))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cLazy_Sequence.small_lazy'_rel) @ V1))))))))
(TLazy_Sequence.small_lazy'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((cLazy_Sequence.small_lazy'_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))) @ V2)))))))))) @ V2)))))))))
(TLazy_Sequence.small_lazy'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.small_lazy'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V3) @ V4)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V4)) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))) @ ((cLazy_Sequence.small_lazy'_graph @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int)))))))))))))))))))
(TLazy_Sequence.small_lazy'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy_list.pinduct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy_list_rel) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cLazy_Sequence.small_lazy_list_rel) @ V2)) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V2)) @ (V1 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V1 @ V2)))))) @ (V1 @ V0))))))))
(TLazy_Sequence.small_lazy_list_rel_def,((c== @ cLazy_Sequence.small_lazy_list_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V3)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)))))))))))
(TLifting_Option.left_unique_option_rel,(call @ (^[V0]: ((c==> @ (cLifting.left_unique @ V0)) @ (cLifting.left_unique @ (cLifting_Option.option_rel @ V0))))))
(TLifting_Option.right_total_option_rel,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ (cTransfer.right_total @ (cLifting_Option.option_rel @ V0))))))
(TLifting_Product.right_unique_prod_rel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_unique @ V0)) @ ((c==> @ (cTransfer.right_unique @ V1)) @ (cTransfer.right_unique @ ((cLifting_Product.prod_rel @ V0) @ V1)))))))))
(TLifting_Set.right_total_UNIV_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ (((cLifting_Set.set_rel @ V0) @ (cSet.Collect @ (cRelation.Domainp @ V0))) @ cOrderings.top_class.top)))))
(TLimited_Sequence.neg_iterate_upto_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLimited_Sequence.neg_iterate_upto @ V0) @ V1) @ V2)) @ (^[V3]: (((cLazy_Sequence.iterate_upto @ (^[V4]: (cOption.option.Some @ (V0 @ V4)))) @ V1) @ V2))))))))))
(TLimited_Sequence.pos_iterate_upto_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLimited_Sequence.pos_iterate_upto @ V0) @ V1) @ V2)) @ (^[V3]: (((cLazy_Sequence.iterate_upto @ V0) @ V1) @ V2))))))))))
(TList.linorder.comp_fun_commute_insort,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ (cFinite_Set.comp_fun_commute @ ((cList.linorder.insort_key @ V0) @ (^[V2]: V2)))))))))
(TList.linorder_class.set_insort_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cList.set @ (((cList.linorder_class.insort_insert_key @ (^[V2]: V2)) @ V0) @ V1))) @ ((cSet.insert @ V0) @ (cList.set @ V1))))))))
(TList.linorder_class.sorted_insort_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2)))) @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ V2))))))))))
(TList.list_ex_iff_not_all_inverval_int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_ex @ V0) @ ((cList.upto @ V1) @ V2))) @ (cHOL.Not @ (((cList.all_interval_int @ ((cFun.comp @ cHOL.Not) @ V0)) @ V1) @ V2))))))))))
(TList.list_ex_iff_not_all_inverval_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cList.list_ex @ V0) @ ((cList.upt @ V1) @ V2))) @ (cHOL.Not @ (((cList.all_interval_nat @ ((cFun.comp @ cHOL.Not) @ V0)) @ V1) @ V2))))))))))
(TList.monoid_add.fold_plus_listsum_rev,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((cList.fold @ V0) @ V2)) @ (V0 @ (((cList.monoid_add.listsum @ V0) @ V1) @ (cList.rev @ V2))))))))))))
(TList.setsum_set_upto_conv_listsum_int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ (cList.set @ ((cList.upto @ V1) @ V2)))) @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ ((cList.upto @ V1) @ V2)))))))))))
(TNat.semiring_1_class.of_nat_aux.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNat.semiring_1_class.of_nat_aux @ V0) @ (cNat.Suc @ V1)) @ V2)) @ (((cNat.semiring_1_class.of_nat_aux @ V0) @ V1) @ (V0 @ V2))))))))))
(TNat.semiring_1_class.of_nat_aux.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cNat.semiring_1_class.of_nat_aux @ V0) @ cNat.zero_nat_inst.zero_nat) @ V1)) @ V1))))))
(TNitpick.arity_full_exhaustive_fun_box,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TNitpick.arity_partial_term_of_fun_box,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TNitpick.fun_box.fun_box_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cNitpick.fun_box.fun_box_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cNitpick.fun_box.FunBox @ V4))) @ ((c==> @ ((cHOL.eq @ V2) @ (V0 @ V4))) @ V3))))) @ V3)))))))))))
(TNitpick.fun_box.fun_box_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNitpick.fun_box.fun_box_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cNitpick.fun_box.FunBox @ V3))) @ ((cHOL.eq @ V2) @ (V0 @ V3)))))))))))))
(TNitpick.pair_box.Abs_pair_box_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cNitpick.pair_box.pair_box_rep_set))) @ ((cHOL.eq @ (cNitpick.Rep_pair_box @ (cNitpick.Abs_pair_box @ V0))) @ V0)))))
(TNitpick.pair_box.Rep_pair_box_inverse,(call @ (^[V0]: ((cHOL.eq @ (cNitpick.Abs_pair_box @ (cNitpick.Rep_pair_box @ V0))) @ V0))))
(TNitpick.pair_box.pair_box_rec_set_def,((c== @ cNitpick.pair_box.pair_box_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cNitpick.pair_box.PairBox @ V4) @ V5))) @ ((cHOL.eq @ V3) @ ((V0 @ V4) @ V5))))))))))))))
(TNitpick.pair_box.pair_box_rep_set_def,((c== @ cNitpick.pair_box.pair_box_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V1) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3)))))))))))))
(TNitpick.partial_term_of_pair_box_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TNitpick.word.size_word_inst.size_word,((c== @ cNitpick.word.size_word_inst.size_word) @ cNitpick.word.size_word_inst.size_word))
(TNitpick.word.word_size_overloaded_def,((c== @ cNat.size_class.size) @ (cNitpick.word.word_rec @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TNum.classrel_semiring_numeral_numeral,(cNum.numeral_class @ cTYPE))
(TNum.linordered_idom_class.abs_numeral,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.linordered_semidom.numeral_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V3) @ V0) @ V7))) @ ((cNum.ord_num_inst.less_eq_num @ V6) @ V7))))))))))))))))))))
(TNum.linordered_semidom.one_le_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V3) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))))))))))))))))))
(TNum.neg_numeral.add_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V6))) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ ((cNum.plus_num_inst.plus_num @ V5) @ V6)))))))))))))))))))
(TNum.neg_numeral.add_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5)) @ (((cNum.numeral.numeral @ V4) @ V1) @ V6))) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V6) @ V5))))))))))))))))))
(TNum.neg_numeral.add_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ (((cNum.numeral.numeral @ V4) @ V1) @ V5)) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V6))) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ V5) @ V6))))))))))))))))))
(TNum.neg_numeral_class.neg_numeral_def,(call @ (^[V0]: ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0))))))
(TNum.numeral_class.add_numeral_special_3,((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNum.numeral_class.add_numeral_special_2,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0))))))
(TNum.numeral_class.add_numeral_special_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.numeral_class.numeral.numeral_One,((cHOL.eq @ (cNum.numeral_class.numeral @ cNum.num.One)) @ cGroups.one_class.one))
(TNumeral_Simprocs.nat_mult_div_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cDivides.div_nat_inst.div_nat @ V1) @ V2))))))))))
(TNumeral_Simprocs.nat_mult_dvd_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))
(TOption.equal_option_inst.equal_option,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TOrderings.class.dense_linorder.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cOrderings.class.linorder @ V0) @ V1)))))))
(TOrderings.class.dense_linorder.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cOrderings.class.dense_order @ V0) @ V1)))))))
(TOrderings.class.linorder_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cHOL.disj @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (cOrderings.class.linorder_axioms @ V0)))))
(TOrderings.ord_class.ord_eq_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.ord_class.ord_less_eq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_class.dual_order.asym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ cHOL.False)))))))
(TOrderings.order_class.dual_order.refl,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ V0))))
(TOrderings.order_class.less_imp_not_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ cHOL.False)))))))
(TOrderings.order_class.strict_mono_def,(call @ (^[V0]: ((cHOL.eq @ (cOrderings.order_class.strict_mono @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TOrderings.preorder_class.less_not_sym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TOrderings.wellorder.LeastI2_wellorder,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V2 @ V5)) @ ((c==> @ (cHOL.All @ (^[V6]: ((cHOL.implies @ (V2 @ V6)) @ ((V0 @ V5) @ V6))))) @ (V4 @ V5)))))) @ (V4 @ ((cOrderings.ord.Least @ V0) @ V2))))))))))))))))
(TOrderings.wellorder_class.less_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V3) @ V2)) @ (V0 @ V3))))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TPartial_Function.tailrec.fixp_rule_uc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ (cPartial_Function.flat_ord @ cHOL.undefined)) @ (^[V5]: ((V0 @ (V1 @ (V2 @ V5))) @ V4)))))) @ ((c==> @ ((c== @ V3) @ (V2 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cHOL.undefined))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ (^[V4]: (V0 @ (V1 @ (V2 @ V4)))))))) @ ((c==> @ (call @ (^[V4]: ((cHOL.eq @ (V2 @ (V0 @ V4))) @ V4)))) @ ((cHOL.eq @ V3) @ (V1 @ V3))))))))))))))
(TPower.comm_semiring_1_class.dvd_power,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ V1) @ cGroups.one_class.one))) @ ((cRings.dvd_class.dvd @ V1) @ ((cPower.power_class.power @ V1) @ V0))))))))
(TPower.linordered_idom.abs_power_minus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ ((((cPower.power.power @ V7) @ V9) @ (V2 @ V10)) @ V11))) @ (V0 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ V11)))))))))))))))))))))))))))))
(TPower.linordered_idom_class.power_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ (cGroups.abs_class.abs @ V0)) @ V1)))))))
(TPower.linordered_semidom.one_le_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V4 @ V3) @ V6)) @ ((V4 @ V3) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)))))))))))))))))))))
(TPower.linordered_semidom.power_le_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V4 @ V1) @ V6)) @ ((c==> @ ((V4 @ V6) @ V3)) @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ V3)))))))))))))))))))))
(TPower.monoid_mult_class.power_even_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cPower.power_class.power @ ((cPower.power_class.power @ V0) @ V1)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))))
(TPredicate.arity_complete_lattice_pred,(cComplete_Lattices.complete_lattice_class @ cTYPE))
(TPredicate.seq.seq_size_overloaded_def,((c== @ cNat.size_class.size) @ (((cPredicate.seq.seq_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat))) @ (^[V0]: (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TPredicate.singleton_sup_single_single,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPredicate.singleton @ V0) @ ((cLattices.sup_class.sup @ (cPredicate.single @ V1)) @ (cPredicate.single @ V2)))) @ (((cHOL.If @ ((cHOL.eq @ V1) @ V2)) @ V1) @ (V0 @ cProduct_Type.Unity))))))))))
(TProduct_Type.bool.bool_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TProduct_Type.bool.bool_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((((cProduct_Type.bool.bool_rec_set @ V0) @ V1) @ cHOL.False) @ V1))))))
(TProduct_Type.bool.bool_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cProduct_Type.bool.bool_rec_set @ V0) @ V1) @ cHOL.True) @ V0))))))
(TProduct_Type.prod.prod_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TProduct_Type.prod.prod_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((cProduct_Type.prod.prod_rec_set @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((V0 @ V1) @ V2)))))))))
(TProduct_Type.unit.unit_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TProduct_Type.unit.unit_rec_set.intros,(call @ (^[V0]: (((cProduct_Type.unit.unit_rec_set @ V0) @ cProduct_Type.Unity) @ V0))))
(TQuickcheck_Exhaustive.mk_map_term_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.mk_map_term @ V0) @ V1) @ V2) @ V3)) @ (^[V4]: ((cHOL.Let @ (V0 @ cProduct_Type.Unity)) @ (^[V5]: ((cHOL.Let @ (V1 @ cProduct_Type.Unity)) @ (^[V6]: ((cHOL.Let @ (^[V7]: (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ V5) @ ((cList.list.Cons @ V6) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ V5) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ V6) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ V5) @ ((cList.list.Cons @ V6) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ V7)) @ V8)) @ V9)))))) @ (^[V7]: (((cList.foldl @ V7) @ (((cCode_Evaluation.Abs @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil))) @ V5) @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ V6))) @ ((cList.zip @ (V2 @ cProduct_Type.Unity)) @ (V3 @ cProduct_Type.Unity))))))))))))))))))))
(TQuickcheck_Exhaustive.unknown.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Exhaustive.unknown.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.unknown.Known @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Exhaustive.unknown.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Exhaustive.unknown.Known @ V2))))) @ (V0 @ V1))))))))
(TQuickcheck_Narrowing.arity_equal_cfun,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Narrowing.arity_equal_ffun,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Narrowing.conv.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Narrowing.conv_rel) @ V1)))))))
(TQuickcheck_Narrowing.conv_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.conv_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V5))))) @ V2))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cQuickcheck_Narrowing.nth @ V4) @ V5) @ V6))) @ V2))))))))))) @ V2))))))))))
(TQuickcheck_Narrowing.conv_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.conv_graph @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5)))) @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V4)))))))))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5)))) @ ((cHOL.eq @ V1) @ (((cQuickcheck_Narrowing.nth @ V3) @ V4) @ V5))))))))))))))))))
(TQuickcheck_Narrowing.conv_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.conv_rel @ V0) @ V1)) @ ((V2 @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.non_empty.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.non_empty.pelims_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cQuickcheck_Narrowing.non_empty @ V0))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ ((c==> @ (cHOL.Not @ (cHOL.Not @ (cList.null @ V2)))) @ V1)))))) @ V1))))))))
(TQuickcheck_Narrowing.non_empty.pelims_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.non_empty @ V0)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ ((c==> @ (cHOL.Not @ (cList.null @ V2))) @ V1)))))) @ V1))))))))
(TQuickcheck_Narrowing.non_empty.pelims_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cQuickcheck_Narrowing.non_empty @ V0)) @ V1)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ ((c==> @ ((cHOL.eq @ V1) @ (cHOL.Not @ (cList.null @ V3)))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ V2)))))) @ V2))))))))))
(TQuickcheck_Narrowing.non_empty.psimps,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0))) @ ((cHOL.eq @ (cQuickcheck_Narrowing.non_empty @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0))) @ (cHOL.Not @ (cList.null @ V0)))))))
(TQuickcheck_Narrowing.property.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Narrowing.property.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ (((cQuickcheck_Narrowing.property.Universal @ V2) @ V3) @ V4))) @ V1)))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ (((cQuickcheck_Narrowing.property.Existential @ V2) @ V3) @ V4))) @ V1)))))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.property.Property @ V2))) @ V1)))) @ V1))))))))
(TQuickcheck_Narrowing.property.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (V0 @ (V3 @ V5))))) @ (V0 @ (((cQuickcheck_Narrowing.property.Universal @ V2) @ V3) @ V4)))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (V0 @ (V3 @ V5))))) @ (V0 @ (((cQuickcheck_Narrowing.property.Existential @ V2) @ V3) @ V4)))))))))) @ ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Narrowing.property.Property @ V2))))) @ (V0 @ V1)))))))))
(TQuickcheck_Narrowing.typerep_cfun_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TQuickcheck_Narrowing.typerep_ffun_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TQuickcheck_Random.arity_random_itself,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_nibble,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_option,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.random_aux_list_def,((c== @ cQuickcheck_Random.random_aux_list) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (V2 @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_pred_def,((c== @ cQuickcheck_Random.random_aux_pred) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.pred.Pred) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.pred.Pred) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_prod_def,((c== @ cQuickcheck_Random.random_aux_prod) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cProduct_Type.Pair) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cProduct_Type.Pair) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_term_def,((c== @ cQuickcheck_Random.random_aux_term) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cCode_Evaluation.term.dummy_term) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cCode_Evaluation.term.dummy_term) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_unit_def,((c== @ cQuickcheck_Random.random_aux_unit) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cProduct_Type.Unity) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cProduct_Type.Unity) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_finite_1_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_finite_1_inst.random_finite_1 @ V0)) @ ((cQuickcheck_Random.random_aux_finite_1 @ V0) @ V0)))))
(TQuickcheck_Random.random_finite_2_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_finite_2_inst.random_finite_2 @ V0)) @ ((cQuickcheck_Random.random_aux_finite_2 @ V0) @ V0)))))
(TQuickcheck_Random.random_finite_3_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_finite_3_inst.random_finite_3 @ V0)) @ ((cQuickcheck_Random.random_aux_finite_3 @ V0) @ V0)))))
(TQuickcheck_Random.random_finite_4_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_finite_4_inst.random_finite_4 @ V0)) @ ((cQuickcheck_Random.random_aux_finite_4 @ V0) @ V0)))))
(TQuickcheck_Random.random_finite_5_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_finite_5_inst.random_finite_5 @ V0)) @ ((cQuickcheck_Random.random_aux_finite_5 @ V0) @ V0)))))
(TQuickcheck_Random.random_fun_lift_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_fun_lift @ V0)) @ ((((((cQuickcheck_Random.random_fun_aux @ (cTyperep.typerep_class.typerep @ cTYPE)) @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cHOL.eq) @ cCode_Evaluation.term_of_class.term_of) @ V0) @ cRandom.split_seed)))))
(TQuotient.Quotient3_to_Quotient_equivp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuotient.Quotient3 @ V0) @ V1) @ V2)) @ ((c==> @ ((c== @ V3) @ (^[V4]: (^[V5]: ((cHOL.eq @ (V1 @ V4)) @ V5))))) @ ((c==> @ (cEquiv_Relations.equivp @ V0)) @ ((((cLifting.Quotient @ V0) @ V1) @ V2) @ V3)))))))))))))
(TRecord.arity_random_tuple_isomorphism,(cQuickcheck_Random.random_class @ cTYPE))
(TRecord.term_of_tuple_isomorphism_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TRings.class.linordered_semidom.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((cRings.class.linordered_semidom_axioms @ V1) @ V3) @ V5)))))))))))))))
(TRings.class.linordered_semidom.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V4) @ V5) @ V1) @ V2)))))))))))))))
(TRings.class.linordered_semidom.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)))))))))))))))
(TRings.class.linordered_semiring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V3) @ V1) @ V2) @ V4)) @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TRings.class.linordered_semiring_1_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cRings.class.linordered_semiring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((((cRings.class.semiring_1 @ V5) @ V4) @ V0) @ V3))))))))))))))))
(TRings.class.ordered_comm_semiring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.ordered_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (((cRings.class.comm_semiring_0 @ V0) @ V3) @ V4)) @ (((cRings.class.ordered_comm_semiring_axioms @ V1) @ V3) @ V4)))))))))))))))
(TRings.class.ring_no_zero_divisors_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.ring_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cRings.class.no_zero_divisors @ V0) @ V1)) @ (((((cRings.class.ring @ V2) @ V1) @ V3) @ V4) @ V0))))))))))))))
(TRings.classrel_comm_semiring_semiring,(cRings.semiring_class @ cTYPE))
(TRings.classrel_ring_semiring_0_cancel,(cRings.semiring_0_cancel_class @ cTYPE))
(TRings.comm_ring_1_class.dvd_minus_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TRings.comm_ring_1_class.minus_dvd_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TRings.comm_semiring_1_class.dvd_mult2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TRings.comm_semiring_1_class.dvd_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TRings.idom_class.dvd_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))
(TRings.linordered_idom_class.sgn_1_neg,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.sgn_class.sgn @ V0)) @ (cGroups.uminus_class.uminus @ cGroups.one_class.one))) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TRings.linordered_idom_class.sgn_1_pos,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.sgn_class.sgn @ V0)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TRings.linordered_idom_class.sgn_times,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.sgn_class.sgn @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cGroups.times_class.times @ (cGroups.sgn_class.sgn @ V0)) @ (cGroups.sgn_class.sgn @ V1))))))))
(TRings.linordered_semidom.less_add_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V5 @ V6) @ ((V0 @ V6) @ V3))))))))))))))))))
(TRings.linordered_semidom_class.axioms,(((cRings.class.linordered_semidom_axioms @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cOrderings.ord_class.less))
(TRings.linordered_semiring_1_class_def,((c== @ (cRings.linordered_semiring_1_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.linordered_semiring_class @ cTYPE)) @ (cRings.semiring_1_class @ cTYPE))))
(TRings.linordered_semiring_class.intro,((c==> @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cRings.ordered_semiring_class @ cTYPE)) @ (cRings.linordered_semiring_class @ cTYPE))))
(TRings.linordered_semiring_class.super_2,((c==> @ (cRings.linordered_semiring_class @ cTYPE)) @ (cRings.ordered_semiring_class @ cTYPE)))
(TRings.linordered_semiring_class.super_1,((c==> @ (cRings.linordered_semiring_class @ cTYPE)) @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)))
(TRings.mult_zero_class.mult_zero_right,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TRings.ordered_comm_semiring_class_def,((c== @ (cRings.ordered_comm_semiring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_semiring_0_class @ cTYPE)) @ (((cRings.class.ordered_comm_semiring_axioms @ cOrderings.ord_class.less_eq) @ cGroups.zero_class.zero) @ cGroups.times_class.times)))))
(TRings.ordered_ring.mult_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V2 @ V7) @ V8)) @ ((c==> @ ((V2 @ V9) @ V1)) @ ((V2 @ ((V4 @ V9) @ V8)) @ ((V4 @ V9) @ V7))))))))))))))))))))))))))
(TRings.ordered_ring.mult_nonpos_nonpos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V2 @ V7) @ V1)) @ ((c==> @ ((V2 @ V8) @ V1)) @ ((V2 @ V1) @ ((V4 @ V7) @ V8))))))))))))))))))))))))
(TRings.ordered_semiring.mult_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((c==> @ ((V2 @ V1) @ V7)) @ ((V2 @ ((V4 @ V7) @ V5)) @ ((V4 @ V7) @ V6))))))))))))))))))))))
(TRings.ring_1.square_diff_one_factored,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ ((V1 @ V6) @ V6)) @ V0)) @ ((V1 @ ((V2 @ V6) @ V0)) @ ((V4 @ V6) @ V0)))))))))))))))))))
(TRings.ring_no_zero_divisors_class_def,((c== @ (cRings.ring_no_zero_divisors_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.no_zero_divisors_class @ cTYPE)) @ (cRings.ring_class @ cTYPE))))
(TRings.zero_neq_one_class.one_neq_zero,(cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TRings.zero_neq_one_class.zero_neq_one,(cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ cGroups.one_class.one)))
(TSet_Interval.card_atLeastLessThan_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ V1) @ V0))))))))
(TSet_Interval.card_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ ((cNat.minus_nat_inst.minus_nat @ V1) @ (cNat.Suc @ V0))))))))
(TSet_Interval.ex_bij_betw_nat_finite_1,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: (((cFun.bij_betw @ V1) @ ((cSet_Interval.ord_class.atLeastAtMost @ cNat.one_nat_inst.one_nat) @ (cFinite_Set.card @ V0))) @ V0)))))))
(TSet_Interval.finite_atLeastAtMost_int,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)))))))
(TSet_Interval.finite_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)))))))
(TSet_Interval.lessThan_Suc_eq_insert_0,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.lessThan @ (cNat.Suc @ V0))) @ ((cSet.insert @ cNat.zero_nat_inst.zero_nat) @ ((cSet.image @ cNat.Suc) @ (cSet_Interval.ord_class.lessThan @ V0)))))))
(TSet_Interval.order.Icc_subset_Ici_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet_Interval.ord.atLeast @ V0) @ V4))) @ ((cHOL.disj @ (cHOL.Not @ ((V0 @ V2) @ V3))) @ ((V0 @ V4) @ V2)))))))))))))))
(TSet_Interval.order.Icc_subset_Iic_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet_Interval.ord.atMost @ V0) @ V4))) @ ((cHOL.disj @ (cHOL.Not @ ((V0 @ V2) @ V3))) @ ((V0 @ V3) @ V4)))))))))))))))
(TSet_Interval.setsum_natinterval_difff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cGroups.minus_class.minus @ (V0 @ V3)) @ (V0 @ ((cNat.plus_nat_inst.plus_nat @ V3) @ cNat.one_nat_inst.one_nat))))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cGroups.minus_class.minus @ (V0 @ V1)) @ (V0 @ ((cNat.plus_nat_inst.plus_nat @ V2) @ cNat.one_nat_inst.one_nat)))) @ cGroups.zero_class.zero)))))))))
(TString.equal_nibble_inst.equal_nibble,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TString.size_literal_inst.size_literal,((c== @ cString.size_literal_inst.size_literal) @ cString.size_literal_inst.size_literal))
(TTransfer.right_total_Domainp_transfer,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ ((cTransfer.fun_rel @ V1) @ cHOL.eq)) @ (^[V2]: (^[V3]: ((cSet.Bex @ (cSet.Collect @ (cRelation.Domainp @ V0))) @ (^[V4]: ((V2 @ V3) @ V4)))))) @ cRelation.Domainp)))))))
(TTransitive_Closure.Not_Domain_rtrancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cRelation.Domain @ V1)))) @ ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V2)) @ (cTransitive_Closure.rtrancl @ V1))) @ ((cHOL.eq @ V0) @ V2))))))))))
(TTransitive_Closure.converse_rtranclE2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cTransitive_Closure.rtrancl @ V4))) @ ((c==> @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V5)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ V4)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cTransitive_Closure.rtrancl @ V4))) @ V5))))))) @ V5))))))))))))))))
(TTransitive_Closure.converse_rtranclpE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V1) @ V4)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V4) @ V2)) @ V3))))) @ V3))))))))))))
(TTransitive_Closure.relpow_imp_rtrancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ ((cNat.compow @ V1) @ V2))) @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ V2))))))))))
(TTransitive_Closure.rtrancl_Int_subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cRelation.Id) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.relcomp @ ((cLattices.inf_class.inf @ (cTransitive_Closure.rtrancl @ V1)) @ V0)) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ (cTransitive_Closure.rtrancl @ V1)) @ V0))))))))
(TTransitive_Closure.rtrancl_Un_rtrancl,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ ((cLattices.sup_class.sup @ (cTransitive_Closure.rtrancl @ V0)) @ (cTransitive_Closure.rtrancl @ V1)))) @ (cTransitive_Closure.rtrancl @ ((cLattices.sup_class.sup @ V0) @ V1))))))))
(TTransitive_Closure.rtrancl_imp_relpow,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ V1))) @ (cHOL.Ex @ (^[V2]: ((cSet.member @ V0) @ ((cNat.compow @ V2) @ V1))))))))))
(TTransitive_Closure.rtranclp_converseD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.rtranclp @ (cRelation.conversep @ V0)) @ V1) @ V2)) @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V1)))))))))
(TTransitive_Closure.rtranclp_converseI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ (((cTransitive_Closure.rtranclp @ (cRelation.conversep @ V0)) @ V2) @ V1)))))))))
(TTransitive_Closure.rtranclp_r_diff_Id,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtranclp @ ((cLattices.inf_class.inf @ V0) @ (^[V1]: (^[V2]: (cHOL.Not @ ((cHOL.eq @ V1) @ V2))))))) @ (cTransitive_Closure.rtranclp @ V0)))))
(TTransitive_Closure.trancl_into_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.trancl_unfold_left,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.trancl @ V0)) @ ((cRelation.relcomp @ V0) @ (cTransitive_Closure.rtrancl @ V0))))))
(TBig_Operators.comm_monoid_set.If_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V6]: (((cHOL.If @ (V3 @ V6)) @ (V4 @ V6)) @ (V5 @ V6)))) @ V2)) @ ((V0 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cLattices.inf_class.inf @ V2) @ (cSet.Collect @ (^[V6]: (V3 @ V6)))))) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V5) @ ((cLattices.inf_class.inf @ V2) @ (cGroups.uminus_class.uminus @ (cSet.Collect @ (^[V6]: (V3 @ V6)))))))))))))))))))))))
(TBig_Operators.comm_monoid_set.infinite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V2))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V3) @ V2)) @ V1))))))))))))
(TBig_Operators.lattice_class.Inf_le_Sup,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)))))))
(TBig_Operators.linorder.hom_Max_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (V2 @ (((cOrderings.ord.max @ V0) @ V4) @ V5))) @ (((cOrderings.ord.max @ V0) @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V2 @ ((cBig_Operators.linorder.Max @ V0) @ V3))) @ ((cBig_Operators.linorder.Max @ V0) @ ((cSet.image @ V2) @ V3))))))))))))))))
(TBig_Operators.linorder.hom_Min_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (V2 @ (((cOrderings.ord.min @ V0) @ V4) @ V5))) @ (((cOrderings.ord.min @ V0) @ (V2 @ V4)) @ (V2 @ V5)))))))) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V2 @ ((cBig_Operators.linorder.Min @ V0) @ V3))) @ ((cBig_Operators.linorder.Min @ V0) @ ((cSet.image @ V2) @ V3))))))))))))))))
(TBig_Operators.linorder_class.Least_Min,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ (cSet.Collect @ (^[V1]: (V0 @ V1))))) @ ((c==> @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ ((cHOL.eq @ (cOrderings.ord_class.Least @ (^[V1]: (V0 @ V1)))) @ (cBig_Operators.linorder_class.Min @ (cSet.Collect @ (^[V1]: (V0 @ V1))))))))))
(TBig_Operators.linorder_class.Max.union,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cOrderings.ord_class.max @ (cBig_Operators.linorder_class.Max @ V0)) @ (cBig_Operators.linorder_class.Max @ V1))))))))))))
(TBig_Operators.linorder_class.Min.union,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cOrderings.ord_class.min @ (cBig_Operators.linorder_class.Min @ V0)) @ (cBig_Operators.linorder_class.Min @ V1))))))))))))
(TBig_Operators.semilattice_set.eq_fold',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ V1)) @ (cOption.the @ (((cFinite_Set.fold @ (^[V2]: (^[V3]: (cOption.option.Some @ (((cOption.option.option_case @ V2) @ (^[V4]: ((V0 @ V2) @ V4))) @ V3))))) @ cOption.option.None) @ V1)))))))))
(TCode_Evaluation.arity_term_of_finite_1,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_finite_2,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_finite_3,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_finite_4,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_term_of_finite_5,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Numeral.int_of_integer_of_natural,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_natural @ V0))) @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_natural @ V0))))))
(TCode_Numeral.integer_of_natural.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_natural @ (cCode_Numeral.natural_of_nat @ V0))) @ (cCode_Numeral.integer_of_int @ (cNat.semiring_1_class.of_nat @ V0))))))
(TCode_Numeral.integer_of_natural.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_natural @ V0))) @ (cNat.semiring_1_class.of_nat @ (cCode_Numeral.nat_of_natural @ V0))))))
(TCode_Numeral.integer_of_natural_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_natural @ (cNat.semiring_1_class.of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TCode_Numeral.natural_of_integer.abs_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.natural_of_integer @ (cCode_Numeral.integer_of_int @ V0))) @ (cCode_Numeral.natural_of_nat @ (cInt.nat @ V0))))))
(TCode_Numeral.natural_of_integer.rep_eq,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ (cCode_Numeral.natural_of_integer @ V0))) @ (cInt.nat @ (cCode_Numeral.int_of_integer @ V0))))))
(TComplete_Lattices.Inf_fun_inst.Inf_fun,((c== @ cComplete_Lattices.Inf_fun_inst.Inf_fun) @ cComplete_Lattices.Inf_fun_inst.Inf_fun))
(TComplete_Lattices.Inf_set_inst.Inf_set,((c== @ cComplete_Lattices.Inf_set_inst.Inf_set) @ cComplete_Lattices.Inf_set_inst.Inf_set))
(TComplete_Lattices.Sup_fun_inst.Sup_fun,((c== @ cComplete_Lattices.Sup_fun_inst.Sup_fun) @ cComplete_Lattices.Sup_fun_inst.Sup_fun))
(TComplete_Lattices.Sup_set_inst.Sup_set,((c== @ cComplete_Lattices.Sup_set_inst.Sup_set) @ cComplete_Lattices.Sup_set_inst.Sup_set))
(TComplete_Partial_Order.admissible_True,(call @ (^[V0]: (call @ (^[V1]: (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V2]: cHOL.True)))))))
(TComplete_Partial_Order.admissible_ball,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ (((cComplete_Partial_Order.ccpo.admissible @ V1) @ V2) @ (^[V5]: ((V3 @ V5) @ V4))))))) @ (((cComplete_Partial_Order.ccpo.admissible @ V1) @ V2) @ (^[V4]: ((cSet.Ball @ V0) @ (^[V5]: ((V3 @ V4) @ V5)))))))))))))))
(TComplete_Partial_Order.admissible_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V4]: (V2 @ V4)))) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V4]: (V3 @ V4)))) @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V4]: ((cHOL.conj @ (V2 @ V4)) @ (V3 @ V4)))))))))))))))
(TDivides.arity_semiring_numeral_div_int,(cDivides.semiring_numeral_div_class @ cTYPE))
(TDivides.arity_semiring_numeral_div_nat,(cDivides.semiring_numeral_div_class @ cTYPE))
(TDivides.class.semiring_numeral_div_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c== @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.conj @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((((cRings.class.linordered_semidom @ V3) @ V4) @ V0) @ V5) @ V7) @ V8)) @ (((((((((cDivides.class.semiring_numeral_div_axioms @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)))))))))))))))))))))))
(TDivides.ring_div_class.div_minus_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.div @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cDivides.div_class.div @ V0) @ V1)))))))
(TDivides.ring_div_class.div_minus_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.div @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cDivides.div_class.div @ (cGroups.uminus_class.uminus @ V0)) @ V1)))))))
(TDivides.ring_div_class.mod_minus_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cDivides.div_class.mod @ V0) @ V1))))))))
(TDivides.ring_div_class.mod_minus_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cDivides.div_class.mod @ (cGroups.uminus_class.uminus @ V0)) @ V1))))))))
(TDivides.ring_div_class.ring_div_axioms,((((((((cDivides.class.ring_div @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TDivides.semiring_div.div_mod_equality2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V3 @ ((V3 @ ((V0 @ V6) @ ((V1 @ V7) @ V6))) @ ((V2 @ V7) @ V6))) @ V8)) @ ((V3 @ V7) @ V8))))))))))))))))))))))
(TDivides.semiring_div.div_mult_mult1_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V1 @ ((V0 @ V6) @ V7)) @ ((V0 @ V6) @ V8))) @ (((cHOL.If @ ((cHOL.eq @ V6) @ V4)) @ V4) @ ((V1 @ V7) @ V8)))))))))))))))))))))))
(TDivides.semiring_div.dvd_div_mult_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((V0 @ ((V1 @ V7) @ V6)) @ V6)) @ V7))))))))))))))))))))
(TDivides.semiring_div.mod_div_equality',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V3 @ ((V2 @ V6) @ V7)) @ ((V0 @ ((V1 @ V6) @ V7)) @ V7))) @ V6)))))))))))))))))))
(TDivides.semiring_div.mod_div_equality2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V3 @ ((V0 @ V6) @ ((V1 @ V7) @ V6))) @ ((V2 @ V7) @ V6))) @ V7)))))))))))))))))))
(TDivides.semiring_div.mod_mult_right_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ V8)) @ ((V2 @ ((V0 @ V6) @ ((V2 @ V7) @ V8))) @ V8))))))))))))))))))))))
(TDivides.semiring_div_class.div_dvd_div,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cDivides.div_class.div @ V1) @ V0)) @ ((cDivides.div_class.div @ V2) @ V0))) @ ((cRings.dvd_class.dvd @ V1) @ V2)))))))))))
(TDivides.semiring_div_class.dvd_mod_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ ((cDivides.div_class.mod @ V2) @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TDivides.semiring_div_class.mod_mult_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ ((cDivides.div_class.mod @ V0) @ V2)) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)))))))))
(TDivides.semiring_numeral_div.diff_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ ((V6 @ V9) @ V4)) @ V9)))))))))))))))))))))))
(TDivides.semiring_numeral_div_class_def,((c== @ (cDivides.semiring_numeral_div_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cDivides.semiring_div_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.linordered_semidom_class @ cTYPE)) @ (((((((((cDivides.class.semiring_numeral_div_axioms @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cGroups.minus_class.minus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less)))))
(TEnum.finite_1.finite_1_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_1.finite_1_rep_set @ V0)) @ ((c==> @ (V1 @ cHOL.undefined)) @ (V1 @ V0))))))))
(TEnum.finite_2.finite_2_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_2.finite_2_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (V1 @ (cDatatype.In1 @ cHOL.undefined))) @ (V1 @ V0)))))))))
(TEnum.finite_3.finite_3_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_3.finite_3_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))) @ (V1 @ V0))))))))))
(TEnum.finite_4.finite_4_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_4.finite_4_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))) @ (V1 @ V0)))))))))))
(TEnum.finite_5.finite_5_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cEnum.finite_5.finite_5_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In0 @ (cDatatype.In1 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined)))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In0 @ cHOL.undefined))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))) @ (V1 @ V0))))))))))))
(TEquiv_Relations.card_quotient_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cFun.inj_on @ (^[V2]: ((cEquiv_Relations.quotient @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)) @ V1))) @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ ((cEquiv_Relations.quotient @ V0) @ V1))) @ (cFinite_Set.card @ V0)))))))))
(TExtraction.sumbool.Abs_sumbool_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cExtraction.sumbool.sumbool_rep_set))) @ ((cHOL.eq @ (cExtraction.Rep_sumbool @ (cExtraction.Abs_sumbool @ V0))) @ V0)))))
(TExtraction.sumbool.Rep_sumbool_inverse,(call @ (^[V0]: ((cHOL.eq @ (cExtraction.Abs_sumbool @ (cExtraction.Rep_sumbool @ V0))) @ V0))))
(TExtraction.sumbool.sumbool_rec_set_def,((c== @ cExtraction.sumbool.sumbool_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Left)) @ ((cHOL.eq @ V4) @ V0))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cExtraction.sumbool.Right)) @ ((cHOL.eq @ V4) @ V1)))))))))))
(TExtraction.sumbool.sumbool_rep_set_def,((c== @ cExtraction.sumbool.sumbool_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ cHOL.undefined))))))))
(TFields.class.field_inverse_zero.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cFields.class.field_inverse_zero_axioms @ V0) @ V5)))))))))))))))))))
(TFields.class.field_inverse_zero.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TFields.division_ring.divide_minus_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ (V7 @ V8)) @ V9)) @ (V7 @ ((V1 @ V8) @ V9)))))))))))))))))))))))))
(TFields.division_ring.inverse_eq_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ V8)) @ ((V1 @ V2) @ V8))))))))))))))))))))))
(TFields.division_ring.minus_divide_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V7 @ ((V1 @ V8) @ V9))) @ ((V1 @ (V7 @ V8)) @ V9))))))))))))))))))))))))
(TFields.division_ring_class.divide_self,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V0)) @ cGroups.one_class.one)))))
(TFields.field_inverse_zero.add_frac_num,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V4 @ ((V1 @ V9) @ V8)) @ V10)) @ ((V1 @ ((V4 @ V9) @ ((V2 @ V10) @ V8))) @ V8)))))))))))))))))))))))))))
(TFields.field_inverse_zero.add_num_frac,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V4 @ V9) @ ((V1 @ V10) @ V8))) @ ((V1 @ ((V4 @ V10) @ ((V2 @ V9) @ V8))) @ V8)))))))))))))))))))))))))))
(TFields.field_inverse_zero.divide_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ V10)) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ V8) @ ((V2 @ V10) @ V9))) @ ((cHOL.eq @ V10) @ V5)))))))))))))))))))))))))))
(TFields.field_inverse_zero.eq_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ V8) @ ((V1 @ V9) @ V10))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V10) @ V5))) @ ((cHOL.eq @ ((V2 @ V8) @ V10)) @ V9)) @ ((cHOL.eq @ V8) @ V5)))))))))))))))))))))))))))
(TFields.field_inverse_zero_class.axioms,((cFields.class.field_inverse_zero_axioms @ cFields.inverse_class.inverse) @ cGroups.zero_class.zero))
(TFields.linordered_field.divide_neg_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V10 @ V5) @ ((V1 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.divide_neg_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((c==> @ ((V10 @ V5) @ V13)) @ ((V10 @ ((V1 @ V12) @ V13)) @ V5)))))))))))))))))))))))))))))))))
(TFields.linordered_field.divide_pos_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V10 @ ((V1 @ V12) @ V13)) @ V5)))))))))))))))))))))))))))))))))
(TFields.linordered_field.divide_pos_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V10 @ V5) @ V13)) @ ((V10 @ V5) @ ((V1 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.one_le_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V9 @ V12) @ V3)) @ ((V9 @ V3) @ (V0 @ V12))))))))))))))))))))))))))))))))
(TFinite_Set.comp_fun_idem.comp_fun_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V1))) @ (V0 @ V1))))))))
(TFinite_Set.comp_fun_idem.fun_left_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V1) @ V2))) @ ((V0 @ V1) @ V2))))))))))
(TGroups.ab_group_add_class.diff_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TGroups.ab_semigroup_mult_class.mult_ac_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TGroups.ab_semigroup_mult_class.mult_ac_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TGroups.ab_semigroup_mult_class.mult_ac_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TGroups.class.ab_group_add_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((cHOL.eq @ ((V0 @ (V1 @ V4)) @ V4)) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((V3 @ V4) @ V5)) @ ((V0 @ V4) @ (V1 @ V5)))))))) @ ((((cGroups.class.ab_group_add_axioms @ V0) @ V2) @ V3) @ V1))))))))))))
(TGroups.classrel_ab_group_add_group_add,(cGroups.group_add_class @ cTYPE))
(TGroups.group_add.neg_0_equal_iff_equal,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V2) @ (V3 @ V4))) @ ((cHOL.eq @ V2) @ V4))))))))))))))
(TGroups.group_add.neg_equal_0_iff_equal,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cGroups.class.group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ (V3 @ V4)) @ V2)) @ ((cHOL.eq @ V4) @ V2))))))))))))))
(TGroups.group_add_class.add_diff_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V1)) @ V0))))))
(TGroups.group_add_class.diff_add_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V1)) @ V0))))))
(TGroups.group_add_class.diff_eq_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.minus_class.minus @ V2) @ V3))) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TGroups.ordered_ab_group_add.diff_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ ((V2 @ V6) @ V7)) @ V8)) @ ((V4 @ V6) @ ((V0 @ V8) @ V7)))))))))))))))))))))))
(TGroups.ordered_ab_group_add.le_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V6) @ ((V2 @ V7) @ V8))) @ ((V4 @ ((V0 @ V6) @ V8)) @ V7))))))))))))))))))))))
(TGroups.semigroup_mult_class.mult.assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TGroups.semigroup_mult_class.mult_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(THilbert_Choice.bij_vimage_eq_inv_image,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cFun.bij_betw @ V0) @ cOrderings.top_class.top) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cSet.vimage @ V0) @ V1)) @ ((cSet.image @ ((cHilbert_Choice.inv_into @ cOrderings.top_class.top) @ V0)) @ V1))))))))
(TLattices.boolean_algebra.compl_inf_bot,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ (V1 @ V8)) @ V8)) @ V6)))))))))))))))))))))
(TLattices.boolean_algebra.compl_sup_top,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ (V1 @ V8)) @ V8)) @ V7)))))))))))))))))))))
(TLattices.boolean_algebra.inf_compl_bot,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V8) @ (V1 @ V8))) @ V6)))))))))))))))))))))
(TLattices.boolean_algebra.sup_compl_top,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ V8) @ (V1 @ V8))) @ V7)))))))))))))))))))))
(TLattices.boolean_algebra_class.diff_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TLattices.bounded_lattice_bot_class_def,((c== @ (cLattices.bounded_lattice_bot_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.lattice_class @ cTYPE)) @ (cOrderings.order_bot_class @ cTYPE))))
(TLattices.bounded_lattice_top_class_def,((c== @ (cLattices.bounded_lattice_top_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.lattice_class @ cTYPE)) @ (cOrderings.order_top_class @ cTYPE))))
(TLattices.class.bounded_lattice_bot_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ (((cOrderings.class.order_bot @ V4) @ V1) @ V2))))))))))))))
(TLattices.class.bounded_lattice_top_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ (((cOrderings.class.order_top @ V1) @ V2) @ V4))))))))))))))
(TLattices.distrib_lattice_class.distrib_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TLattices.distrib_lattice_class.distrib_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TLattices.distrib_lattice_class.distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.distrib_lattice_class.distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TLattices.linorder_class.max.cobounded1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TLattices.linorder_class.max.cobounded2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TLattices.linorder_class.max.right_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V1)) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TLattices.linorder_class.min.cobounded1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V0))))))
(TLattices.linorder_class.min.cobounded2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V1))))))
(TLattices.linorder_class.min.right_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V1)) @ ((cOrderings.ord_class.min @ V0) @ V1)))))))
(TLattices.semilattice_inf.inf_left_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V3) @ V4))) @ ((V0 @ V3) @ V4))))))))))))))
(TLattices.semilattice_inf_class.inf_aci_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TLattices.semilattice_inf_class.inf_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TLattices.semilattice_inf_class.inf_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TLattices.semilattice_inf_class.inf_aci_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V1) @ V0)))))))
(TLattices.semilattice_inf_class.inf_le1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0))))))
(TLattices.semilattice_inf_class.inf_le2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V1))))))
(TLattices.semilattice_inf_class.le_infE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.semilattice_inf_class.le_infI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2)))))))))))
(TLattices.semilattice_neutr_order.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cLattices.semilattice_neutr @ V0) @ V1)) @ ((c==> @ (((cLattices.semilattice_order @ V0) @ V2) @ V3)) @ ((((cLattices.semilattice_neutr_order @ V0) @ V1) @ V2) @ V3))))))))))))
(TLattices.semilattice_order.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ V3) @ ((V0 @ V4) @ V5))) @ ((cHOL.conj @ ((V1 @ V3) @ V4)) @ ((V1 @ V3) @ V5)))))))))))))))))
(TLattices.semilattice_order.coboundedI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ ((V0 @ V3) @ V5)) @ V4))))))))))))))))
(TLattices.semilattice_order.coboundedI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ ((V0 @ V5) @ V3)) @ V4))))))))))))))))
(TLattices.semilattice_sup.sup_left_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V3) @ V4))) @ ((V0 @ V3) @ V4))))))))))))))
(TLattices.semilattice_sup_class.le_supE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.semilattice_sup_class.le_supI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V2)) @ V1))))))))))
(TLattices.semilattice_sup_class.sup_aci_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TLattices.semilattice_sup_class.sup_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ V1) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TLattices.semilattice_sup_class.sup_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.sup_aci_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TLattices.semilattice_sup_class.sup_ge1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TLattices.semilattice_sup_class.sup_ge2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TLazy_Sequence.arity_type_lazy_sequence,(cHOL.type_class @ cTYPE))
(TLazy_Sequence.equal_lazy_sequence_code,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (((cOption.option.option_case @ (((cOption.option.option_case @ cHOL.True) @ (^[V4]: cHOL.False)) @ V3)) @ (^[V4]: ((cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (((cOption.option.option_case @ cHOL.False) @ (^[V7]: ((cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: ((cHOL.conj @ ((cHOL.eq @ V5) @ V8)) @ ((cHOL.equal_class.equal @ V0) @ V1))))) @ V7))) @ V3)))) @ V4))) @ V2)))) @ ((cProduct_Type.Pair @ (cLazy_Sequence.yield @ V0)) @ (cLazy_Sequence.yield @ V1)))))))))
(TLazy_Sequence.iterate_upto.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V3) @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ V3))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cLazy_Sequence.iterate_upto_rel) @ V1))))))))
(TLazy_Sequence.iterate_upto_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.iterate_upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((cLazy_Sequence.iterate_upto_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ V2)))))))))))) @ V2)))))))))
(TLazy_Sequence.iterate_upto_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.iterate_upto_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (cLazy_Sequence.Lazy_Sequence @ (^[V6]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V3 @ V4)) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))))))))) @ (cHOL.All @ (^[V6]: ((cHOL.implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ ((cLazy_Sequence.iterate_upto_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))))))))))))))))))))))
(TLazy_Sequence.iterate_upto_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.iterate_upto_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V4))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((cLazy_Sequence.small_lazy'_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ V1))) @ ((cLazy_Sequence.small_lazy'_graph @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))))) @ ((cLazy_Sequence.small_lazy'_graph @ ((cProduct_Type.Pair @ V0) @ V1)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V1)) @ (V2 @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))))))))))))))
(TLazy_Sequence.small_lazy_list_sumC_def,((c== @ cLazy_Sequence.small_lazy_list_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cLazy_Sequence.small_lazy_list_graph @ V0) @ V1))))))
(TLifting_Option.right_unique_option_rel,(call @ (^[V0]: ((c==> @ (cTransfer.right_unique @ V0)) @ (cTransfer.right_unique @ (cLifting_Option.option_rel @ V0))))))
(TLifting_Product.prod_invariant_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLifting_Product.prod_rel @ (cLifting.invariant @ V0)) @ (cLifting.invariant @ V1))) @ (cLifting.invariant @ ((cLifting_Product.prod_pred @ V0) @ V1))))))))
(TLifting_Set.right_total_Compl_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ V0)) @ (cLifting_Set.set_rel @ V0)) @ (^[V1]: ((cLattices.inf_class.inf @ (cGroups.uminus_class.uminus @ V1)) @ (cSet.Collect @ (cRelation.Domainp @ V0))))) @ cGroups.uminus_class.uminus))))))
(TLifting_Set.right_total_Inter_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.bi_unique @ V0)) @ ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ (cLifting_Set.set_rel @ (cLifting_Set.set_rel @ V0))) @ (cLifting_Set.set_rel @ V0)) @ (^[V1]: ((cLattices.inf_class.inf @ (cComplete_Lattices.Inf_class.Inf @ V1)) @ (cSet.Collect @ (cRelation.Domainp @ V0))))) @ (^[V1]: (cComplete_Lattices.Inf_class.Inf @ V1))))))))
(TList.comm_monoid_add_class.listsum_rev,(call @ (^[V0]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ (cList.rev @ V0))) @ (cList.monoid_add_class.listsum @ V0)))))
(TList.linorder.insort_insert_insort_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ (V2 @ V3)) @ ((cSet.image @ V2) @ (cList.set @ V4))))) @ ((cHOL.eq @ ((((cList.linorder.insort_insert_key @ V0) @ V2) @ V3) @ V4)) @ ((((cList.linorder.insort_key @ V0) @ V2) @ V3) @ V4)))))))))))))))
(TList.linorder.sorted_insort_insert_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ V3))) @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ ((((cList.linorder.insort_insert_key @ V0) @ V2) @ V4) @ V3))))))))))))))))
(TList.linorder.sorted_list_of_set_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted_list_of_set @ V0) @ cOrderings.bot_class.bot)) @ cList.list.Nil)))))))
(TList.linorder_class.filter_insort_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ (V0 @ V1))) @ ((cHOL.eq @ ((cList.filter @ V0) @ (((cList.linorder_class.insort_key @ V2) @ V1) @ V3))) @ ((cList.filter @ V0) @ V3))))))))))))
(TList.linorder_class.insort_insert_triv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cHOL.eq @ (((cList.linorder_class.insort_insert_key @ (^[V2]: V2)) @ V0) @ V1)) @ V1)))))))
(TList.linorder_class.insort_key_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((c==> @ (cList.linorder_class.sorted @ ((cList.map @ V2) @ V1))) @ ((c==> @ ((cHOL.eq @ (cList.hd @ ((cList.filter @ (^[V3]: ((cHOL.eq @ (V2 @ V0)) @ (V2 @ V3)))) @ V1))) @ V0)) @ ((cHOL.eq @ (((cList.linorder_class.insort_key @ V2) @ V0) @ ((cList.remove1 @ V0) @ V1))) @ V1)))))))))))
(TList.linorder_class.sort_key_conv_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ (cList.set @ V1))) @ ((cHOL.eq @ ((cList.linorder_class.sort_key @ V0) @ V1)) @ (((cList.fold @ (cList.linorder_class.insort_key @ V0)) @ V1) @ cList.list.Nil))))))))
(TList.linorder_class.sorted_list_of_set,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.conj @ ((cHOL.eq @ (cList.set @ (cList.linorder_class.sorted_list_of_set @ V0))) @ V0)) @ ((cHOL.conj @ (cList.linorder_class.sorted @ (cList.linorder_class.sorted_list_of_set @ V0))) @ (cList.distinct @ (cList.linorder_class.sorted_list_of_set @ V0))))))))
(TList.linorder_class.sorted_map_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ V1))) @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ ((cList.remove1 @ V2) @ V1)))))))))))
(TList.linorder_class.sorted_remdups_adj,(call @ (^[V0]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ (cList.remdups_adj @ V0))))))
(TList.monoid_add.list_size_conv_listsum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((cList.list.list_size @ V2) @ V3)) @ ((cNat.plus_nat_inst.plus_nat @ (cList.monoid_add_class.listsum @ ((cList.map @ V2) @ V3))) @ (cNat.size_class.size @ V3)))))))))))))
(TNat.class.semiring_char_0_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ (((cNat.semiring_1.of_nat @ V0) @ V1) @ V2)) @ cOrderings.top_class.top)) @ (((cNat.class.semiring_char_0_axioms @ V0) @ V1) @ V2)))))))))
(TNat.linordered_semidom.of_nat_0_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V1) @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6))))))))))))))))))
(TNat.linordered_semidom.of_nat_le_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6)) @ V1)) @ ((cHOL.eq @ V6) @ cNat.zero_nat_inst.zero_nat))))))))))))))))))
(TNat.linordered_semidom.of_nat_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6)) @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V7))) @ ((cNat.ord_nat_inst.less_nat @ V6) @ V7))))))))))))))))))))
(TNat.order_class.lift_Suc_mono_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cOrderings.ord_class.less @ (V0 @ V3)) @ (V0 @ (cNat.Suc @ V3)))))) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TNat_Transfer.transfer_int_nat_numerals_4,((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ (cNat.semiring_1_class.of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One)))))
(TNat_Transfer.transfer_int_nat_numerals_3,((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cNat.semiring_1_class.of_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))
(TNat_Transfer.transfer_int_nat_numerals_2,((cHOL.eq @ cInt.one_int_inst.one_int) @ (cNat.semiring_1_class.of_nat @ cNat.one_nat_inst.one_nat)))
(TNat_Transfer.transfer_int_nat_numerals_1,((cHOL.eq @ cInt.zero_int_inst.zero_int) @ (cNat.semiring_1_class.of_nat @ cNat.zero_nat_inst.zero_nat)))
(TNat_Transfer.transfer_int_nat_set_cong,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2))))) @ ((cHOL.eq @ (cSet.Collect @ (^[V2]: (V0 @ V2)))) @ (cSet.Collect @ (^[V2]: (V1 @ V2))))))))))
(TNat_Transfer.transfer_int_nat_sum_prod_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (V1 @ (cNat.semiring_1_class.of_nat @ V2)))) @ ((cSet.image @ cInt.nat) @ V0)))))))))
(TNat_Transfer.transfer_int_nat_sum_prod_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V1 @ (cNat.semiring_1_class.of_nat @ V2)))) @ ((cSet.image @ cInt.nat) @ V0)))))))))
(TNat_Transfer.transfer_morphism_int_nat,((cNat_Transfer.transfer_morphism @ cNat.semiring_1_class.of_nat) @ (^[V0]: cHOL.True)))
(TNat_Transfer.transfer_morphism_nat_int,((cNat_Transfer.transfer_morphism @ cInt.nat) @ (cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int)))
(TNat_Transfer.transfer_nat_int_numerals_4,((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))) @ (cInt.nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One)))))
(TNat_Transfer.transfer_nat_int_numerals_3,((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cInt.nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))
(TNat_Transfer.transfer_nat_int_numerals_2,((cHOL.eq @ cNat.one_nat_inst.one_nat) @ (cInt.nat @ cInt.one_int_inst.one_int)))
(TNat_Transfer.transfer_nat_int_numerals_1,((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ (cInt.nat @ cInt.zero_int_inst.zero_int)))
(TNat_Transfer.transfer_nat_int_set_cong,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((cHOL.eq @ (V0 @ V2)) @ (V1 @ V2)))))) @ ((cHOL.eq @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ (V0 @ V2))))) @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ (V1 @ V2)))))))))))
(TNat_Transfer.transfer_nat_int_sum_prod_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (V0 @ (cInt.nat @ V2)))) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1))))))))
(TNat_Transfer.transfer_nat_int_sum_prod_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (V0 @ (cInt.nat @ V2)))) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1))))))))
(TNitpick.arity_full_exhaustive_pair_box,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TNitpick.arity_partial_term_of_pair_box,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TNitpick.fun_box.fun_box_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TNitpick.fun_box.fun_box_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (((cNitpick.fun_box.fun_box_rec_set @ V0) @ (cNitpick.fun_box.FunBox @ V1)) @ (V0 @ V1)))))))
(TNitpick.fun_box.fun_box_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNitpick.fun_box.fun_box_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TNitpick.fun_box.fun_box_rep_set.intros,(call @ (^[V0]: (cNitpick.fun_box.fun_box_rep_set @ (cDatatype.Leaf @ V0)))))
(TNitpick.term_of_word_inst.term_of_word,((c== @ cNitpick.term_of_word_inst.term_of_word) @ cNitpick.term_of_word_inst.term_of_word))
(TNitpick.typerep_word_inst.typerep_word,((c== @ cNitpick.typerep_word_inst.typerep_word) @ cNitpick.typerep_word_inst.typerep_word))
(TNum.linordered_idom.neg_numeral_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11))) @ ((cNum.ord_num_inst.less_eq_num @ V11) @ V10))))))))))))))))))))))))))))
(TNum.linordered_idom.neg_numeral_le_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V7)))))))))))))))))))))))))
(TNum.linordered_idom_class.sub_negative,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cNum.neg_numeral_class.sub @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.linordered_idom_class.sub_positive,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cNum.neg_numeral_class.sub @ V0) @ V1))) @ ((cNum.ord_num_inst.less_num @ V1) @ V0)))))))
(TNum.linordered_semidom.zero_le_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V1) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))))))))))))))))))
(TNum.neg_numeral_class.is_num_normalize_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ ((cGroups.plus_class.plus @ V0) @ V1))) @ V1))))))
(TNum.neg_numeral_class.is_num_normalize_10,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V1))) @ V1))))))
(TNum.neg_numeral_class.is_num_normalize_9,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.plus_class.plus @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TNum.neg_numeral_class.is_num_normalize_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TNum.neg_numeral_class.is_num_normalize_7,(call @ (^[V0]: (cNum.neg_numeral_class.is_num @ (cNum.numeral_class.numeral @ V0)))))
(TNum.neg_numeral_class.is_num_normalize_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V1)) @ (cNum.neg_numeral_class.is_num @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TNum.neg_numeral_class.is_num_normalize_5,(call @ (^[V0]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ (cNum.neg_numeral_class.is_num @ (cGroups.uminus_class.uminus @ V0))))))
(TNum.neg_numeral_class.is_num_normalize_4,(cNum.neg_numeral_class.is_num @ cGroups.one_class.one))
(TNum.neg_numeral_class.is_num_normalize_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))))
(TNum.neg_numeral_class.is_num_normalize_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))))
(TNum.neg_numeral_class.is_num_normalize_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TNum.numeral_class.numeral.numeral_Bit0,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V0))) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V0))))))
(TNum.numeral_class.numeral.numeral_Bit1,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V0))) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V0))) @ cGroups.one_class.one)))))
(TNum.numeral_class.numeral_plus_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_12,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_11,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_10,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_9,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_8,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0)))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_7,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One)))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_6,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_5,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ V0) @ cNum.num.One))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ V1) @ V0))))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)))))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1)))))))))
(TNum.ring_1_class.eq_numeral_iff_iszero_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.ring_1_class.iszero @ ((cNum.neg_numeral_class.sub @ V0) @ V1))))))))
(TNum.semiring_char_0.numeral_eq_one_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V4)) @ V0)) @ ((cHOL.eq @ V4) @ cNum.num.One))))))))))))))
(TNum.semiring_char_0.one_eq_numeral_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cNat.class.semiring_char_0 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ (((cNum.numeral.numeral @ V0) @ V2) @ V4))) @ ((cHOL.eq @ cNum.num.One) @ V4))))))))))))))
(TNumeral_Simprocs.left_add_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ V2) @ V1)) @ V3))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V2)) @ V1)) @ V3)))))))))))
(TNumeral_Simprocs.nat_mult_less_cancel1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TOrderings.class.dense_order_axioms_def,(call @ (^[V0]: ((c== @ (cOrderings.class.dense_order_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.implies @ ((V0 @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((V0 @ V1) @ V3)) @ ((V0 @ V3) @ V2)))))))))))))
(TOrderings.class.order_bot_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((V0 @ V1) @ V2)))) @ ((cOrderings.class.order_bot_axioms @ V1) @ V0)))))))
(TOrderings.class.order_top_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((V0 @ V2) @ V1)))) @ ((cOrderings.class.order_top_axioms @ V0) @ V1)))))))
(TOrderings.class.wellorder_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ (V1 @ V2))))))) @ (cOrderings.class.wellorder_axioms @ V0)))))
(TOrderings.linorder.strict_mono_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.strict_mono @ V1) @ V2)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (V2 @ V3)) @ (V2 @ V4))) @ ((V0 @ V3) @ V4)))))))))))))))
(TOrderings.linorder_class.antisym_conv1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.linorder_class.antisym_conv2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.linorder_class.antisym_conv3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V1) @ V0))) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.linorder_class.dual_linorder,((cOrderings.class.linorder @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TOrderings.ord_class.ord_class.max_dict,((c== @ cOrderings.ord_class.max) @ (cOrderings.ord.max @ cOrderings.ord_class.less_eq)))
(TOrderings.ord_class.ord_class.min_dict,((c== @ cOrderings.ord_class.min) @ (cOrderings.ord.min @ cOrderings.ord_class.less_eq)))
(TOrderings.order_bot_class.bot.extremum,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cOrderings.bot_class.bot) @ V0))))
(TOrderings.order_bot_class.not_less_bot,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ cOrderings.bot_class.bot)))))
(TOrderings.order_class.dual_order.trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))))))))
(TOrderings.order_class.less_imp_not_eq2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ V1) @ V0)) @ cHOL.False)))))))
(TOrderings.order_class.strict_mono_mono,(call @ (^[V0]: ((c==> @ (cOrderings.order_class.strict_mono @ V0)) @ (cOrderings.order_class.mono @ V0)))))
(TOrderings.order_top_class.not_top_less,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cOrderings.top_class.top) @ V0)))))
(TOrderings.order_top_class.top.extremum,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.top_class.top))))
(TOrderings.order_top_class.top_greatest,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.top_class.top))))
(TOrderings.ordering_top.extremum_strict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ (cHOL.Not @ ((V1 @ V2) @ V3))))))))))))
(TOrderings.ordering_top.extremum_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V3) @ V2))))))))))))
(TOrderings.ordering_top.not_eq_extremum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V3) @ V2))) @ ((V1 @ V3) @ V2))))))))))))
(TOrderings.preorder_class.dual_preorder,((cOrderings.class.preorder @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TOrderings.preorder_class.le_less_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.preorder_class.less_imp_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)) @ cHOL.True)))))))))
(TOrderings.preorder_class.less_le_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TPartial_Function.option.fixp_induct_uc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (^[V6]: ((V0 @ (V1 @ (V2 @ V6))) @ V5)))))) @ ((c==> @ ((c== @ V3) @ (V2 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (^[V5]: (V0 @ (V1 @ (V2 @ V5)))))))) @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ (V0 @ (V2 @ V5))) @ V5)))) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ V4)) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V4 @ (V0 @ V5))) @ (V4 @ (V0 @ (V1 @ V5))))))) @ (V4 @ (V0 @ V3))))))))))))))))))
(TPartial_Function.option.mono_body_fixp,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (^[V2]: ((V0 @ V2) @ V1)))))) @ ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ V0)) @ (V0 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cOption.option.None))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cOption.option.None))) @ V0)))))))
(TPartial_Function.partial_function_lift,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((cPartial_Function.partial_function_definitions @ (cPartial_Function.fun_ord @ V0)) @ (cPartial_Function.fun_lub @ V1))))))))
(TPower.comm_semiring_1.le_imp_power_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V4) @ V5)) @ (((cRings.dvd.dvd @ V0) @ ((((cPower.power.power @ V1) @ V0) @ V6) @ V4)) @ ((((cPower.power.power @ V1) @ V0) @ V6) @ V5)))))))))))))))))))
(TPower.field_class.nonzero_power_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cPower.power_class.power @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cFields.inverse_class.divide @ ((cPower.power_class.power @ V1) @ V2)) @ ((cPower.power_class.power @ V0) @ V2)))))))))))
(TPower.linordered_idom.zero_less_power2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V3) @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ (cHOL.Not @ ((cHOL.eq @ V10) @ V3)))))))))))))))))))))))))))
(TPower.linordered_idom_class.abs_power2,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TPower.linordered_idom_class.power2_abs,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ (cGroups.abs_class.abs @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TPower.linordered_semidom.zero_le_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V4 @ V1) @ V6)) @ ((V4 @ V1) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)))))))))))))))))))))
(TPower.monoid_mult_class.power3_eq_cube,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One)))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V0)) @ V0)))))
(TPower.monoid_mult_class.power_commutes,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V1)) @ V0)) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPredicate.uminus_pred_inst.uminus_pred,((c== @ cPredicate.uminus_pred_inst.uminus_pred) @ cPredicate.uminus_pred_inst.uminus_pred))
(TProduct_Type.map_pair.compositionality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((cProduct_Type.map_pair @ V0) @ V1) @ (((cProduct_Type.map_pair @ V2) @ V3) @ V4))) @ (((cProduct_Type.map_pair @ ((cFun.comp @ V0) @ V2)) @ ((cFun.comp @ V1) @ V3)) @ V4)))))))))))))
(TQuickcheck_Exhaustive.termify_pair_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.term_syntax.termify_pair @ cTYPE) @ cTYPE) @ V0) @ V1)) @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ V0)) @ V1)))))))
(TQuickcheck_Exhaustive.unknown.distinct_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Exhaustive.unknown.Known @ V0)) @ cQuickcheck_Exhaustive.unknown.Unknown)))))
(TQuickcheck_Exhaustive.unknown.distinct_1,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.unknown.Unknown) @ (cQuickcheck_Exhaustive.unknown.Known @ V0))))))
(TQuickcheck_Exhaustive.unknown.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.unknown.Unknown) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ cHOL.True))
(TQuickcheck_Exhaustive.unknown.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Exhaustive.unknown.Known @ V0)) @ (cQuickcheck_Exhaustive.unknown.Known @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.unknown.eq.simps_2,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.unknown.Unknown) @ (cQuickcheck_Exhaustive.unknown.Known @ V0))) @ cHOL.False))))
(TQuickcheck_Exhaustive.unknown.eq.simps_1,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Exhaustive.unknown.Known @ V0)) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ cHOL.False))))
(TQuickcheck_Exhaustive.unknown.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.unknown.Known @ V1))))))))
(TQuickcheck_Narrowing.arity_random_cfun,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Narrowing.arity_random_ffun,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V2)) @ V1)))) @ V1))))))
(TQuickcheck_Narrowing.around_zero.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cQuickcheck_Narrowing.around_zero @ V0)) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (cQuickcheck_Narrowing.around_zero @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V3)) @ cList.list.Nil))))))) @ V2))))) @ V2)))))))))
(TQuickcheck_Narrowing.around_zero.simps,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.around_zero @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (cQuickcheck_Narrowing.around_zero @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V0)) @ cList.list.Nil)))))))))
(TQuickcheck_Narrowing.cfun.Constant_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Narrowing.cfun.Constant @ V0)) @ (cQuickcheck_Narrowing.Abs_cfun @ (cDatatype.Leaf @ V0))))))
(TQuickcheck_Narrowing.cfun.cfun_rec_def,((c== @ cQuickcheck_Narrowing.cfun.cfun_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cQuickcheck_Narrowing.cfun.cfun_rec_set @ V0) @ V1) @ V2)))))))
(TQuickcheck_Narrowing.conv_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.conv_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V5) @ V6))) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V5))))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V5) @ V6))) @ (((cQuickcheck_Narrowing.nth @ V4) @ V5) @ V6))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Narrowing.conv_graph.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cQuickcheck_Narrowing.conv_graph @ ((cProduct_Type.Pair @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V1) @ V2))) @ (((cQuickcheck_Narrowing.nth @ V0) @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.conv_graph.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cQuickcheck_Narrowing.conv_graph @ ((cProduct_Type.Pair @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V1) @ V2))) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V1)))))))))))
(TQuickcheck_Narrowing.ffun.Constant_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Narrowing.ffun.Constant @ V0)) @ (cQuickcheck_Narrowing.Abs_ffun @ (cDatatype.In0 @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))))))))
(TQuickcheck_Narrowing.ffun.ffun_rec_def,((c== @ cQuickcheck_Narrowing.ffun.ffun_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TQuickcheck_Narrowing.narrowing_int_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_int_inst.narrowing_int @ V0)) @ ((cHOL.Let @ cQuickcheck_Narrowing.conv) @ (^[V1]: ((cHOL.Let @ (cCode_Numeral.int_of_integer @ V0)) @ (^[V2]: (cQuickcheck_Narrowing.drawn_from @ (cQuickcheck_Narrowing.around_zero @ V2))))))))))
(TQuickcheck_Narrowing.narrowing_set_def,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cList.set)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)))
(TQuickcheck_Narrowing.non_empty.pinduct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ (V1 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2)))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.non_empty_rel_def,((c== @ cQuickcheck_Narrowing.non_empty_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: cHOL.False))))))
(TQuickcheck_Narrowing.property.distinct_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (((cQuickcheck_Narrowing.property.Existential @ V1) @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.property.distinct_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.property.Property @ V3))))))))))))
(TQuickcheck_Narrowing.property.distinct_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (((cQuickcheck_Narrowing.property.Universal @ V1) @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.property.distinct_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.property.Property @ V3))))))))))))
(TQuickcheck_Narrowing.property.distinct_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))))))))))))))))
(TQuickcheck_Narrowing.property.distinct_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (cHOL.Not @ ((cHOL.eq @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))))))))))))))))
(TQuickcheck_Narrowing.property.eq.simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.property.eq.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.eq @ V2) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.property.eq.simps_7,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (cQuickcheck_Narrowing.property.Property @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.property.eq.simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Existential @ V3) @ V4) @ V5))) @ cHOL.False))))))))))))))
(TQuickcheck_Narrowing.property.eq.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (((cQuickcheck_Narrowing.property.Universal @ V3) @ V4) @ V5))) @ cHOL.False))))))))))))))
(TQuickcheck_Narrowing.property.eq.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.property.Property @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.property.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (((cQuickcheck_Narrowing.property.Universal @ V1) @ V2) @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.property.eq.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.property.Property @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.property.eq.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (((cQuickcheck_Narrowing.property.Existential @ V1) @ V2) @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.property.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V0) @ (((cQuickcheck_Narrowing.property.Universal @ V1) @ V2) @ V3))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V0) @ (((cQuickcheck_Narrowing.property.Existential @ V1) @ V2) @ V3))))))))) @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.property.Property @ V1)))))))))
(TQuickcheck_Narrowing.term_of_cfun_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TQuickcheck_Narrowing.term_of_ffun_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TQuickcheck_Random.arity_random_integer,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_literal,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_natural,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_typerep,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.num.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_num @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_num @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNum.num.Bit0) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V3)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_num @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cNum.num.Bit1) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V3)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cNum.num.One) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))) @ V2)))))))))
(TQuickcheck_Random.random_aux_set.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Random.random_aux_set @ (cCode_Numeral.Suc @ V0)) @ V1)) @ (cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V0)) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V2]: ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_set @ V0) @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V2) @ V3)))))))) @ cList.list.Nil))))))))))
(TQuickcheck_Random.random_aux_set.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cQuickcheck_Random.random_aux_set @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ (cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ cList.list.Nil)))))))
(TQuickcheck_Random.seq.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_seq @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_seq @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.seq.Join) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cPredicate.seq.Empty) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.seq.Insert) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))))) @ V2)))))))))
(TQuickcheck_Random.sum.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_sum @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inl) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inr) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Random.valterm_emptyset_def,((cHOL.eq @ cQuickcheck_Random.term_syntax.valterm_emptyset) @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ (^[V0]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TRandom_Sequence.neg_if_random_dseq_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.neg_if_random_dseq @ V0)) @ (((cHOL.If @ V0) @ (cRandom_Sequence.neg_single @ cProduct_Type.Unity)) @ cRandom_Sequence.neg_empty)))))
(TRandom_Sequence.pos_if_random_dseq_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.pos_if_random_dseq @ V0)) @ (((cHOL.If @ V0) @ (cRandom_Sequence.pos_single @ cProduct_Type.Unity)) @ cRandom_Sequence.pos_empty)))))
(TRecord.arity_term_of_tuple_isomorphism,(cCode_Evaluation.term_of_class @ cTYPE))
(TRecord.arity_typerep_tuple_isomorphism,(cTyperep.typerep_class @ cTYPE))
(TRecord.update_accessor_cong_assist_idI,((cRecord.iso_tuple_update_accessor_cong_assist @ cFun.id) @ cFun.id))
(TRelation.comp_fun_commute_relcomp_fold,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.comp_fun_commute @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (^[V3]: (((cFinite_Set.fold @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (^[V6]: (((cHOL.If @ ((cHOL.eq @ V2) @ V4)) @ ((cSet.insert @ ((cProduct_Type.Pair @ V1) @ V5)) @ V6)) @ V6)))))) @ V3) @ V0))))))))))
(TRings.class.comm_semiring_0_cancel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.comm_semiring_0_cancel @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((cRings.class.comm_semiring @ V0) @ V2))))))))))
(TRings.class.comm_semiring_1_cancel_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cHOL.conj @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((cGroups.class.comm_monoid_mult @ V2) @ V3))) @ ((cHOL.conj @ ((cRings.class.comm_semiring @ V0) @ V2)) @ ((cRings.class.zero_neq_one @ V3) @ V1)))))))))))))
(TRings.class.comm_semiring_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((V0 @ ((V1 @ V2) @ V3)) @ V4)) @ ((V1 @ ((V0 @ V2) @ V4)) @ ((V0 @ V3) @ V4)))))))))) @ ((cRings.class.comm_semiring_axioms @ V1) @ V0)))))))
(TRings.class.linordered_ring_strict_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((cHOL.conj @ ((((cGroups.class.abs_if @ V0) @ V2) @ V3) @ V5)) @ ((((((cGroups.class.ordered_ab_group_add @ V6) @ V3) @ V1) @ V2) @ V4) @ V5))) @ ((cHOL.conj @ (((((cRings.class.linordered_semiring_strict @ V6) @ V3) @ V4) @ V5) @ V7)) @ (((((cRings.class.ring @ V6) @ V3) @ V1) @ V2) @ V7)))))))))))))))))))))
(TRings.class.linordered_semiring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cRings.class.ordered_semiring @ V0) @ V3) @ V1) @ V2) @ V4)))))))))))))
(TRings.class.linordered_semiring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)))))))))))))
(TRings.comm_ring_class.comm_ring_axioms,(((((cRings.class.comm_ring @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.times_class.times))
(TRings.comm_semiring_0_cancel_class_def,((c== @ (cRings.comm_semiring_0_cancel_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cRings.comm_semiring_class @ cTYPE))))
(TRings.comm_semiring_1_cancel_class_def,((c== @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cGroups.comm_monoid_mult_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.comm_semiring_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))))
(TRings.comm_semiring_1_class.dvd_0_left,(call @ (^[V0]: ((c==> @ ((cRings.dvd_class.dvd @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TRings.idom_class.dvd_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TRings.linordered_ring_strict_class_def,((c== @ (cRings.linordered_ring_strict_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.abs_if_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ (cRings.ring_class @ cTYPE)))))
(TRings.linordered_semidom.zero_less_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V5 @ V1) @ V3)))))))))))))))
(TRings.linordered_semidom.zero_less_two,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V5 @ V1) @ ((V0 @ V3) @ V3))))))))))))))))
(TRings.mult_zero_class.mult_zero_axioms,((cRings.class.mult_zero @ cGroups.times_class.times) @ cGroups.zero_class.zero))
(TRings.ordered_ring.mult_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ (((((((cRings.class.ordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V2 @ V7) @ V8)) @ ((c==> @ ((V2 @ V9) @ V1)) @ ((V2 @ ((V4 @ V8) @ V9)) @ ((V4 @ V7) @ V9))))))))))))))))))))))))))
(TRings.ordered_ring_class.less_add_iff1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V1)) @ V4))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V3)) @ V1)) @ V2)) @ V4)))))))))))))
(TRings.ordered_ring_class.less_add_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V1)) @ V4))) @ ((cOrderings.ord_class.less @ V2) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V3) @ V0)) @ V1)) @ V4))))))))))))))
(TRings.ordered_semiring.mult_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((c==> @ ((V2 @ V1) @ V7)) @ ((V2 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V7))))))))))))))))))))))
(TRings.ordered_semiring_class.mult_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))))
(TSMT.random_pattern_inst.random_pattern,((c== @ cSMT.random_pattern_inst.random_pattern) @ cSMT.random_pattern_inst.random_pattern))
(TSet_Interval.atLeastLessThan_singleton,(call @ (^[V0]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ (cNat.Suc @ V0))) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TSet_Interval.bounded_nat_set_is_finite,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ V2) @ V1)))) @ (cFinite_Set.finite @ V0)))))))
(TSet_Interval.dvd.atLeastLessThan_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((((cSet_Interval.ord.atLeastLessThan @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TSet_Interval.dvd.greaterThanAtMost_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((((cSet_Interval.ord.greaterThanAtMost @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.greaterThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0)) @ ((cSet_Interval.ord.atMost @ cRings.dvd_class.dvd) @ V1))))))))
(TSet_Interval.dvd.greaterThanAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((((cSet_Interval.ord.greaterThanAtMost @ cRings.dvd_class.dvd) @ (^[V3]: (^[V4]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V3) @ V4)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V4) @ V3)))))) @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))) @ ((cRings.dvd_class.dvd @ V0) @ V2))))))))))
(TSet_Interval.image_Suc_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cNat.Suc) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ (cNat.Suc @ V0)) @ (cNat.Suc @ V1))))))))
(TSet_Interval.image_add_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ (^[V3]: ((cNat.plus_nat_inst.plus_nat @ V3) @ V0))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastLessThan @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V0)) @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V0))))))))))
(TSet_Interval.image_int_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TSet_Interval.linorder_class.Int_atMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atMost @ V0)) @ (cSet_Interval.ord_class.atMost @ V1))) @ (cSet_Interval.ord_class.atMost @ ((cOrderings.ord_class.min @ V0) @ V1))))))))
(TSet_Interval.no_bot.lessThan_non_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.lessThan @ V1) @ V2)) @ cOrderings.bot_class.bot))))))))))
(TSet_Interval.ord.greaterThanAtMost_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V2) @ V3)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.greaterThan @ V1) @ V2)) @ ((cSet_Interval.ord.atMost @ V0) @ V3))))))))))))
(TSet_Interval.ord.greaterThanAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((cSet.member @ V0) @ ((((cSet_Interval.ord.greaterThanAtMost @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((V2 @ V3) @ V0)) @ ((V1 @ V0) @ V4))))))))))))))
(TSet_Interval.ord_class.greaterThan_def,(call @ (^[V0]: ((c== @ (cSet_Interval.ord_class.greaterThan @ V0)) @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less @ V0) @ V1)))))))
(TSet_Interval.ord_class.greaterThan_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TSet_Interval.order.atLeastatMost_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ V2)) @ cOrderings.bot_class.bot))))))))))))
(TString.enum_nibble_inst.enum_ex_nibble,((c== @ cString.enum_nibble_inst.enum_ex_nibble) @ cString.enum_nibble_inst.enum_ex_nibble))
(TTransfer.right_total_relcompp_transfer,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V0) @ cHOL.eq))) @ ((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ ((cTransfer.fun_rel @ V2) @ cHOL.eq))) @ ((cTransfer.fun_rel @ V1) @ ((cTransfer.fun_rel @ V2) @ cHOL.eq)))) @ (^[V3]: (^[V4]: (^[V5]: (^[V6]: ((cSet.Bex @ (cSet.Collect @ (cRelation.Domainp @ V0))) @ (^[V7]: ((cHOL.conj @ ((V3 @ V5) @ V7)) @ ((V4 @ V7) @ V6))))))))) @ cRelation.relcompp)))))))))
(TTransitive_Closure.Image_closed_trancl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cRelation.Image @ V0) @ V1)) @ V1)) @ ((cHOL.eq @ ((cRelation.Image @ (cTransitive_Closure.rtrancl @ V0)) @ V1)) @ V1)))))))
(TTransitive_Closure.converse_rtranclpE2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ ((cHOL.eq @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V3) @ V4))) @ V5)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((V0 @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V6) @ V7))) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V3) @ V4))) @ V5))))))) @ V5))))))))))))))))
(TTransitive_Closure.rtranclp_rtrancl_eq,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtranclp @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ V0))))) @ (^[V1]: (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cTransitive_Closure.rtrancl @ V0))))))))
(TTransitive_Closure.trancl_into_rtrancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))))))))))
(TTransitive_Closure.trancl_into_trancl2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.trancl_subset_Sigma,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cProduct_Type.Sigma @ V1) @ (^[V2]: V1)))) @ ((cOrderings.ord_class.less_eq @ (cTransitive_Closure.trancl @ V0)) @ ((cProduct_Type.Sigma @ V1) @ (^[V2]: V1)))))))))
(TTransitive_Closure.trancl_trans_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((V3 @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V6)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((V3 @ V4) @ V6)))))))))))) @ ((V3 @ V0) @ V1)))))))))))))
(TTransitive_Closure.trancl_unfold_right,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.trancl @ V0)) @ ((cRelation.relcomp @ (cTransitive_Closure.rtrancl @ V0)) @ V0)))))
(TTyperep.typerep.typerep_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TTyperep.typerep.typerep_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cTyperep.typerep.typerep_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V5) @ V6)) @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ ((cList.list.Cons @ V3) @ V5)) @ ((((V2 @ V3) @ V5) @ V4) @ V6)))))))))))))))))))
(TTyperep.typerep.typerep_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ cList.list.Nil) @ V1))))))))
(TTyperep.typerep.typerep_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cTyperep.typerep.typerep_rec_set_1 @ V0) @ V1) @ V2) @ ((cTyperep.typerep.Typerep @ V5) @ V3)) @ (((V0 @ V5) @ V3) @ V4))))))))))))))))
(TTyperep.typerep.typerep_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V4)) @ ((c==> @ (V0 @ V4)) @ (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V5)) @ V4))))))))) @ ((c==> @ (V0 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cTyperep.typerep.typerep_rep_set_1 @ V4)) @ ((c==> @ (V1 @ V4)) @ ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V5)) @ ((c==> @ (V0 @ V5)) @ (V0 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ ((cHOL.conj @ ((cHOL.implies @ (cTyperep.typerep.typerep_rep_set_1 @ V2)) @ (V1 @ V2))) @ ((cHOL.implies @ (cTyperep.typerep.typerep_rep_set_2 @ V3)) @ (V0 @ V3)))))))))))))))
(TTyperep.typerep.typerep_rep_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTyperep.typerep.typerep_rep_set_1 @ V0)) @ ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V1)) @ (cTyperep.typerep.typerep_rep_set_2 @ (cDatatype.In1 @ ((cDatatype.Scons @ V0) @ V1))))))))))
(TTyperep.typerep.typerep_rep_set.intros_2,(cTyperep.typerep.typerep_rep_set_2 @ (cDatatype.In0 @ cHOL.undefined)))
(TTyperep.typerep.typerep_rep_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V0)) @ (cTyperep.typerep.typerep_rep_set_1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V1)) @ V0))))))))
(TTyperep.typerep_bool_inst.typerep_bool,((c== @ cTyperep.typerep_bool_inst.typerep_bool) @ cTyperep.typerep_bool_inst.typerep_bool))
(TTyperep.typerep_char_inst.typerep_char,((c== @ cTyperep.typerep_char_inst.typerep_char) @ cTyperep.typerep_char_inst.typerep_char))
(TTyperep.typerep_list_inst.typerep_list,((c== @ cTyperep.typerep_list_inst.typerep_list) @ cTyperep.typerep_list_inst.typerep_list))
(TTyperep.typerep_node_inst.typerep_node,((c== @ cTyperep.typerep_node_inst.typerep_node) @ cTyperep.typerep_node_inst.typerep_node))
(TTyperep.typerep_prod_inst.typerep_prod,((c== @ cTyperep.typerep_prod_inst.typerep_prod) @ cTyperep.typerep_prod_inst.typerep_prod))
(TTyperep.typerep_unit_inst.typerep_unit,((c== @ cTyperep.typerep_unit_inst.typerep_unit) @ cTyperep.typerep_unit_inst.typerep_unit))
(TWellfounded.finite_acyclic_wf_converse,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cTransitive_Closure.acyclic @ V0)) @ (cWellfounded.wf @ (cRelation.converse @ V0)))))))
(TBig_Operators.complete_linorder.Max_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.linorder.Max @ V3) @ V8)) @ (V1 @ V8))))))))))))))))))))))))
(TBig_Operators.complete_linorder.Min_Inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.linorder.Min @ V3) @ V8)) @ (V0 @ V8))))))))))))))))))))))))
(TBig_Operators.linorder.mono_Max_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.mono @ V0) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V2 @ ((cBig_Operators.linorder.Max @ V0) @ V3))) @ (cBig_Operators.linorder_class.Max @ ((cSet.image @ V2) @ V3))))))))))))))))
(TBig_Operators.linorder.mono_Min_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.order.mono @ V0) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V2 @ ((cBig_Operators.linorder.Min @ V0) @ V3))) @ (cBig_Operators.linorder_class.Min @ ((cSet.image @ V2) @ V3))))))))))))))))
(TBig_Operators.linorder_class.Max.closed,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cSet.member @ ((cOrderings.ord_class.max @ V1) @ V2)) @ ((cSet.insert @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))) @ ((cSet.member @ (cBig_Operators.linorder_class.Max @ V0)) @ V0)))))))
(TBig_Operators.linorder_class.Max.insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cSet.insert @ V1) @ V0))) @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Max @ V0))))))))))
(TBig_Operators.linorder_class.Max.remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ V0)) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Max @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))))
(TBig_Operators.linorder_class.Max.subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ (cBig_Operators.linorder_class.Max @ V1)) @ (cBig_Operators.linorder_class.Max @ V0))) @ (cBig_Operators.linorder_class.Max @ V0))))))))))
(TBig_Operators.linorder_class.Max_ge_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.linorder_class.Max @ V0))) @ ((cSet.Bex @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V1) @ V2)))))))))))
(TBig_Operators.linorder_class.Max_gr_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V1) @ (cBig_Operators.linorder_class.Max @ V0))) @ ((cSet.Bex @ V0) @ (^[V2]: ((cOrderings.ord_class.less @ V1) @ V2)))))))))))
(TBig_Operators.linorder_class.Max_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cSet.insert @ V1) @ V0))) @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Max @ V0))))))))))
(TBig_Operators.linorder_class.Max_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Max @ V0)) @ V1)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))))
(TBig_Operators.linorder_class.Min.closed,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cSet.member @ ((cOrderings.ord_class.min @ V1) @ V2)) @ ((cSet.insert @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))) @ ((cSet.member @ (cBig_Operators.linorder_class.Min @ V0)) @ V0)))))))
(TBig_Operators.linorder_class.Min.insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cSet.insert @ V1) @ V0))) @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Min @ V0))))))))))
(TBig_Operators.linorder_class.Min.remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ V0)) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Min @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))))
(TBig_Operators.linorder_class.Min.subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ (cBig_Operators.linorder_class.Min @ V1)) @ (cBig_Operators.linorder_class.Min @ V0))) @ (cBig_Operators.linorder_class.Min @ V0))))))))))
(TBig_Operators.linorder_class.Min_ge_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V1) @ V2)))))))))))
(TBig_Operators.linorder_class.Min_gr_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less @ V1) @ V2)))))))))))
(TBig_Operators.linorder_class.Min_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cSet.insert @ V1) @ V0))) @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Min @ V0))))))))))
(TBig_Operators.linorder_class.Min_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Min @ V0)) @ V1)) @ ((cSet.Bex @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))))
(TBig_Operators.semilattice_neutr_set_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((cLattices.semilattice_neutr @ V0) @ V1)))))))
(TBig_Operators.semilattice_order_set_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ (cBig_Operators.semilattice_set @ V0))))))))))
(TBig_Operators.semilattice_set.singleton,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ V1)))))))
(TBig_Operators.setsum_mult_setsum_if_inj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cFun.inj_on @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cGroups.times_class.times @ (V0 @ V4)) @ (V1 @ V5)))))) @ ((cProduct_Type.Sigma @ V2) @ (^[V4]: V3)))) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V3))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ cFun.id) @ (cSet.Collect @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cGroups.times_class.times @ (V0 @ V5)) @ (V1 @ V6)))) @ ((cHOL.conj @ ((cSet.member @ V5) @ V2)) @ ((cSet.member @ V6) @ V3)))))))))))))))))))))
(TCode_Evaluation.term.term_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cCode_Evaluation.term.term_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cCode_Evaluation.term.dummy_term)) @ ((c==> @ ((cHOL.eq @ V2) @ V0)) @ V3))) @ V3)))))))))))
(TCode_Evaluation.term.term_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cCode_Evaluation.term.term_rec_set @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ cCode_Evaluation.term.dummy_term)) @ ((cHOL.eq @ V2) @ V0))))))))))
(TCode_Numeral.arity_semiring_div_natural,(cDivides.semiring_div_class @ cTYPE))
(TCode_Numeral.int_of_integer_neg_numeral,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TCode_Numeral.natural.arity_size_natural,(cNat.size_class @ cTYPE))
(TComplete_Partial_Order.admissible_False,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V2]: cHOL.False))))))))
(TComplete_Partial_Order.admissible_const,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V3]: V2))) @ V2))))))))
(TComplete_Partial_Order.ccpo.admissibleD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V3)) @ (V2 @ V4))))) @ (V2 @ (V0 @ V3))))))))))))))
(TComplete_Partial_Order.ccpo.admissibleI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: (V1 @ V4)))) @ (V1 @ (V2 @ V3))))))) @ (((cComplete_Partial_Order.ccpo.admissible @ V2) @ V0) @ V1)))))))))
(TComplete_Partial_Order.ccpo.fixp_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ V3)) @ ((c==> @ (((cComplete_Partial_Order.monotone @ V1) @ V1) @ V4)) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V3 @ V5)) @ (V3 @ (V4 @ V5)))))) @ (V3 @ (((cComplete_Partial_Order.ccpo.fixp @ V0) @ V1) @ V4)))))))))))))))))
(TComplete_Partial_Order.ccpo.fixp_unfold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ (((cComplete_Partial_Order.monotone @ V1) @ V1) @ V3)) @ ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.fixp @ V0) @ V1) @ V3)) @ (V3 @ (((cComplete_Partial_Order.ccpo.fixp @ V0) @ V1) @ V3))))))))))))))
(TComplete_Partial_Order.ccpo_class.intro,((c==> @ (cComplete_Lattices.Sup_class @ cTYPE)) @ ((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ ((cComplete_Partial_Order.class.ccpo_axioms @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq)) @ (cComplete_Partial_Order.ccpo_class @ cTYPE)))))
(TComplete_Partial_Order.ccpo_class.super_2,((c==> @ (cComplete_Partial_Order.ccpo_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TComplete_Partial_Order.ccpo_class.super_1,((c==> @ (cComplete_Partial_Order.ccpo_class @ cTYPE)) @ (cComplete_Lattices.Sup_class @ cTYPE)))
(TComplete_Partial_Order.class.ccpo.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cComplete_Partial_Order.class.ccpo_axioms @ V2) @ V0)) @ (((cComplete_Partial_Order.class.ccpo @ V2) @ V0) @ V1))))))))))
(TDivides.class.semiring_div_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ ((V0 @ ((V1 @ ((V2 @ V5) @ V6)) @ V6)) @ ((V3 @ V5) @ V6))) @ V5)))))) @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ ((V2 @ V5) @ V4)) @ V4)))) @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ ((V2 @ V4) @ V5)) @ V4)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ V4))) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ ((V1 @ V7) @ V5))) @ V5)) @ ((V0 @ V7) @ ((V2 @ V6) @ V5))))))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ V4))) @ ((cHOL.eq @ ((V2 @ ((V1 @ V5) @ V6)) @ ((V1 @ V5) @ V7))) @ ((V2 @ V6) @ V7)))))))))) @ (((((cDivides.class.semiring_div_axioms @ V1) @ V2) @ V3) @ V0) @ V4)))))))))))))))))
(TDivides.ring_div_class.div_minus1_right,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.div @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))) @ (cGroups.uminus_class.uminus @ V0)))))
(TDivides.ring_div_class.mod_diff_left_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ ((cDivides.div_class.mod @ V0) @ V2)) @ V1)) @ V2)))))))))
(TDivides.ring_div_class.mod_minus1_right,(call @ (^[V0]: ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One))) @ cGroups.zero_class.zero))))
(TDivides.semiring_div_class.dvd_div_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cDivides.div_class.div @ V1) @ V0)) @ V2)) @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V1) @ V2)) @ V0))))))))))
(TDivides.semiring_div_class.mod_add_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ V1)) @ ((cDivides.div_class.mod @ V2) @ V1))) @ ((c==> @ ((cHOL.eq @ ((cDivides.div_class.mod @ V3) @ V1)) @ ((cDivides.div_class.mod @ V4) @ V1))) @ ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V3)) @ V1)) @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V2) @ V4)) @ V1)))))))))))))))
(TDivides.semiring_numeral_div.divmod_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ V9) @ V10)) @ ((cProduct_Type.Pair @ ((V1 @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)) @ (((cNum.numeral.numeral @ V5) @ V3) @ V10))) @ ((V2 @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)) @ (((cNum.numeral.numeral @ V5) @ V3) @ V10))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.fst_divmod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ (cProduct_Type.fst @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ V9) @ V10))) @ ((V1 @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)) @ (((cNum.numeral.numeral @ V5) @ V3) @ V10)))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.snd_divmod,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ (cProduct_Type.snd @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ V9) @ V10))) @ ((V2 @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)) @ (((cNum.numeral.numeral @ V5) @ V3) @ V10)))))))))))))))))))))))))))
(TEnum.equal_finite_1_inst.equal_finite_1,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TEnum.equal_finite_2_inst.equal_finite_2,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TEnum.equal_finite_3_inst.equal_finite_3,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TEnum.equal_finite_4_inst.equal_finite_4,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TEnum.equal_finite_5_inst.equal_finite_5,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TEnum.ord_finite_1_inst.less_eq_finite_1,((c== @ cEnum.ord_finite_1_inst.less_eq_finite_1) @ cEnum.ord_finite_1_inst.less_eq_finite_1))
(TEnum.ord_finite_2_inst.less_eq_finite_2,((c== @ cEnum.ord_finite_2_inst.less_eq_finite_2) @ cEnum.ord_finite_2_inst.less_eq_finite_2))
(TEnum.ord_finite_3_inst.less_eq_finite_3,((c== @ cEnum.ord_finite_3_inst.less_eq_finite_3) @ cEnum.ord_finite_3_inst.less_eq_finite_3))
(TEquiv_Relations.equiv_class_nondisjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ ((cLattices.inf_class.inf @ ((cRelation.Image @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))) @ ((cRelation.Image @ V1) @ ((cSet.insert @ V4) @ cOrderings.bot_class.bot))))) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V4)) @ V1))))))))))))))
(TFields.class.division_ring_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.eq @ ((V1 @ (V2 @ V5)) @ V5)) @ V3))))) @ ((c==> @ (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.eq @ ((V1 @ V5) @ (V2 @ V5))) @ V3))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ ((V4 @ V5) @ V6)) @ ((V1 @ V5) @ (V2 @ V6)))))))) @ (((((cFields.class.division_ring_axioms @ V2) @ V4) @ V3) @ V1) @ V0)))))))))))))))
(TFields.division_ring.add_divide_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ ((V4 @ V8) @ V9)) @ V10)) @ ((V4 @ ((V1 @ V8) @ V10)) @ ((V1 @ V9) @ V10)))))))))))))))))))))))))))
(TFields.division_ring_class.left_inverse,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cFields.inverse_class.inverse @ V0)) @ V0)) @ cGroups.one_class.one)))))
(TFields.field_class.field_divide_inverse,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ (cFields.inverse_class.inverse @ V1))))))))
(TFields.field_class.times_divide_eq_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cFields.inverse_class.divide @ V0) @ V1)) @ V2)) @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.frac_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V3)) @ ((cFields.inverse_class.divide @ V1) @ V2)))))))))))))))
(TFinite_Set.comp_fun_commute.fold_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V1))) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V3) @ ((cSet.insert @ V2) @ V1))) @ ((V0 @ V2) @ (((cFinite_Set.fold @ V0) @ V3) @ V1)))))))))))))))
(TFinite_Set.comp_fun_commute_filter_fold,(call @ (^[V0]: (cFinite_Set.comp_fun_commute @ (^[V1]: (^[V2]: (((cHOL.If @ (V0 @ V1)) @ ((cSet.insert @ V1) @ V2)) @ V2)))))))
(TGroups.ab_group_add_class.ab_diff_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TGroups.ab_group_add_class.ab_left_minus,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ cGroups.zero_class.zero))))
(TGroups.cancel_comm_monoid_add_class_def,((c== @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE))))
(TGroups.cancel_semigroup_add_class.intro,((c==> @ (cGroups.semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.class.cancel_semigroup_add_axioms @ cGroups.plus_class.plus)) @ (cGroups.cancel_semigroup_add_class @ cTYPE))))
(TGroups.cancel_semigroup_add_class.super,((c==> @ (cGroups.cancel_semigroup_add_class @ cTYPE)) @ (cGroups.semigroup_add_class @ cTYPE)))
(TGroups.class.cancel_comm_monoid_add_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((cHOL.conj @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1))))))))
(TGroups.class.cancel_semigroup_add.intro,(call @ (^[V0]: ((c==> @ (cGroups.class.semigroup_add @ V0)) @ ((c==> @ (cGroups.class.cancel_semigroup_add_axioms @ V0)) @ (cGroups.class.cancel_semigroup_add @ V0))))))
(TGroups.class.comm_monoid_add_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.comm_monoid_add_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))))))))
(TGroups.class.ordered_ab_group_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V4) @ V5)) @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TGroups.comm_monoid_diff_class.diff_zero,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TGroups.comm_monoid_diff_class.zero_diff,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TGroups.group_add_class.add_minus_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V1))) @ V1))))))
(TGroups.group_add_class.eq_iff_diff_eq_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cGroups.zero_class.zero)))))))
(TGroups.group_add_class.group_add_axioms,((((cGroups.class.group_add @ cGroups.minus_class.minus) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus))
(TGroups.group_add_class.minus_add_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ ((cGroups.plus_class.plus @ V0) @ V1))) @ V1))))))
(TGroups.ordered_ab_group_add_abs.abs_leI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V5 @ V7) @ V8)) @ ((c==> @ ((V5 @ (V4 @ V7)) @ V8)) @ ((V5 @ (V0 @ V7)) @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_class.intro,((c==> @ (cGroups.ab_group_add_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_class @ cTYPE))))
(TGroups.ordered_ab_group_add_class.super_2,((c==> @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)))
(TGroups.ordered_ab_group_add_class.super_1,((c==> @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ (cGroups.ab_group_add_class @ cTYPE)))
(TInductive.complete_lattice.lfp_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((V3 @ (V8 @ V10)) @ V10)) @ ((V3 @ V9) @ V10))))) @ ((V3 @ V9) @ (((cInductive.complete_lattice.lfp @ V0) @ V3) @ V8)))))))))))))))))))))))))
(TInt.linordered_idom_class.of_int_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)))))))
(TInt.ring_1_class.ring_1_class.Ints_dict,((c== @ cInt.ring_1_class.Ints) @ ((((cInt.ring_1.Ints @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus)))
(TLattices.boolean_algebra.compl_le_swap1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V3 @ V8) @ (V1 @ V9))) @ ((V3 @ V9) @ (V1 @ V8)))))))))))))))))))))))))
(TLattices.boolean_algebra.compl_le_swap2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V3 @ (V1 @ V8)) @ V9)) @ ((V3 @ (V1 @ V9)) @ V8))))))))))))))))))))))))
(TLattices.linorder_class.max.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TLattices.linorder_class.max.coboundedI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TLattices.linorder_class.max.coboundedI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V2) @ V1))))))))))
(TLattices.linorder_class.min.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TLattices.linorder_class.min.coboundedI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V2)) @ V1)))))))))
(TLattices.linorder_class.min.coboundedI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V2) @ V0)) @ V1)))))))))
(TLattices.semilattice_inf.inf_right_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V3) @ V4)) @ V4)) @ ((V0 @ V3) @ V4))))))))))))))
(TLattices.semilattice_inf_class.inf.idem,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V0)) @ V0))))
(TLattices.semilattice_inf_class.inf.mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V3)))))))))))))
(TLattices.semilattice_inf_class.inf_idem,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V0)) @ V0))))
(TLattices.semilattice_inf_class.inf_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V3)))))))))))))
(TLattices.semilattice_inf_class.le_infI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V2)) @ V1)))))))))
(TLattices.semilattice_inf_class.le_infI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V2) @ V0)) @ V1)))))))))
(TLattices.semilattice_inf_class.mono_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ (V0 @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TLattices.semilattice_neutr_order.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.semilattice_neutr_order @ V0) @ V1) @ V2) @ V3)) @ (((cLattices.semilattice_order @ V0) @ V2) @ V3)))))))))))
(TLattices.semilattice_neutr_order.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.semilattice_neutr_order @ V0) @ V1) @ V2) @ V3)) @ ((cLattices.semilattice_neutr @ V0) @ V1)))))))))))
(TLattices.semilattice_order_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((V0 @ V3) @ V4)) @ ((cHOL.eq @ V3) @ ((V1 @ V3) @ V4)))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((V2 @ V3) @ V4)) @ ((cHOL.conj @ ((V0 @ V3) @ V4)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))))))))) @ (((cLattices.semilattice_order_axioms @ V1) @ V0) @ V2))))))))))
(TLattices.semilattice_sup_class.le_supI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.le_supI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V2) @ V1))))))))))
(TLattices.semilattice_sup_class.mono_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (V0 @ V1)) @ (V0 @ V2))) @ (V0 @ ((cLattices.sup_class.sup @ V1) @ V2)))))))))))
(TLattices.semilattice_sup_class.sup.idem,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V0)) @ V0))))
(TLattices.semilattice_sup_class.sup.mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V3)))))))))))))
(TLattices.semilattice_sup_class.sup_idem,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V0)) @ V0))))
(TLattices.semilattice_sup_class.sup_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V3)))))))))))))
(TLazy_Sequence.arity_equal_lazy_sequence,(cHOL.equal_class @ cTYPE))
(TLazy_Sequence.iterate_upto_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.iterate_upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((cLazy_Sequence.iterate_upto_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.iterate_upto_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cLazy_Sequence.iterate_upto_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0)))))))) @ ((cLazy_Sequence.iterate_upto_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V1) @ V0))) @ (cLazy_Sequence.Lazy_Sequence @ (^[V4]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V2 @ V1)) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0)))))))))))))))))))
(TLazy_Sequence.list_of_lazy_sequence_def,((c== @ cLazy_Sequence.list_of_lazy_sequence) @ (^[V0]: ((cLazy_Sequence.lazy_sequence.lazy_sequence_rec @ (^[V1]: V1)) @ V0))))
(TLazy_Sequence.list_of_lazy_sequence_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ ((cLazy_Sequence.map @ V0) @ V1))) @ ((cList.map @ V0) @ (cLazy_Sequence.list_of_lazy_sequence @ V1))))))))
(TLazy_Sequence.small_lazy'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((cLazy_Sequence.small_lazy'_graph @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cLazy_Sequence.empty) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy_list_graph_def,((c== @ cLazy_Sequence.small_lazy_list_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (cLazy_Sequence.single @ ((cList.list.Cons @ V5) @ V6))))))) @ cLazy_Sequence.empty)))) @ ((cHOL.induct_implies @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((V0 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))))
(TLazy_Sequence.small_lazy_list_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy_list_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)) @ V2)))))) @ V2)))))))))
(TLazy_Sequence.small_lazy_list_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.small_lazy_list_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V2)))))))))))
(TLifting_Option.option_invariant_commute,(call @ (^[V0]: ((cHOL.eq @ (cLifting_Option.option_rel @ (cLifting.invariant @ V0))) @ (cLifting.invariant @ ((cOption.option.option_case @ cHOL.True) @ V0))))))
(TList.comm_monoid_add_class.listsum_addf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: ((cGroups.plus_class.plus @ (V0 @ V3)) @ (V1 @ V3)))) @ V2))) @ ((cGroups.plus_class.plus @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ V2))) @ (cList.monoid_add_class.listsum @ ((cList.map @ V1) @ V2)))))))))))
(TList.linorder.sorted_list_of_set_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((cList.linorder.sorted_list_of_set @ V0) @ ((cSet.insert @ V3) @ V2))) @ ((((cList.linorder.insort_key @ V0) @ (^[V4]: V4)) @ V3) @ ((cList.linorder.sorted_list_of_set @ V0) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))))))))))))))))
(TList.linorder.sorted_list_of_set_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((cList.linorder.sorted_list_of_set @ V0) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))) @ ((cList.remove1 @ V3) @ ((cList.linorder.sorted_list_of_set @ V0) @ V2))))))))))))))
(TList.linorder_class.sorted_rev_nth_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ V0))) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V2) @ (cNat.size_class.size @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cList.nth @ V0) @ V2)) @ ((cList.nth @ V0) @ V1))))))))))))
(TList.set_take_disj_set_drop_if_distinct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.distinct @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cList.set @ ((cList.take @ V1) @ V0))) @ (cList.set @ ((cList.drop @ V2) @ V0)))) @ cOrderings.bot_class.bot))))))))))
(TList.transfer_nat_int_list_return_embed,(call @ (^[V0]: ((cHOL.implies @ (cList.nat_list @ V0)) @ ((cHOL.eq @ (cList.embed_list @ (cList.return_list @ V0))) @ V0)))))
(TMain.random_sumbool_inst.random_sumbool,((c== @ cMain.random_sumbool_inst.random_sumbool) @ cMain.random_sumbool_inst.random_sumbool))
(TNat.dvd.dual_order.strict_implies_order,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat.semiring_char_0_class.of_nat_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat_Transfer.transfer_int_nat_functions_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cNat.semiring_1_class.of_nat @ V0)) @ V1)) @ (cNat.semiring_1_class.of_nat @ ((cPower.power_class.power @ V0) @ V1))))))))
(TNat_Transfer.transfer_int_nat_functions_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat_Transfer.tsub @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ (cNat.semiring_1_class.of_nat @ ((cNat.minus_nat_inst.minus_nat @ V0) @ V1))))))))
(TNat_Transfer.transfer_int_nat_functions_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.times_int_inst.times_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ (cNat.semiring_1_class.of_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1))))))))
(TNat_Transfer.transfer_int_nat_functions_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.plus_int_inst.plus_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ (cNat.semiring_1_class.of_nat @ ((cNat.plus_nat_inst.plus_nat @ V0) @ V1))))))))
(TNat_Transfer.transfer_int_nat_relations_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TNat_Transfer.transfer_int_nat_relations_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_eq_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNat_Transfer.transfer_int_nat_relations_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cInt.ord_int_inst.less_int @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat_Transfer.transfer_int_nat_relations_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNat_Transfer.transfer_int_nat_sum_prod2_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (cNat_Transfer.is_nat @ (V1 @ V2)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ (cNat.semiring_1_class.of_nat @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (cInt.nat @ (V1 @ V2)))) @ V0)))))))))
(TNat_Transfer.transfer_int_nat_sum_prod2_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ (cNat_Transfer.is_nat @ (V1 @ V2)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ (cNat.semiring_1_class.of_nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cInt.nat @ (V1 @ V2)))) @ V0)))))))))
(TNat_Transfer.transfer_nat_int_functions_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cPower.power_class.power @ (cInt.nat @ V0)) @ V1)) @ (cInt.nat @ ((cPower.power_class.power @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_functions_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cNat.minus_nat_inst.minus_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ (cInt.nat @ ((cNat_Transfer.tsub @ V0) @ V1))))))))))
(TNat_Transfer.transfer_nat_int_functions_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ (cInt.nat @ ((cInt.times_int_inst.times_int @ V0) @ V1))))))))))
(TNat_Transfer.transfer_nat_int_functions_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cNat.plus_nat_inst.plus_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ (cInt.nat @ ((cInt.plus_int_inst.plus_int @ V0) @ V1))))))))))
(TNat_Transfer.transfer_nat_int_relations_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_relations_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_relations_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cInt.ord_int_inst.less_int @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_relations_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (cInt.nat @ V0)) @ (cInt.nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_sum_prod2_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1)) @ (cInt.nat @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V2]: (cNat.semiring_1_class.of_nat @ (V0 @ V2)))) @ V1))))))))
(TNat_Transfer.transfer_nat_int_sum_prod2_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ (cInt.nat @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: (cNat.semiring_1_class.of_nat @ (V0 @ V2)))) @ V1))))))))
(TNitpick.fun_box.fun_box_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNitpick.fun_box.fun_box_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TNitpick.pair_box.pair_box_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cNitpick.pair_box.pair_box_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cNitpick.pair_box.PairBox @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V2) @ ((V0 @ V4) @ V5))) @ V3))))))) @ V3)))))))))))
(TNitpick.pair_box.pair_box_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cNitpick.pair_box.pair_box_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cNitpick.pair_box.PairBox @ V3) @ V4))) @ ((cHOL.eq @ V2) @ ((V0 @ V3) @ V4)))))))))))))))
(TNitpick.word.full_exhaustive_word.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cNitpick.word.Word @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TNum.linordered_idom.neg_numeral_le_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V3)))))))))))))))))))))))))
(TNum.linordered_semidom.le_numeral_extra_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V3) @ V3)))))))))))))))
(TNum.linordered_semidom.le_numeral_extra_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V1) @ V1)))))))))))))))
(TNum.linordered_semidom.le_numeral_extra_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V4 @ V3) @ V1))))))))))))))))
(TNum.linordered_semidom.le_numeral_extra_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V1) @ V3)))))))))))))))
(TNum.linordered_semidom.le_numeral_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V4 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V1))))))))))))))))))
(TNum.linordered_semidom.le_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V1) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))))))))))))))))))
(TNum.linordered_semidom.le_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V3)) @ ((cNum.ord_num_inst.less_eq_num @ V6) @ cNum.num.One))))))))))))))))))
(TNum.linordered_semidom.le_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V4 @ V3) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))))))))))))))))))
(TNum.linordered_semidom.le_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V3) @ V0) @ V7))) @ ((cNum.ord_num_inst.less_eq_num @ V6) @ V7))))))))))))))))))))
(TNum.linordered_semidom.numeral_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V3) @ V0) @ V7))) @ ((cNum.ord_num_inst.less_num @ V6) @ V7))))))))))))))))))))
(TNum.neg_numeral.add_neg_numeral_special_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5)) @ V4)) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ cNum.num.One) @ V5))))))))))))))))
(TNum.neg_numeral.add_neg_numeral_special_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V1 @ V4) @ ((((cNum.neg_numeral.neg_numeral @ V1) @ V3) @ V4) @ V5))) @ (((((cNum.neg_numeral.sub @ V0) @ V1) @ V4) @ cNum.num.One) @ V5))))))))))))))))
(TNum.neg_numeral.is_num_add_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cNum.class.neg_numeral @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V5)) @ ((c==> @ ((((cNum.neg_numeral.is_num @ V1) @ V3) @ V4) @ V6)) @ ((cHOL.eq @ ((V1 @ V5) @ ((V1 @ V6) @ V7))) @ ((V1 @ V6) @ ((V1 @ V5) @ V7)))))))))))))))))))))))
(TNum.neg_numeral_class.minus_neg_numeral,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.ring_1_class.mult_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.ring_1_class.mult_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.ring_1_class.mult_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TNum.ring_char_0.neg_numeral_neq_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V7)))))))))))))))))))))
(TNum.ring_char_0.numeral_neq_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cNum.class.ring_char_0 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((cHOL.eq @ (((cNum.numeral.numeral @ V0) @ V2) @ V6)) @ ((((cNum.neg_numeral.neg_numeral @ V2) @ V5) @ V0) @ V7)))))))))))))))))))))
(TNum.semiring_numeral_class.mult_2_right,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cGroups.plus_class.plus @ V0) @ V0)))))
(TNum.semiring_numeral_class.numeral_mult,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TOrderings.dense_linorder_class.dense_ge,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TOrderings.dense_linorder_class.dense_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TOrderings.linorder_class.le_less_linear,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TOrderings.linorder_class.linorder_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)) @ V2))))))))))
(TOrderings.linorder_class.strict_mono_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.strict_mono @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TOrderings.order_class.dual_order.irrefl,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V0)))))
(TOrderings.order_class.le_imp_less_or_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.ordering.strict_implies_order,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((V0 @ V2) @ V3))))))))))))
(TOrderings.ordering_top.extremum_uniqueI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.ordering_top @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ V3) @ V2))))))))))))
(TOrderings.preorder_class.less_le_not_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))))
(TPartial_Function.partial_function_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ (V2 @ V4)) @ (V2 @ V5))) @ ((cHOL.eq @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: ((cHOL.eq @ (V2 @ (V3 @ V4))) @ V4)))) @ ((cPartial_Function.partial_function_definitions @ ((cPartial_Function.img_ord @ V2) @ V0)) @ (((cPartial_Function.img_lub @ V2) @ V3) @ V1))))))))))))))
(TPartial_Function.tailrec.fixp_induct_uc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ (cPartial_Function.flat_ord @ cHOL.undefined)) @ (^[V6]: ((V0 @ (V1 @ (V2 @ V6))) @ V5)))))) @ ((c==> @ ((c== @ V3) @ (V2 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cHOL.undefined))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ (^[V5]: (V0 @ (V1 @ (V2 @ V5)))))))) @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ (V0 @ (V2 @ V5))) @ V5)))) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cHOL.undefined))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ V4)) @ ((c==> @ (call @ (^[V5]: ((c==> @ (V4 @ (V0 @ V5))) @ (V4 @ (V0 @ (V1 @ V5))))))) @ (V4 @ (V0 @ V3))))))))))))))))))
(TPartial_Function.tailrec.mono_body_fixp,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ (cPartial_Function.flat_ord @ cHOL.undefined)) @ (^[V2]: ((V0 @ V2) @ V1)))))) @ ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cHOL.undefined))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ V0)) @ (V0 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ (cPartial_Function.flat_lub @ cHOL.undefined))) @ (cPartial_Function.fun_ord @ (cPartial_Function.flat_ord @ cHOL.undefined))) @ V0)))))))
(TPower.linordered_idom.zero_le_power_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ V3) @ ((((cPower.power.power @ V7) @ V9) @ (V0 @ V10)) @ V11))))))))))))))))))))))))))))
(TPower.linordered_semidom.one_less_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V7)) @ ((V5 @ V3) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7))))))))))))))))))))))
(TPower.linordered_semidom.power_Suc_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V1) @ V6)) @ ((c==> @ ((V5 @ V6) @ V3)) @ ((V5 @ ((V2 @ V6) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7))) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7))))))))))))))))))))))
(TPower.monoid_mult_class.power_one_right,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ cNat.one_nat_inst.one_nat)) @ V0))))
(TPredicate.pred.pred_size_overloaded_def,((c== @ cNat.size_class.size) @ (cPredicate.pred.pred_rec @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TPredicate.pred.size_pred_inst.size_pred,((c== @ cPredicate.pred.size_pred_inst.size_pred) @ cPredicate.pred.size_pred_inst.size_pred))
(TProduct_Type.equal_bool_inst.equal_bool,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TProduct_Type.equal_prod_inst.equal_prod,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TProduct_Type.equal_unit_inst.equal_unit,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Exhaustive.check_all_fun_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_class.check_all @ V0)) @ ((cHOL.Let @ (((cQuickcheck_Exhaustive.mk_map_term @ (^[V1]: (cTyperep.typerep_class.typerep @ cTYPE))) @ (^[V1]: (cTyperep.typerep_class.typerep @ cTYPE))) @ (cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE))) @ (^[V1]: ((cHOL.Let @ cEnum.enum_class.enum) @ (^[V2]: ((cQuickcheck_Exhaustive.check_all_n_lists @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (V0 @ ((cProduct_Type.Pair @ ((cFun.comp @ cOption.the) @ (cMap.map_of @ ((cList.zip @ V2) @ V3)))) @ (V1 @ V4))))))) @ (cCode_Numeral.natural_of_nat @ (cNat.size_class.size @ V2)))))))))))
(TQuickcheck_Exhaustive.check_all_set_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_class.check_all @ V0)) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ ((cList.zip @ cEnum.enum_class.enum) @ ((cList.map @ (^[V1]: (^[V2]: V1))) @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity))))))))
(TQuickcheck_Exhaustive.check_all_sum_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_class.check_all @ V0)) @ ((cQuickcheck_Exhaustive.orelse @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (^[V1]: (V0 @ (cQuickcheck_Exhaustive.term_syntax.valtermify_Inl @ V1))))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (^[V1]: (V0 @ (cQuickcheck_Exhaustive.term_syntax.valtermify_Inr @ V1)))))))))
(TQuickcheck_Exhaustive.equal_unknown_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.term_emptyset_def,((cHOL.eq @ (cQuickcheck_Exhaustive.term_syntax.term_emptyset @ cTYPE)) @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))
(TQuickcheck_Exhaustive.three_valued.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ V2))))))))
(TQuickcheck_Exhaustive.three_valued.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ V0) @ V1) @ V2) @ (cQuickcheck_Exhaustive.three_valued.Value @ V3))) @ (V1 @ V3)))))))))))
(TQuickcheck_Exhaustive.three_valued.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.size_6,((cHOL.eq @ (cNat.size_class.size @ cQuickcheck_Exhaustive.three_valued.No_value)) @ cNat.zero_nat_inst.zero_nat))
(TQuickcheck_Exhaustive.three_valued.size_5,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cQuickcheck_Exhaustive.three_valued.Value @ V0))) @ cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Exhaustive.three_valued.size_4,((cHOL.eq @ (cNat.size_class.size @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ cNat.zero_nat_inst.zero_nat))
(TQuickcheck_Exhaustive.three_valued.size_3,(call @ (^[V0]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.three_valued.three_valued_size @ V0) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Exhaustive.three_valued.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.three_valued.three_valued_size @ V0) @ (cQuickcheck_Exhaustive.three_valued.Value @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Exhaustive.three_valued.size_1,(call @ (^[V0]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.three_valued.three_valued_size @ V0) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Exhaustive.unknown.Known_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Exhaustive.unknown.Known @ V0)) @ (cQuickcheck_Exhaustive.Abs_unknown @ (cDatatype.In1 @ (cDatatype.Leaf @ V0)))))))
(TQuickcheck_Exhaustive.unknown.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Exhaustive.unknown.Known @ V6))) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V2) @ V4) @ V0)) @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V3) @ V5) @ V1))))))))))))))))))
(TQuickcheck_Exhaustive.unknown.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ (cHOL.Not @ (V0 @ V1)))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Exhaustive.unknown.Known @ V4))) @ (cHOL.Not @ (V0 @ (V2 @ V4))))))))))))))))))
(TQuickcheck_Narrowing.arity_term_of_cfun,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_term_of_ffun,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_typerep_cfun,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Narrowing.arity_typerep_ffun,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cInt.zero_int_inst.zero_int))) @ (V0 @ ((cInt.minus_int_inst.minus_int @ V2) @ cInt.one_int_inst.one_int))))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.around_zero.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (cQuickcheck_Narrowing.around_zero @ V0)) @ V1)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.around_zero_rel) @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V3)) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (cQuickcheck_Narrowing.around_zero @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V3)) @ cList.list.Nil))))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.around_zero_rel) @ V3)) @ V2)))))) @ V2))))))))))
(TQuickcheck_Narrowing.around_zero.psimps,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.around_zero_rel) @ V0)) @ ((cHOL.eq @ (cQuickcheck_Narrowing.around_zero @ V0)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (cQuickcheck_Narrowing.around_zero @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V0)) @ cList.list.Nil))))))))))
(TQuickcheck_Narrowing.cfun.cfun_case_def,((c== @ cQuickcheck_Narrowing.cfun.cfun_case) @ (^[V0]: (cQuickcheck_Narrowing.cfun.cfun_rec @ (^[V1]: (V0 @ V1))))))
(TQuickcheck_Narrowing.cfun.cfun_size_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Narrowing.cfun.cfun_size @ V0)) @ (cQuickcheck_Narrowing.cfun.cfun_rec @ (^[V1]: ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Narrowing.conv_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.conv_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V5) @ V6))) @ (cQuickcheck_Narrowing.error @ ((cList.list.Cons @ cQuickcheck_Narrowing.marker) @ ((cList.map @ cQuickcheck_Narrowing.toEnum) @ V5))))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V5) @ V6))) @ (((cQuickcheck_Narrowing.nth @ V4) @ V5) @ V6))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Narrowing.equal_property_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.ffun.ffun_case_def,((c== @ cQuickcheck_Narrowing.ffun.ffun_case) @ (^[V0]: (^[V1]: ((cQuickcheck_Narrowing.ffun.ffun_rec @ (^[V2]: (V0 @ V2))) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: (((V1 @ V2) @ V3) @ V4))))))))))
(TQuickcheck_Narrowing.ffun.ffun_size_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cQuickcheck_Narrowing.ffun.ffun_size @ V0) @ V1)) @ ((cQuickcheck_Narrowing.ffun.ffun_rec @ (^[V2]: ((cNat.plus_nat_inst.plus_nat @ (V1 @ V2)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))) @ (^[V2]: (^[V3]: (^[V4]: (^[V5]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ (V0 @ V2)) @ (V1 @ V3))) @ V5)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))))))
(TQuickcheck_Narrowing.length_around_zero,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ (cNat.size_class.size @ (cQuickcheck_Narrowing.around_zero @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ (cInt.nat @ V0))) @ cNat.one_nat_inst.one_nat))))))
(TQuickcheck_Narrowing.non_empty_sumC_def,((c== @ cQuickcheck_Narrowing.non_empty_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Narrowing.non_empty_graph @ V0) @ V1))))))
(TQuickcheck_Narrowing.property.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((cHOL.eq @ V1) @ (((cQuickcheck_Narrowing.property.Universal @ V8) @ V9) @ V10))) @ ((cHOL.eq @ (((V2 @ V8) @ V9) @ V10)) @ (((V3 @ V8) @ V9) @ V10)))))))))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((cHOL.eq @ V1) @ (((cQuickcheck_Narrowing.property.Existential @ V8) @ V9) @ V10))) @ ((cHOL.eq @ (((V4 @ V8) @ V9) @ V10)) @ (((V5 @ V8) @ V9) @ V10)))))))))) @ ((c==> @ (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.property.Property @ V8))) @ ((cHOL.eq @ (V6 @ V8)) @ (V7 @ V8)))))) @ ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V2) @ V4) @ V6) @ V0)) @ ((((cQuickcheck_Narrowing.property.property_case @ V3) @ V5) @ V7) @ V1)))))))))))))))))))))))
(TQuickcheck_Narrowing.property.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Narrowing.property.property_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Universal @ V5) @ V6) @ V7))) @ (cHOL.Not @ (V0 @ (((V1 @ V5) @ V6) @ V7))))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Existential @ V5) @ V6) @ V7))) @ (cHOL.Not @ (V0 @ (((V2 @ V5) @ V6) @ V7))))))))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cQuickcheck_Narrowing.property.Property @ V5))) @ (cHOL.Not @ (V0 @ (V3 @ V5)))))))))))))))))))))
(TQuickcheck_Random.arity_random_finite_1,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_finite_2,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_finite_3,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_finite_4,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.arity_random_finite_5,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.list.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_list @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Random.pred.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_pred @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cPredicate.pred.Pred) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Random.prod.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_prod @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cProduct_Type.Pair) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Random.random_aux_nibble_def,((c== @ cQuickcheck_Random.random_aux_nibble) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble0) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble4) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble5) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble6) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble7) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble8) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble9) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleA) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleB) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleC) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleD) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleE) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleF) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))))))))))))))))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble0) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble1) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble2) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble3) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble4) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble5) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble6) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble7) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble8) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble9) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleA) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleB) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleC) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleD) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleE) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleF) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))))))))))))))))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_option_def,((c== @ cQuickcheck_Random.random_aux_option) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cOption.option.None) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cOption.option.Some) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil)))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cOption.option.None) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cOption.option.Some) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil)))) @ V4)))))) @ V0))))
(TQuickcheck_Random.term.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_term @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cCode_Evaluation.term.dummy_term) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Random.unit.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_unit @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cProduct_Type.Unity) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Random.valtermify_insert_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V0) @ V1)) @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSet.insert) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)) @ V1)))))))
(TRandom_Sequence.neg_not_random_dseq_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.neg_not_random_dseq @ V0)) @ (^[V1]: (^[V2]: (^[V3]: (cLimited_Sequence.neg_not_seq @ (((V0 @ V1) @ V2) @ V3)))))))))
(TRandom_Sequence.pos_not_random_dseq_def,(call @ (^[V0]: ((cHOL.eq @ (cRandom_Sequence.pos_not_random_dseq @ V0)) @ (^[V1]: (^[V2]: (^[V3]: (cLimited_Sequence.pos_not_seq @ (((V0 @ V1) @ V2) @ V3)))))))))
(TRecord.random_aux_tuple_isomorphism_def,((c== @ cRecord.random_aux_tuple_isomorphism) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cRecord.tuple_isomorphism.Tuple_Isomorphism) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cRecord.tuple_isomorphism.Tuple_Isomorphism) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TRecord.tuple_isomorphism.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V2) @ V0)) @ ((cRecord.tuple_isomorphism.tuple_isomorphism_case @ V2) @ V1))))))))))
(TRecord.update_accessor_cong_assist_triv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)) @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)))))))
(TRecord.update_accessor_congruence_foldE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ (V1 @ V3)) @ V4)) @ ((c==> @ (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V4) @ V7)) @ ((cHOL.eq @ (V5 @ V7)) @ (V6 @ V7)))))) @ ((cHOL.eq @ ((V0 @ V5) @ V2)) @ ((V0 @ V6) @ V3)))))))))))))))))))))
(TRings.class.linordered_semiring_1.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((((cRings.class.semiring_1 @ V5) @ V4) @ V0) @ V3)) @ ((((((cRings.class.linordered_semiring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TRings.class.ordered_cancel_semiring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TRings.class.ordered_comm_semiring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ (((cRings.class.comm_semiring_0 @ V0) @ V3) @ V4)) @ ((c==> @ (((cRings.class.ordered_comm_semiring_axioms @ V1) @ V3) @ V4)) @ (((((cRings.class.ordered_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))
(TRings.class.ordered_ring_abs_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cRings.class.ordered_ring_abs_axioms @ V0) @ V1) @ V2) @ V3)) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.conj @ ((cHOL.disj @ ((V2 @ V1) @ V4)) @ ((V2 @ V4) @ V1))) @ ((cHOL.disj @ ((V2 @ V1) @ V5)) @ ((V2 @ V5) @ V1)))) @ ((cHOL.eq @ (V0 @ ((V3 @ V4) @ V5))) @ ((V3 @ (V0 @ V4)) @ (V0 @ V5))))))))))))))))))
(TRings.class.ordered_semiring_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.ordered_semiring_axioms @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V1 @ V3) @ V4)) @ ((cHOL.implies @ ((V1 @ V0) @ V5)) @ ((V1 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V1 @ V3) @ V4)) @ ((cHOL.implies @ ((V1 @ V0) @ V5)) @ ((V1 @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V5)))))))))))))))))))
(TRings.class.ring_1_no_zero_divisors_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cRings.class.ring_no_zero_divisors @ V1) @ V3) @ V2) @ V4) @ V5))))))))))))))))
(TRings.class.ring_no_zero_divisors.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cRings.class.no_zero_divisors @ V0) @ V1)) @ ((c==> @ (((((cRings.class.ring @ V2) @ V1) @ V3) @ V4) @ V0)) @ (((((cRings.class.ring_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TRings.classrel_ring_1_semiring_1_cancel,(cRings.semiring_1_cancel_class @ cTYPE))
(TRings.comm_semiring_1_class.dvd_0_right,(call @ (^[V0]: ((cRings.dvd_class.dvd @ V0) @ cGroups.zero_class.zero))))
(TRings.linordered_idom.abs_diff_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ (V0 @ ((V1 @ V10) @ V11))) @ V12)) @ ((cHOL.conj @ ((V5 @ ((V1 @ V11) @ V12)) @ V10)) @ ((V5 @ V10) @ ((V6 @ V11) @ V12))))))))))))))))))))))))))))))))
(TRings.linordered_idom_class.abs_dvd_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ (cGroups.abs_class.abs @ V0)) @ V1)) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TRings.linordered_idom_class.dvd_abs_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ (cGroups.abs_class.abs @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TRings.linordered_idom_class.sgn_greater,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cGroups.sgn_class.sgn @ V0))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TRings.linordered_semidom.pos_add_strict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V1) @ V6)) @ ((c==> @ ((V5 @ V7) @ V8)) @ ((V5 @ V7) @ ((V0 @ V6) @ V8))))))))))))))))))))))))
(TRings.linordered_semiring_1_class.intro,((c==> @ (cRings.linordered_semiring_class @ cTYPE)) @ ((c==> @ (cRings.semiring_1_class @ cTYPE)) @ (cRings.linordered_semiring_1_class @ cTYPE))))
(TRings.linordered_semiring_1_class.super_2,((c==> @ (cRings.linordered_semiring_1_class @ cTYPE)) @ (cRings.semiring_1_class @ cTYPE)))
(TRings.linordered_semiring_1_class.super_1,((c==> @ (cRings.linordered_semiring_1_class @ cTYPE)) @ (cRings.linordered_semiring_class @ cTYPE)))
(TRings.no_zero_divisors.no_zero_divisors,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.class.no_zero_divisors @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V1))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ V1))) @ (cHOL.Not @ ((cHOL.eq @ ((V0 @ V2) @ V3)) @ V1))))))))))))))
(TRings.ordered_cancel_semiring_class_def,((c== @ (cRings.ordered_cancel_semiring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cRings.ordered_semiring_class @ cTYPE))))
(TRings.ordered_comm_semiring_class.intro,((c==> @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_0_class @ cTYPE)) @ ((c==> @ (((cRings.class.ordered_comm_semiring_axioms @ cOrderings.ord_class.less_eq) @ cGroups.zero_class.zero) @ cGroups.times_class.times)) @ (cRings.ordered_comm_semiring_class @ cTYPE)))))
(TRings.ordered_comm_semiring_class.super_2,((c==> @ (cRings.ordered_comm_semiring_class @ cTYPE)) @ (cRings.comm_semiring_0_class @ cTYPE)))
(TRings.ordered_comm_semiring_class.super_1,((c==> @ (cRings.ordered_comm_semiring_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)))
(TRings.ordered_semiring_class.mult_mono',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))))
(TRings.ring_1_no_zero_divisors_class_def,((c== @ (cRings.ring_1_no_zero_divisors_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.ring_1_class @ cTYPE)) @ (cRings.ring_no_zero_divisors_class @ cTYPE))))
(TRings.ring_no_zero_divisors_class.intro,((c==> @ (cRings.no_zero_divisors_class @ cTYPE)) @ ((c==> @ (cRings.ring_class @ cTYPE)) @ (cRings.ring_no_zero_divisors_class @ cTYPE))))
(TRings.ring_no_zero_divisors_class.super_2,((c==> @ (cRings.ring_no_zero_divisors_class @ cTYPE)) @ (cRings.ring_class @ cTYPE)))
(TRings.ring_no_zero_divisors_class.super_1,((c==> @ (cRings.ring_no_zero_divisors_class @ cTYPE)) @ (cRings.no_zero_divisors_class @ cTYPE)))
(TSMT.pattern.pattern_size_overloaded_def,((c== @ cSMT.pattern.size_pattern_inst.size_pattern) @ (cSMT.pattern.pattern_rec @ cNat.zero_nat_inst.zero_nat)))
(TSet_Interval.card_greaterThanAtMost_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ V1) @ V0))))))))
(TSet_Interval.dvd.greaterThanLessThan_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cSet_Interval.ord.greaterThanLessThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.greaterThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0)) @ ((cSet_Interval.ord.lessThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1))))))))
(TSet_Interval.finite_atLeastLessThan_int,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)))))))
(TSet_Interval.finite_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)))))))
(TSet_Interval.finite_nat_set_iff_bounded,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cNat.ord_nat_inst.less_nat @ V2) @ V1)))))))))
(TSet_Interval.lessThan_strict_subset_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cSet_Interval.ord_class.lessThan @ V0)) @ (cSet_Interval.ord_class.lessThan @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V1)))))))
(TSet_Interval.linorder.Int_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V4) @ V5))) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ (((cOrderings.ord.max @ V0) @ V2) @ V4)) @ (((cOrderings.ord.min @ V0) @ V3) @ V5)))))))))))))))))
(TSet_Interval.ord.greaterThanLessThan_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cSet_Interval.ord.greaterThanLessThan @ V0) @ V1) @ V2)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.greaterThan @ V0) @ V1)) @ ((cSet_Interval.ord.lessThan @ V0) @ V2))))))))))
(TSet_Interval.setsum_shift_lb_Suc0_0_upt,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (V0 @ cNat.zero_nat_inst.zero_nat)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ V1)))))))))
(TSet_Interval.subset_card_intvl_is_intvl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ (cFinite_Set.card @ V0))))) @ ((cHOL.eq @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ (cFinite_Set.card @ V0))))))))))
(TString.enum_nibble_inst.enum_all_nibble,((c== @ cString.enum_nibble_inst.enum_all_nibble) @ cString.enum_nibble_inst.enum_all_nibble))
(TString.equal_literal_inst.equal_literal,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TTransitive_Closure.finite_trancl_ntranl,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cTransitive_Closure.trancl @ V0)) @ ((cTransitive_Closure.ntrancl @ ((cNat.minus_nat_inst.minus_nat @ (cFinite_Set.card @ V0)) @ cNat.one_nat_inst.one_nat)) @ V0))))))
(TTransitive_Closure.relpowp_imp_rtranclp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cNat.compow @ V0) @ V1) @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V1) @ V2) @ V3)))))))))))
(TTransitive_Closure.rtrancl.rtrancl_refl,(call @ (^[V0]: (call @ (^[V1]: ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V0)) @ (cTransitive_Closure.rtrancl @ V1)))))))
(TTransitive_Closure.rtrancl_eq_or_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))))))))))))
(TTransitive_Closure.rtrancl_into_trancl1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.rtrancl_into_trancl2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.rtrancl_is_UN_relpow,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: ((cNat.compow @ V1) @ V0)))))))
(TTransitive_Closure.rtranclp_imp_relpowp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((((cNat.compow @ V3) @ V0) @ V1) @ V2)))))))))))
(TTransitive_Closure.single_valued_relpow,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRelation.single_valued @ V0)) @ (cRelation.single_valued @ ((cNat.compow @ V1) @ V0))))))))
(TTransitive_Closure.trancl.r_into_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))))))))))
(TTransitive_Closure.trancl_subset_Field2,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cTransitive_Closure.trancl @ V0)) @ ((cProduct_Type.Sigma @ (cRelation.Field @ V0)) @ (^[V1]: (cRelation.Field @ V0)))))))
(TTransitive_Closure.tranclp_trans_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V3 @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V4) @ V5)) @ ((c==> @ ((V3 @ V4) @ V5)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V5) @ V6)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((V3 @ V4) @ V6)))))))))))) @ ((V3 @ V1) @ V2)))))))))))))
(TTyperep.typerep.typerep_rec_set_1.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cTyperep.typerep.typerep_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V3) @ ((cTyperep.typerep.Typerep @ V8) @ V6))) @ ((c==> @ ((cHOL.eq @ V4) @ (((V0 @ V8) @ V6) @ V7))) @ ((c==> @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V6) @ V7)) @ V5)))))))))) @ V5)))))))))))))))
(TTyperep.typerep.typerep_rec_set_1.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((((cTyperep.typerep.typerep_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4)) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cTyperep.typerep.Typerep @ V7) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ (((V0 @ V7) @ V5) @ V6))) @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V5) @ V6)))))))))))))))))))))
(TTyperep.typerep.typerep_rec_set_2.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V4) @ V1)) @ V5))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V6) @ V8))) @ ((c==> @ ((cHOL.eq @ V4) @ ((((V2 @ V6) @ V8) @ V7) @ V9))) @ ((c==> @ (((((cTyperep.typerep.typerep_rec_set_1 @ V0) @ V1) @ V2) @ V6) @ V7)) @ ((c==> @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V8) @ V9)) @ V5))))))))))))) @ V5))))))))))))))))
(TTyperep.typerep.typerep_rec_set_2.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cList.list.Nil)) @ ((cHOL.eq @ V4) @ V1))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cList.list.Cons @ V5) @ V7))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((((V2 @ V5) @ V7) @ V6) @ V8))) @ ((cHOL.conj @ (((((cTyperep.typerep.typerep_rec_set_1 @ V0) @ V1) @ V2) @ V5) @ V6)) @ (((((cTyperep.typerep.typerep_rec_set_2 @ V0) @ V1) @ V2) @ V7) @ V8)))))))))))))))))))))))))
(TTyperep.typerep.typerep_rep_set.inducts_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V0)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V3)) @ ((c==> @ (V1 @ V3)) @ (V2 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V4)) @ V3))))))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cTyperep.typerep.typerep_rep_set_1 @ V3)) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V4)) @ ((c==> @ (V1 @ V4)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ V3) @ V4)))))))))))) @ (V1 @ V0))))))))))))
(TTyperep.typerep.typerep_rep_set.inducts_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cTyperep.typerep.typerep_rep_set_1 @ V0)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V3)) @ ((c==> @ (V1 @ V3)) @ (V2 @ ((cDatatype.Scons @ (cDatatype.Leaf @ V4)) @ V3))))))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cTyperep.typerep.typerep_rep_set_1 @ V3)) @ ((c==> @ (V2 @ V3)) @ ((c==> @ (cTyperep.typerep.typerep_rep_set_2 @ V4)) @ ((c==> @ (V1 @ V4)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ V3) @ V4)))))))))))) @ (V2 @ V0))))))))))))
(TBig_Operators.comm_monoid_add.setsum_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_set.F @ V0) @ V1))))))))
(TBig_Operators.comm_monoid_set.eq_general,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V7]: (cHOL.Ex1 @ (^[V8]: ((cHOL.conj @ ((cSet.member @ V8) @ V3)) @ ((cHOL.eq @ (V4 @ V8)) @ V7))))))) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V7]: ((cHOL.conj @ ((cSet.member @ (V4 @ V7)) @ V2)) @ ((cHOL.eq @ (V5 @ (V4 @ V7))) @ (V6 @ V7)))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V6) @ V3)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V5) @ V2))))))))))))))))))))
(TBig_Operators.linorder_class.Max.eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cSet.insert @ V1) @ V0))) @ (((cFinite_Set.fold @ cOrderings.ord_class.max) @ V1) @ V0))))))))
(TBig_Operators.linorder_class.Max.in_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Max @ V0))) @ (cBig_Operators.linorder_class.Max @ V0)))))))))
(TBig_Operators.linorder_class.Min.eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cSet.insert @ V1) @ V0))) @ (((cFinite_Set.fold @ cOrderings.ord_class.min) @ V1) @ V0))))))))
(TBig_Operators.linorder_class.Min.in_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ (cBig_Operators.linorder_class.Min @ V0)))))))))
(TBig_Operators.setprod_dvd_setprod_subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cRings.dvd_class.dvd @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)))))))))))
(TBig_Operators.setprod_mono_one_cong_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.one_class.one)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V3 @ V4)) @ (V2 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)))))))))))))))
(TBig_Operators.setsum_eq_general_reverses,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V1)) @ ((cHOL.conj @ ((cSet.member @ (V2 @ V6)) @ V0)) @ ((cHOL.eq @ (V3 @ (V2 @ V6))) @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V0)) @ ((cHOL.conj @ ((cSet.member @ (V3 @ V6)) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ (V2 @ (V3 @ V6))) @ V6)) @ ((cHOL.eq @ (V4 @ (V3 @ V6))) @ (V5 @ V6)))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V5) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V4) @ V1)))))))))))))))))))
(TBig_Operators.setsum_mono_zero_cong_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.zero_class.zero)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V3 @ V4)) @ (V2 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)))))))))))))))
(TCode_Evaluation.term.term_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TCode_Evaluation.term.term_rec_set.intros,(call @ (^[V0]: (((cCode_Evaluation.term.term_rec_set @ V0) @ cCode_Evaluation.term.dummy_term) @ V0))))
(TCode_Evaluation.term.term_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cCode_Evaluation.term.term_rep_set @ V0)) @ ((c==> @ (V1 @ cHOL.undefined)) @ (V1 @ V0))))))))
(TCode_Evaluation.term.term_rep_set.intros,(cCode_Evaluation.term.term_rep_set @ cHOL.undefined))
(TCode_Numeral.integer_of_natural.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_natural) @ cCode_Numeral.pcr_integer) @ cNat.semiring_1_class.of_nat) @ cCode_Numeral.integer_of_natural))
(TCode_Numeral.nat_of_integer_non_positive,(call @ (^[V0]: ((c==> @ ((cCode_Numeral.ord_integer_inst.less_eq_integer @ V0) @ cCode_Numeral.zero_integer_inst.zero_integer)) @ ((cHOL.eq @ (cCode_Numeral.nat_of_integer @ V0)) @ cNat.zero_nat_inst.zero_nat)))))
(TCode_Numeral.natural.natural_rec_set_def,((c== @ cCode_Numeral.natural.natural_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((cHOL.eq @ V4) @ V0))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cCode_Numeral.Suc @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((V1 @ V5) @ V6))) @ ((V2 @ V5) @ V6))))))))))))))))
(TCode_Numeral.natural_of_integer.transfer,((((cTransfer.fun_rel @ cCode_Numeral.pcr_integer) @ cCode_Numeral.pcr_natural) @ cInt.nat) @ cCode_Numeral.natural_of_integer))
(TComplete_Lattices.Inf_bool_inst.Inf_bool,((c== @ cComplete_Lattices.Inf_bool_inst.Inf_bool) @ cComplete_Lattices.Inf_bool_inst.Inf_bool))
(TComplete_Lattices.Sup_bool_inst.Sup_bool,((c== @ cComplete_Lattices.Sup_bool_inst.Sup_bool) @ cComplete_Lattices.Sup_bool_inst.Sup_bool))
(TComplete_Partial_Order.ccpo.iterates.Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V5]: ((cSet.member @ V5) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))))) @ ((cSet.member @ (V0 @ V3)) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))))))))))))))))
(TComplete_Partial_Order.ccpo.iterates_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c== @ ((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1)) @ (^[V3]: (cSet.Collect @ (^[V4]: ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V4)))))))))))))
(TComplete_Partial_Order.ccpo_class.axioms,((cComplete_Partial_Order.class.ccpo_axioms @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq))
(TComplete_Partial_Order.class.ccpo.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((cComplete_Partial_Order.class.ccpo_axioms @ V0) @ V1)))))))))
(TComplete_Partial_Order.class.ccpo.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((cOrderings.class.order @ V1) @ V2)))))))))
(TDivides.class.semiring_numeral_div.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((((((cRings.class.linordered_semidom @ V3) @ V4) @ V0) @ V5) @ V6) @ V7)) @ ((c==> @ (((((((((cDivides.class.semiring_numeral_div_axioms @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V8) @ V6) @ V7)) @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V8) @ V6) @ V7)))))))))))))))))))))))
(TDivides.ring_div_class.mod_diff_right_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.minus_class.minus @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)))))))))
(TDivides.semiring_div.div_mult_div_if_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V8) @ V9)) @ ((cHOL.eq @ ((V0 @ ((V1 @ V7) @ V6)) @ ((V1 @ V9) @ V8))) @ ((V1 @ ((V0 @ V7) @ V9)) @ ((V0 @ V6) @ V8)))))))))))))))))))))))))))
(TDivides.semiring_div.dvd_div_div_eq_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V7) @ V4))) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V8)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V7) @ V9)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V8) @ V6)) @ ((V1 @ V9) @ V7))) @ ((cHOL.eq @ ((V0 @ V8) @ V7)) @ ((V0 @ V6) @ V9)))))))))))))))))))))))))))))
(TDivides.semiring_div.dvd_mult_div_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((cRings.dvd.dvd @ V0) @ V6) @ V7)) @ ((cHOL.eq @ ((V0 @ V6) @ ((V1 @ V7) @ V6))) @ V7))))))))))))))))))))
(TDivides.semiring_div.mod_mult_self1_is_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ V6)) @ V4)))))))))))))))))))
(TDivides.semiring_div.mod_mult_self2_is_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ V7)) @ V4)))))))))))))))))))
(TDivides.semiring_div_class.div_add_self1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V0)) @ ((cGroups.plus_class.plus @ ((cDivides.div_class.div @ V1) @ V0)) @ cGroups.one_class.one))))))))
(TDivides.semiring_div_class.div_add_self2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.plus_class.plus @ V1) @ V0)) @ V0)) @ ((cGroups.plus_class.plus @ ((cDivides.div_class.div @ V1) @ V0)) @ cGroups.one_class.one))))))))
(TDivides.semiring_div_class.div_mult_swap,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.times_class.times @ V2) @ ((cDivides.div_class.div @ V1) @ V0))) @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V2) @ V1)) @ V0))))))))))
(TDivides.semiring_div_class.dvd_imp_mod_0,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_class.mod @ V1) @ V0)) @ cGroups.zero_class.zero)))))))
(TDivides.semiring_div_class.mod_add_self1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V0)) @ ((cDivides.div_class.mod @ V1) @ V0)))))))
(TDivides.semiring_div_class.mod_add_self2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V1)) @ ((cDivides.div_class.mod @ V0) @ V1)))))))
(TDivides.semiring_div_class.mod_mult_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ V1)) @ ((cDivides.div_class.mod @ V2) @ V1))) @ ((c==> @ ((cHOL.eq @ ((cDivides.div_class.mod @ V3) @ V1)) @ ((cDivides.div_class.mod @ V4) @ V1))) @ ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V3)) @ V1)) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V2) @ V4)) @ V1)))))))))))))))
(TDivides.semiring_div_class.mult_mod_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cDivides.div_class.mod @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TDivides.semiring_numeral_div_class.intro,((c==> @ (cDivides.semiring_div_class @ cTYPE)) @ ((c==> @ (cGroups.minus_class @ cTYPE)) @ ((c==> @ (cRings.linordered_semidom_class @ cTYPE)) @ ((c==> @ (((((((((cDivides.class.semiring_numeral_div_axioms @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cGroups.minus_class.minus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less)) @ (cDivides.semiring_numeral_div_class @ cTYPE))))))
(TDivides.semiring_numeral_div_class.super_3,((c==> @ (cDivides.semiring_numeral_div_class @ cTYPE)) @ (cRings.linordered_semidom_class @ cTYPE)))
(TDivides.semiring_numeral_div_class.super_2,((c==> @ (cDivides.semiring_numeral_div_class @ cTYPE)) @ (cGroups.minus_class @ cTYPE)))
(TDivides.semiring_numeral_div_class.super_1,((c==> @ (cDivides.semiring_numeral_div_class @ cTYPE)) @ (cDivides.semiring_div_class @ cTYPE)))
(TEnum.enum_finite_1_inst.enum_ex_finite_1,((c== @ cEnum.enum_finite_1_inst.enum_ex_finite_1) @ cEnum.enum_finite_1_inst.enum_ex_finite_1))
(TEnum.enum_finite_2_inst.enum_ex_finite_2,((c== @ cEnum.enum_finite_2_inst.enum_ex_finite_2) @ cEnum.enum_finite_2_inst.enum_ex_finite_2))
(TEnum.enum_finite_3_inst.enum_ex_finite_3,((c== @ cEnum.enum_finite_3_inst.enum_ex_finite_3) @ cEnum.enum_finite_3_inst.enum_ex_finite_3))
(TEnum.enum_finite_4_inst.enum_ex_finite_4,((c== @ cEnum.enum_finite_4_inst.enum_ex_finite_4) @ cEnum.enum_finite_4_inst.enum_ex_finite_4))
(TEnum.enum_finite_5_inst.enum_ex_finite_5,((c== @ cEnum.enum_finite_5_inst.enum_ex_finite_5) @ cEnum.enum_finite_5_inst.enum_ex_finite_5))
(TEquiv_Relations.equivp_reflp_symp_transp,(call @ (^[V0]: ((cHOL.eq @ (cEquiv_Relations.equivp @ V0)) @ ((cHOL.conj @ (cRelation.reflp @ V0)) @ ((cHOL.conj @ (cRelation.symp @ V0)) @ (cRelation.transp @ V0)))))))
(TExtraction.sumbool.sumbool_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cExtraction.sumbool.sumbool_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cExtraction.sumbool.Left)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cExtraction.sumbool.Right)) @ ((c==> @ ((cHOL.eq @ V3) @ V1)) @ V4))) @ V4))))))))))))))
(TExtraction.sumbool.sumbool_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cExtraction.sumbool.sumbool_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cExtraction.sumbool.Left)) @ ((cHOL.eq @ V3) @ V0))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cExtraction.sumbool.Right)) @ ((cHOL.eq @ V3) @ V1)))))))))))))
(TFields.division_ring.diff_divide_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ ((V6 @ V8) @ V9)) @ V10)) @ ((V6 @ ((V1 @ V8) @ V10)) @ ((V1 @ V9) @ V10)))))))))))))))))))))))))))
(TFields.division_ring_class.divide_eq_imp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cGroups.times_class.times @ V2) @ V0))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2))))))))))
(TFields.division_ring_class.eq_divide_imp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ ((cHOL.eq @ ((cGroups.times_class.times @ V1) @ V0)) @ V2)) @ ((cHOL.eq @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0)))))))))))
(TFields.division_ring_class.right_inverse,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ (cFields.inverse_class.inverse @ V0))) @ cGroups.one_class.one)))))
(TFields.field_inverse_zero.inverse_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ ((V1 @ V8) @ V9))) @ ((V1 @ V9) @ V8))))))))))))))))))))))))
(TFields.linordered_field.divide_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V9 @ V5) @ V14)) @ ((c==> @ ((V10 @ V5) @ ((V2 @ V13) @ V12))) @ ((V9 @ ((V1 @ V14) @ V13)) @ ((V1 @ V14) @ V12)))))))))))))))))))))))))))))))))))))
(TFields.linordered_field.field_le_epsilon,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ (call @ (^[V14]: ((c==> @ ((V10 @ V5) @ V14)) @ ((V9 @ V12) @ ((V4 @ V13) @ V14)))))) @ ((V9 @ V12) @ V13))))))))))))))))))))))))))))))))
(TFields.linordered_field.neg_divide_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V13) @ V12)) @ V14)) @ ((V9 @ ((V2 @ V14) @ V12)) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.neg_le_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V9 @ V13) @ ((V1 @ V14) @ V12))) @ ((V9 @ V14) @ ((V2 @ V13) @ V12))))))))))))))))))))))))))))))))))))
(TFields.linordered_field.one_less_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V10 @ V12) @ V3)) @ ((V10 @ V3) @ (V0 @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field.pos_divide_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V13) @ V12)) @ V14)) @ ((V9 @ V13) @ ((V2 @ V14) @ V12))))))))))))))))))))))))))))))))))))
(TFields.linordered_field.pos_le_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V9 @ V13) @ ((V1 @ V14) @ V12))) @ ((V9 @ ((V2 @ V13) @ V12)) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.frac_less2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V3)) @ ((cFields.inverse_class.divide @ V1) @ V2)))))))))))))))
(TFields.linordered_field_class.sign_simps_46,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_45,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)))))))))
(TFields.linordered_field_class.sign_simps_44,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_43,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TFields.linordered_field_class.sign_simps_42,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_41,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_40,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TFields.linordered_field_class.sign_simps_39,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_38,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cGroups.minus_class.minus @ V0) @ V1)))))))
(TFields.linordered_field_class.sign_simps_37,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)))))))))
(TFields.linordered_field_class.sign_simps_36,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.linordered_field_class.sign_simps_35,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_34,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_33,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cGroups.minus_class.minus @ V1) @ V0)))))))
(TFields.linordered_field_class.sign_simps_32,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_31,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_30,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.linordered_field_class.sign_simps_29,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_28,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.linordered_field_class.sign_simps_27,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_26,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_25,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_24,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_21,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TFields.linordered_field_class.sign_simps_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_18,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TFields.linordered_field_class.sign_simps_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_16,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cGroups.minus_class.minus @ V0) @ V1)))))))
(TFields.linordered_field_class.sign_simps_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)))))))))
(TFields.linordered_field_class.sign_simps_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.linordered_field_class.sign_simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_11,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cGroups.minus_class.minus @ V1) @ V0)))))))
(TFields.linordered_field_class.sign_simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.linordered_field_class.sign_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.linordered_field_class.sign_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.sign_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TFields.linordered_field_class.sign_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TFinite_Set.comp_fun_commute.fold_insert2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V1))) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V3) @ ((cSet.insert @ V2) @ V1))) @ (((cFinite_Set.fold @ V0) @ ((V0 @ V2) @ V3)) @ V1))))))))))))))
(TFinite_Set.comp_fun_commute_product_fold,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.comp_fun_commute @ (^[V1]: (^[V2]: (((cFinite_Set.fold @ (^[V3]: (cSet.insert @ ((cProduct_Type.Pair @ V1) @ V3)))) @ V2) @ V0))))))))
(TFinite_Set.complete_lattice.INF_fold_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ V9)) @ (((cFinite_Set.fold @ ((cFun.comp @ V2) @ V9)) @ V7) @ V8)))))))))))))))))))))))))
(TFinite_Set.complete_lattice.Inf_fold_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ (V0 @ V8)) @ (((cFinite_Set.fold @ V2) @ V7) @ V8)))))))))))))))))))))))
(TFinite_Set.complete_lattice.SUP_fold_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ V9)) @ (((cFinite_Set.fold @ ((cFun.comp @ V5) @ V9)) @ V6) @ V8)))))))))))))))))))))))))
(TFinite_Set.complete_lattice.Sup_fold_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ (V1 @ V8)) @ (((cFinite_Set.fold @ V5) @ V6) @ V8)))))))))))))))))))))))
(TGroups.ab_group_add.add_diff_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6))) @ ((V2 @ V5) @ V6))))))))))))))))))
(TGroups.ab_group_add.uminus_add_conv_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ (V3 @ V4)) @ V5)) @ ((V2 @ V5) @ V4))))))))))))))))
(TGroups.ab_semigroup_add.add_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ V2) @ ((V0 @ V1) @ V3)))))))))))))
(TGroups.add_mono_thms_linordered_semiring_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.add_mono_thms_linordered_semiring_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ V2) @ V3))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.add_mono_thms_linordered_semiring_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.add_mono_thms_linordered_semiring_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TGroups.cancel_ab_semigroup_add_class_def,((c== @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ (cGroups.class.cancel_ab_semigroup_add_axioms @ cGroups.plus_class.plus))))
(TGroups.cancel_semigroup_add_class.axioms,(cGroups.class.cancel_semigroup_add_axioms @ cGroups.plus_class.plus))
(TGroups.class.ab_semigroup_add_axioms_def,(call @ (^[V0]: ((c== @ (cGroups.class.ab_semigroup_add_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.class.cancel_ab_semigroup_add_def,(call @ (^[V0]: ((c== @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ ((cHOL.conj @ (cGroups.class.ab_semigroup_add @ V0)) @ (cGroups.class.cancel_ab_semigroup_add_axioms @ V0))))))
(TGroups.class.cancel_semigroup_add.axioms_2,(call @ (^[V0]: ((c==> @ (cGroups.class.cancel_semigroup_add @ V0)) @ (cGroups.class.cancel_semigroup_add_axioms @ V0)))))
(TGroups.class.cancel_semigroup_add.axioms_1,(call @ (^[V0]: ((c==> @ (cGroups.class.cancel_semigroup_add @ V0)) @ (cGroups.class.semigroup_add @ V0)))))
(TGroups.class.comm_monoid_diff_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cGroups.class.comm_monoid_diff_axioms @ V0) @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V2 @ V3) @ V1)) @ V3)))) @ (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V2 @ V1) @ V3)) @ V1))))) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V2 @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5))) @ ((V2 @ V4) @ V5))))))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V2 @ ((V2 @ V3) @ V4)) @ V5)) @ ((V2 @ V3) @ ((V0 @ V4) @ V5)))))))))))))))))))
(TGroups.class.comm_monoid_mult_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.comm_monoid_mult_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))))))))
(TGroups.class.linordered_ab_group_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cOrderings.class.linorder @ V4) @ V5))))))))))))))))
(TGroups.class.ordered_ab_group_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V4) @ V5)))))))))))))))
(TGroups.class.ordered_ab_group_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cGroups.class.ab_group_add @ V0) @ V1) @ V2) @ V3)))))))))))))))
(TGroups.class.ordered_comm_monoid_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V2) @ V3))))))))))))
(TGroups.comm_monoid_diff.add_implies_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ V5)) @ ((cHOL.eq @ V3) @ ((V2 @ V5) @ V4)))))))))))))))))
(TGroups.group_add_class.diff_minus_eq_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))
(TGroups.linordered_ab_group_add_class_def,((c== @ (cGroups.linordered_ab_group_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE))))
(TGroups.monoid_add_class.add.left_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TGroups.ordered_ab_group_add.diff_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ ((V2 @ V6) @ V7)) @ V8)) @ ((V5 @ V6) @ ((V0 @ V8) @ V7)))))))))))))))))))))))
(TGroups.ordered_ab_group_add.le_minus_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V6) @ (V3 @ V7))) @ ((V4 @ V7) @ (V3 @ V6)))))))))))))))))))))
(TGroups.ordered_ab_group_add.less_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V6) @ ((V2 @ V7) @ V8))) @ ((V5 @ ((V0 @ V6) @ V8)) @ V7))))))))))))))))))))))
(TGroups.ordered_ab_group_add.minus_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (V3 @ V6)) @ V7)) @ ((V4 @ (V3 @ V7)) @ V6))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_0_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((cHOL.eq @ V2) @ (V0 @ V7))) @ ((cHOL.eq @ V7) @ V2))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_eq_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V7)) @ V2)) @ ((cHOL.eq @ V7) @ V2))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ (V0 @ V2)) @ V2)))))))))))))))))
(TGroups.ordered_ab_semigroup_add.add_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V6)) @ ((V1 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TGroups.ordered_comm_monoid_add_class_def,((c== @ (cGroups.ordered_comm_monoid_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.comm_monoid_add_class @ cTYPE)) @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE))))
(THilbert_Choice.ex_has_greatest_nat_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (V0 @ V1)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ (V0 @ V5)) @ (cHOL.Not @ ((cNat.ord_nat_inst.less_eq_nat @ (V2 @ V5)) @ (V2 @ V4)))))))))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ (V0 @ V4)) @ (cHOL.Not @ ((cNat.ord_nat_inst.less_nat @ (V2 @ V4)) @ ((cNat.plus_nat_inst.plus_nat @ (V2 @ V1)) @ V3)))))))))))))))))
(TInductive.complete_lattice_class.gfp_def,(call @ (^[V0]: ((cHOL.eq @ (cInductive.complete_lattice_class.gfp @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ (V0 @ V1)))))))))
(TInductive.complete_lattice_class.lfp_def,(call @ (^[V0]: ((cHOL.eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ (cSet.Collect @ (^[V1]: ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V1))))))))
(TInt.classrel_linordered_idom_ring_char_0,(cNum.ring_char_0_class @ cTYPE))
(TLattices.boolean_algebra_class.compl_inf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TLattices.boolean_algebra_class.compl_sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TLattices.bounded_lattice_bot_class.intro,((c==> @ (cLattices.lattice_class @ cTYPE)) @ ((c==> @ (cOrderings.order_bot_class @ cTYPE)) @ (cLattices.bounded_lattice_bot_class @ cTYPE))))
(TLattices.bounded_lattice_bot_class.super_2,((c==> @ (cLattices.bounded_lattice_bot_class @ cTYPE)) @ (cOrderings.order_bot_class @ cTYPE)))
(TLattices.bounded_lattice_bot_class.super_1,((c==> @ (cLattices.bounded_lattice_bot_class @ cTYPE)) @ (cLattices.lattice_class @ cTYPE)))
(TLattices.bounded_lattice_top_class.intro,((c==> @ (cLattices.lattice_class @ cTYPE)) @ ((c==> @ (cOrderings.order_top_class @ cTYPE)) @ (cLattices.bounded_lattice_top_class @ cTYPE))))
(TLattices.bounded_lattice_top_class.super_2,((c==> @ (cLattices.bounded_lattice_top_class @ cTYPE)) @ (cOrderings.order_top_class @ cTYPE)))
(TLattices.bounded_lattice_top_class.super_1,((c==> @ (cLattices.bounded_lattice_top_class @ cTYPE)) @ (cLattices.lattice_class @ cTYPE)))
(TLattices.class.bounded_lattice_bot.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cOrderings.class.order_bot @ V4) @ V1) @ V2)) @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TLattices.class.bounded_lattice_top.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((cOrderings.class.order_top @ V1) @ V2) @ V4)) @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TLattices.distrib_lattice.inf_sup_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V3 @ V4) @ V5)) @ V6)) @ ((V3 @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.inf_sup_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V3 @ V5) @ V6))) @ ((V3 @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.sup_inf_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ ((V0 @ V4) @ V5)) @ V6)) @ ((V0 @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.sup_inf_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V3 @ V4) @ V5)) @ ((V3 @ V4) @ V6)))))))))))))))))))
(TLattices.linorder_class.max.left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ V1) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TLattices.linorder_class.min.left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ V1) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TLattices.semilattice_inf_class.inf.assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TLattices.semilattice_inf_class.inf_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.sup.assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.sup_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.sup_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V2)) @ V1))))))))))
(TLazy_Sequence.iterate_upto_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.iterate_upto_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((cLazy_Sequence.iterate_upto_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((c==> @ (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (cLazy_Sequence.Lazy_Sequence @ (^[V7]: (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V5)) @ cOption.option.None) @ (cOption.option.Some @ ((cProduct_Type.Pair @ (V4 @ V5)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.list_of_lazy_sequence_flat,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ (cLazy_Sequence.flat @ V0))) @ (cList.concat @ ((cList.map @ cLazy_Sequence.list_of_lazy_sequence) @ (cLazy_Sequence.list_of_lazy_sequence @ V0)))))))
(TLazy_Sequence.small_lazy_list_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy_list_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)) @ ((V2 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ V3))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy_list_rel.intros,(call @ (^[V0]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ ((cLazy_Sequence.small_lazy_list_rel @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V0)))))
(TLifting.is_equality_Quotient_composition,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cTransfer.is_equality @ V0)) @ ((c==> @ (cLifting.left_total @ V1)) @ ((c==> @ (cLifting.left_unique @ V1)) @ (cTransfer.is_equality @ ((cRelation.relcompp @ V1) @ ((cRelation.relcompp @ V0) @ (cRelation.conversep @ V1))))))))))))
(TLifting_Set.right_total_Collect_transfer,(call @ (^[V0]: ((c==> @ (cTransfer.right_total @ V0)) @ ((((cTransfer.fun_rel @ ((cTransfer.fun_rel @ V0) @ cHOL.eq)) @ (cLifting_Set.set_rel @ V0)) @ (^[V1]: (cSet.Collect @ (^[V2]: ((cHOL.conj @ (V1 @ V2)) @ ((cRelation.Domainp @ V0) @ V2)))))) @ cSet.Collect)))))
(TList.comm_monoid_add.listsum_map_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cSet.member @ V2) @ (cList.set @ V3))) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V4) @ V3))) @ ((V0 @ (V4 @ V2)) @ (((cList.monoid_add.listsum @ V0) @ V1) @ ((cList.map @ V4) @ ((cList.remove1 @ V2) @ V3))))))))))))))))))
(TList.complete_lattice_class.INF_set_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ (cList.set @ V0)) @ V1)) @ (((cList.fold @ ((cFun.comp @ cLattices.inf_class.inf) @ V1)) @ V0) @ cOrderings.top_class.top)))))))
(TList.complete_lattice_class.Inf_set_fold,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ (cList.set @ V0))) @ (((cList.fold @ cLattices.inf_class.inf) @ V0) @ cOrderings.top_class.top)))))
(TList.complete_lattice_class.SUP_set_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cList.set @ V0)) @ V1)) @ (((cList.fold @ ((cFun.comp @ cLattices.sup_class.sup) @ V1)) @ V0) @ cOrderings.bot_class.bot)))))))
(TList.complete_lattice_class.Sup_set_fold,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ (cList.set @ V0))) @ (((cList.fold @ cLattices.sup_class.sup) @ V0) @ cOrderings.bot_class.bot)))))
(TList.linorder.sorted_distinct_set_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V2)) @ ((c==> @ (cList.distinct @ V2)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ V3)) @ ((c==> @ (cList.distinct @ V3)) @ ((c==> @ ((cHOL.eq @ (cList.set @ V2)) @ (cList.set @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))))))
(TList.linorder_class.insort_insert_insort,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cSet.member @ V0) @ (cList.set @ V1)))) @ ((cHOL.eq @ (((cList.linorder_class.insort_insert_key @ (^[V2]: V2)) @ V0) @ V1)) @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V0) @ V1))))))))
(TList.linorder_class.insort_key_left_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2)))) @ ((cHOL.eq @ (((cList.linorder_class.insort_key @ V0) @ V2) @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V3))) @ (((cList.linorder_class.insort_key @ V0) @ V1) @ (((cList.linorder_class.insort_key @ V0) @ V2) @ V3)))))))))))))
(TList.linorder_class.sorted_insort_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ (cList.linorder_class.sorted @ (((cList.linorder_class.insort_insert_key @ (^[V2]: V2)) @ V1) @ V0))))))))
(TList.listrel_rtrancl_eq_rtrancl_listrel1,(call @ (^[V0]: ((cHOL.eq @ (cList.listrel @ (cTransitive_Closure.rtrancl @ V0))) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V0))))))
(TList.monoid_add_class.listsum_map_filter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cList.set @ V0))) @ ((c==> @ (cHOL.Not @ (V1 @ V3))) @ ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero)))))) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V2) @ ((cList.filter @ V1) @ V0)))) @ (cList.monoid_add_class.listsum @ ((cList.map @ V2) @ V0)))))))))))
(TList.monoid_add_class.listsum_setsum_nth,(call @ (^[V0]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V1]: ((cList.nth @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ cNat.zero_nat_inst.zero_nat) @ (cNat.size_class.size @ V0)))))))
(TList.semiring_0_class.listsum_const_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: ((cGroups.times_class.times @ V0) @ (V1 @ V3)))) @ V2))) @ ((cGroups.times_class.times @ V0) @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: (V1 @ V3))) @ V2)))))))))))
(TList.semiring_0_class.listsum_mult_const,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: ((cGroups.times_class.times @ (V0 @ V3)) @ V1))) @ V2))) @ ((cGroups.times_class.times @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: (V0 @ V3))) @ V2))) @ V1)))))))))
(TNat.dvd.dual_order.strict_implies_not_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0)))) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))))))))
(TNat.linordered_semidom.of_nat_0_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V1) @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6))) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V6))))))))))))))))))
(TNat.linordered_semidom.of_nat_less_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6)) @ V1))))))))))))))))))
(TNitpick.equal_fun_box_inst.equal_fun_box,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TNitpick.pair_box.pair_box_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TNitpick.pair_box.pair_box_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((cNitpick.pair_box.pair_box_rec_set @ V0) @ ((cNitpick.pair_box.PairBox @ V1) @ V2)) @ ((V0 @ V1) @ V2)))))))))
(TNitpick.pair_box.pair_box_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNitpick.pair_box.pair_box_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))) @ (V1 @ V0))))))))
(TNitpick.pair_box.pair_box_rep_set.intros,(call @ (^[V0]: (call @ (^[V1]: (cNitpick.pair_box.pair_box_rep_set @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1)))))))))
(TNum.classrel_linordered_idom_ring_char_0,(cNum.ring_char_0_class @ cTYPE))
(TNum.classrel_semiring_1_semiring_numeral,(cNum.semiring_numeral_class @ cTYPE))
(TNum.linordered_idom.le_neg_numeral_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V4 @ V7) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_idom.le_neg_numeral_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V7)))))))))))))))))))))))))
(TNum.linordered_idom.le_neg_numeral_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V4 @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_idom.le_neg_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V3)))))))))))))))))))))))))
(TNum.linordered_idom.le_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V4 @ (((cNum.numeral.numeral @ V7) @ V6) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11)))))))))))))))))))))))))))))
(TNum.linordered_idom.le_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ (((cNum.numeral.numeral @ V7) @ V6) @ V11))))))))))))))))))))))))))))
(TNum.linordered_idom.le_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11))) @ ((cNum.ord_num_inst.less_eq_num @ V11) @ V10))))))))))))))))))))))))))))
(TNum.linordered_idom.neg_numeral_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11))) @ ((cNum.ord_num_inst.less_num @ V11) @ V10))))))))))))))))))))))))))))
(TNum.linordered_idom.neg_numeral_less_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V7)))))))))))))))))))))))))
(TNum.linordered_semidom.zero_less_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V5 @ V1) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))))))))))))))))))
(TNum.neg_numeral_class.diff_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNum.neg_numeral_class.diff_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.neg_numeral_class.diff_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.neg_numeral_class.diff_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TNum.neg_numeral_class.is_num_add_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))))
(TNum.neg_numeral_class.neg_numeral_axioms,((((cNum.class.neg_numeral @ cGroups.minus_class.minus) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus))
(TNum.ring_char_0_class.neg_numeral_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.ring_char_0_class.not_iszero_numeral,(call @ (^[V0]: (cHOL.Not @ (cNum.ring_1_class.iszero @ (cNum.numeral_class.numeral @ V0))))))
(TNum.ring_char_0_class.ring_char_0_axioms,((((((cNum.class.ring_char_0 @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TNum.semiring_char_0_class.numeral_eq_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNumeral_Simprocs.nat_mult_eq_cancel_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TNumeral_Simprocs.nat_mult_le_cancel_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_eq_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2))))))))))
(TOption.option.option_size_overloaded_def,((c== @ cNat.size_class.size) @ ((cOption.option.option_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TOrderings.class.dense_order_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((V0 @ V1) @ V3)) @ ((V0 @ V3) @ V2)))))))))) @ (cOrderings.class.dense_order_axioms @ V0)))))
(TOrderings.linorder.not_less_iff_gr_or_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((V1 @ V2) @ V3))) @ ((cHOL.disj @ ((V1 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.linorder_class.le_max_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TOrderings.linorder_class.linorder_axioms,((cOrderings.class.linorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.linorder_class.min_le_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TOrderings.ord_class.ord_class.Least_dict,((c== @ cOrderings.ord_class.Least) @ (cOrderings.ord.Least @ cOrderings.ord_class.less_eq)))
(TOrderings.order_class.dual_order.antisym,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.order_class.order.strict_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.ordering.strict_implies_not_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TOrderings.preorder_class.preorder_axioms,((cOrderings.class.preorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.wellorder_class.not_less_Least,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (cOrderings.ord_class.Least @ (^[V2]: (V1 @ V2))))) @ (cHOL.Not @ (V1 @ V0))))))))
(TPower.comm_semiring_1_class.dvd_power_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V3)) @ ((cRings.dvd_class.dvd @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V1) @ V3)))))))))))))
(TPower.comm_semiring_1_class.power_le_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ ((cPower.power_class.power @ V0) @ V1)) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V1)) @ ((cRings.dvd_class.dvd @ ((cPower.power_class.power @ V0) @ V3)) @ V2))))))))))))
(TPower.linordered_idom.sum_power2_ge_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ V3) @ ((V6 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V7) @ V9) @ V11) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))))))))))))))))))))))))))
(TPower.linordered_semidom.power_gt1_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((V5 @ V3) @ ((V2 @ V6) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7))))))))))))))))))))))
(TPower.linordered_semidom.zero_less_power,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V1) @ V6)) @ ((V5 @ V1) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)))))))))))))))))))))
(TPower.linordered_semidom_class.power_gt1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1)))))))))
(TPower.monoid_mult_class.power2_eq_square,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cGroups.times_class.times @ V0) @ V0)))))
(TPower.power_class.power_class.power_dict,((c== @ cPower.power_class.power) @ ((cPower.power.power @ cGroups.one_class.one) @ cGroups.times_class.times)))
(TPower.semiring_numeral_class.numeral_pow,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNum.numeral_class.numeral @ ((cNum.pow @ V0) @ V1))) @ ((cPower.power_class.power @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TPower.semiring_numeral_class.numeral_sqr,(call @ (^[V0]: ((cHOL.eq @ (cNum.numeral_class.numeral @ (cNum.sqr @ V0))) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V0))))))
(TQuickcheck_Exhaustive.arity_type_unknown,(cHOL.type_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_bool_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_bool_inst.check_all_bool @ V0)) @ (((cOption.option.option_case @ (V0 @ ((cProduct_Type.Pair @ cHOL.True) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)))))) @ (^[V1]: (cOption.option.Some @ V1))) @ (V0 @ ((cProduct_Type.Pair @ cHOL.False) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil))))))))))
(TQuickcheck_Exhaustive.check_all_char_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_char_inst.check_all_char @ V0)) @ (cQuickcheck_Exhaustive.check_all_nibble_inst.check_all_nibble @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.check_all_nibble_inst.check_all_nibble @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (V0 @ ((cProduct_Type.Pair @ ((cString.char.Char @ V1) @ V3)) @ (^[V5]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ (cCode_Evaluation.term_of_class.term_of @ cString.char.Char)) @ (V2 @ cProduct_Type.Unity))) @ (V4 @ cProduct_Type.Unity)))))))))))))))))
(TQuickcheck_Exhaustive.check_all_prod_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_class.check_all @ V0)) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (^[V1]: (cQuickcheck_Exhaustive.check_all_class.check_all @ (^[V2]: (V0 @ ((cQuickcheck_Exhaustive.term_syntax.valtermify_pair @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.check_all_unit_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_unit_inst.check_all_unit @ V0)) @ (V0 @ ((cProduct_Type.Pair @ cProduct_Type.Unity) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ cList.list.Nil)))))))))
(TQuickcheck_Exhaustive.exhaustive_fun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ V0) @ V1) @ V1)))))))
(TQuickcheck_Exhaustive.exhaustive_int_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_int_inst.exhaustive_int @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V0) @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_natural @ V1))) @ (cInt.uminus_int_inst.uminus_int @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_natural @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_nat_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_nat_inst.exhaustive_nat @ V0) @ V1)) @ ((cQuickcheck_Exhaustive.exhaustive_natural_inst.exhaustive_natural @ (^[V2]: (V0 @ (cCode_Numeral.nat_of_natural @ V2)))) @ V1)))))))
(TQuickcheck_Exhaustive.exhaustive_set_def,((c== @ cQuickcheck_Exhaustive.exhaustive_class.exhaustive) @ (^[V0]: (^[V1]: (cQuickcheck_Exhaustive.exhaustive_set_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TQuickcheck_Exhaustive.random_unknown_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Exhaustive.random_aux_unknown @ V0) @ V0)))))
(TQuickcheck_Exhaustive.termify_insert_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.term_syntax.termify_insert @ cTYPE) @ V0) @ V1)) @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ V0)) @ V1)))))))
(TQuickcheck_Exhaustive.three_valued.cases_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ V2))))))))
(TQuickcheck_Exhaustive.three_valued.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V0) @ V1) @ V2) @ (cQuickcheck_Exhaustive.three_valued.Value @ V3))) @ (V1 @ V3)))))))))))
(TQuickcheck_Exhaustive.three_valued.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.simps_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ V2))))))))
(TQuickcheck_Exhaustive.three_valued.simps_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ V0) @ V1) @ V2) @ (cQuickcheck_Exhaustive.three_valued.Value @ V3))) @ (V1 @ V3)))))))))))
(TQuickcheck_Exhaustive.three_valued.simps_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ V2))))))))
(TQuickcheck_Exhaustive.three_valued.simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V0) @ V1) @ V2) @ (cQuickcheck_Exhaustive.three_valued.Value @ V3))) @ (V1 @ V3)))))))))))
(TQuickcheck_Exhaustive.three_valued.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.simps_7,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.No_value) @ (cQuickcheck_Exhaustive.three_valued.Value @ V0))))))
(TQuickcheck_Exhaustive.three_valued.simps_6,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ cQuickcheck_Exhaustive.three_valued.No_value)))))
(TQuickcheck_Exhaustive.three_valued.simps_5,(cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.No_value) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)))
(TQuickcheck_Exhaustive.three_valued.simps_4,(cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ cQuickcheck_Exhaustive.three_valued.No_value)))
(TQuickcheck_Exhaustive.three_valued.simps_3,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)))))
(TQuickcheck_Exhaustive.three_valued.simps_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (cQuickcheck_Exhaustive.three_valued.Value @ V0))))))
(TQuickcheck_Exhaustive.three_valued.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ (cQuickcheck_Exhaustive.three_valued.Value @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.three_valued.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ (V0 @ V1))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cQuickcheck_Exhaustive.three_valued.Value @ V5))) @ (V0 @ (V2 @ V5)))))) @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ (V0 @ V3))))))))))))))))
(TQuickcheck_Exhaustive.valtermify_Inl_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.term_syntax.valtermify_Inl @ V0)) @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inl) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)))))
(TQuickcheck_Exhaustive.valtermify_Inr_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.term_syntax.valtermify_Inr @ V0)) @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inr) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)))))
(TQuickcheck_Narrowing.arity_narrowing_int,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_nat,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_num,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_set,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_sum,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_type_property,(cHOL.type_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero.pinduct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.around_zero_rel) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Narrowing.around_zero_rel) @ V2)) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cInt.zero_int_inst.zero_int))) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V2) @ cInt.one_int_inst.one_int))))) @ (V1 @ V2)))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.around_zero_rel_def,((c== @ cQuickcheck_Narrowing.around_zero_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int))) @ (cHOL.Not @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)))))))))))))
(TQuickcheck_Narrowing.cfun.Abs_cfun_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Abs_cfun @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set))) @ V1))))) @ V1))))))
(TQuickcheck_Narrowing.cfun.Rep_cfun_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Rep_cfun @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Narrowing.cfun.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V2) @ V0)) @ ((cQuickcheck_Narrowing.cfun.cfun_case @ V2) @ V1))))))))))
(TQuickcheck_Narrowing.ensure_testable_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.ensure_testable @ V0)) @ V0))))
(TQuickcheck_Narrowing.ffun.Abs_ffun_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Abs_ffun @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set))) @ V1))))) @ V1))))))
(TQuickcheck_Narrowing.ffun.Rep_ffun_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Rep_ffun @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Narrowing.ffun.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V2) @ V3) @ V0)) @ (((cQuickcheck_Narrowing.ffun.ffun_case @ V2) @ V3) @ V1))))))))))))
(TQuickcheck_Narrowing.narrowing_class_def,((c== @ (cQuickcheck_Narrowing.narrowing_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TQuickcheck_Narrowing.narrowing_cons.recs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_cons.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cNat.size_class.size @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TQuickcheck_Narrowing.narrowing_cons.size_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_size @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2))) @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Narrowing.narrowing_term.recs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ ((((V3 @ V4) @ V5) @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ V5))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ cList.list.Nil)) @ V2))))))))))
(TQuickcheck_Narrowing.narrowing_term.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ V0) @ V1) @ V2) @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5))) @ (((V1 @ V4) @ V5) @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ V5))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ V0) @ V1) @ V2) @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))) @ ((V0 @ V4) @ V5)))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.size_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_term.size_narrowing_term_inst.size_narrowing_term @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ cQuickcheck_Narrowing.narrowing_term.size_narrowing_term_inst.size_narrowing_term) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Narrowing.narrowing_term.size_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_term.size_narrowing_term_inst.size_narrowing_term @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TQuickcheck_Narrowing.narrowing_term.size_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_size @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_size) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Narrowing.narrowing_term.size_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_size @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1))) @ cNat.zero_nat_inst.zero_nat))))))
(TQuickcheck_Narrowing.narrowing_type.recs_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ ((((V4 @ V5) @ V6) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.recs_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ cList.list.Nil)) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_type.recs_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ ((((V2 @ V5) @ V6) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.recs_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ cList.list.Nil)) @ V1))))))))))))
(TQuickcheck_Narrowing.narrowing_type.recs_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V5))) @ ((V0 @ V5) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.size_2,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_type.size_narrowing_type_inst.size_narrowing_type @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ (cList.list.list_size @ cQuickcheck_Narrowing.narrowing_type.size_narrowing_type_inst.size_narrowing_type)) @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TQuickcheck_Narrowing.narrowing_type.size_1,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_size @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0))) @ ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ (cList.list.list_size @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_size)) @ V0)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))
(TQuickcheck_Narrowing.non_empty_graph_def,((c== @ cQuickcheck_Narrowing.non_empty_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4))) @ ((cHOL.eq @ V2) @ (cHOL.Not @ (cList.null @ V4))))))))))))))
(TQuickcheck_Narrowing.non_empty_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.non_empty_rel @ V0) @ V1)) @ V2))))))))
(TQuickcheck_Narrowing.non_empty_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.non_empty_rel @ V0) @ V1)) @ cHOL.False))))))
(TQuickcheck_Narrowing.random_aux_cfun_def,((c== @ cQuickcheck_Narrowing.random_aux_cfun) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.cfun.Constant) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.cfun.Constant) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Narrowing.random_aux_ffun_def,((c== @ cQuickcheck_Narrowing.random_aux_ffun) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.ffun.Constant) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V6]: ((cProduct_Type.scomp @ (V2 @ V3)) @ (^[V7]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.ffun.Update) @ (^[V8]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)) @ V7)))))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.ffun.Constant) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil)))) @ V4)))))) @ V0))))
(TQuickcheck_Narrowing.random_property_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.random_property_inst.random_property @ V0)) @ ((cQuickcheck_Narrowing.random_aux_property @ V0) @ V0)))))
(TRecord.type_definition_tuple_isomorphism,(((cTypedef.type_definition @ cRecord.Rep_tuple_isomorphism) @ cRecord.Abs_tuple_isomorphism) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set)))
(TRings.class.comm_semiring_0_cancel.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cRings.class.comm_semiring @ V0) @ V2)) @ (((cRings.class.comm_semiring_0_cancel @ V0) @ V1) @ V2))))))))))
(TRings.class.comm_semiring_1_cancel.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cGroups.class.comm_monoid_mult @ V2) @ V3)) @ ((c==> @ ((cRings.class.comm_semiring @ V0) @ V2)) @ ((c==> @ ((cRings.class.zero_neq_one @ V3) @ V1)) @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3))))))))))))))
(TRings.class.linordered_ring_strict.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cGroups.class.abs_if @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V4) @ V2) @ V5) @ V1) @ V6) @ V3)) @ ((c==> @ (((((cRings.class.linordered_semiring_strict @ V4) @ V2) @ V6) @ V3) @ V7)) @ ((c==> @ (((((cRings.class.ring @ V4) @ V2) @ V5) @ V1) @ V7)) @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V5) @ V1) @ V2) @ V6) @ V3) @ V4) @ V7))))))))))))))))))))))
(TRings.class.linordered_semiring_1.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semiring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cRings.class.semiring_1 @ V5) @ V4) @ V0) @ V3)))))))))))))))
(TRings.class.linordered_semiring_1.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semiring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))
(TRings.class.ordered_comm_semiring.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cRings.class.ordered_comm_semiring_axioms @ V1) @ V3) @ V4)))))))))))))
(TRings.class.ordered_comm_semiring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cRings.class.comm_semiring_0 @ V0) @ V3) @ V4)))))))))))))
(TRings.class.ordered_comm_semiring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)))))))))))))
(TRings.class.ring_no_zero_divisors.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ring_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cRings.class.ring @ V2) @ V1) @ V3) @ V4) @ V0)))))))))))))
(TRings.class.ring_no_zero_divisors.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ring_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cRings.class.no_zero_divisors @ V0) @ V1)))))))))))))
(TRings.comm_semiring_0_cancel_class.intro,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_class @ cTYPE)) @ (cRings.comm_semiring_0_cancel_class @ cTYPE))))
(TRings.comm_semiring_0_cancel_class.super_2,((c==> @ (cRings.comm_semiring_0_cancel_class @ cTYPE)) @ (cRings.comm_semiring_class @ cTYPE)))
(TRings.comm_semiring_0_cancel_class.super_1,((c==> @ (cRings.comm_semiring_0_cancel_class @ cTYPE)) @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)))
(TRings.comm_semiring_1_cancel_class.intro,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.comm_monoid_mult_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_class @ cTYPE)) @ ((c==> @ (cRings.zero_neq_one_class @ cTYPE)) @ (cRings.comm_semiring_1_cancel_class @ cTYPE))))))
(TRings.comm_semiring_1_cancel_class.super_4,((c==> @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ (cRings.zero_neq_one_class @ cTYPE)))
(TRings.comm_semiring_1_cancel_class.super_3,((c==> @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ (cRings.comm_semiring_class @ cTYPE)))
(TRings.comm_semiring_1_cancel_class.super_2,((c==> @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ (cGroups.comm_monoid_mult_class @ cTYPE)))
(TRings.comm_semiring_1_cancel_class.super_1,((c==> @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)))
(TRings.linordered_idom_class.abs_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.abs_class.abs @ V0)) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ V1))))))))
(TRings.linordered_idom_class.abs_mult_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cGroups.abs_class.abs @ V1)) @ V0)) @ (cGroups.abs_class.abs @ ((cGroups.times_class.times @ V1) @ V0)))))))))
(TRings.linordered_idom_class.mult_sgn_abs,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cGroups.sgn_class.sgn @ V0)) @ (cGroups.abs_class.abs @ V0))) @ V0))))
(TRings.linordered_ring_strict_class.intro,((c==> @ (cGroups.abs_if_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ ((c==> @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ ((c==> @ (cRings.ring_class @ cTYPE)) @ (cRings.linordered_ring_strict_class @ cTYPE))))))
(TRings.linordered_ring_strict_class.super_4,((c==> @ (cRings.linordered_ring_strict_class @ cTYPE)) @ (cRings.ring_class @ cTYPE)))
(TRings.linordered_ring_strict_class.super_3,((c==> @ (cRings.linordered_ring_strict_class @ cTYPE)) @ (cRings.linordered_semiring_strict_class @ cTYPE)))
(TRings.linordered_ring_strict_class.super_2,((c==> @ (cRings.linordered_ring_strict_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_class @ cTYPE)))
(TRings.linordered_ring_strict_class.super_1,((c==> @ (cRings.linordered_ring_strict_class @ cTYPE)) @ (cGroups.abs_if_class @ cTYPE)))
(TRings.linordered_semidom.not_one_le_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V4 @ V3) @ V1))))))))))))))))
(TRings.ordered_comm_semiring_class.axioms,(((cRings.class.ordered_comm_semiring_axioms @ cOrderings.ord_class.less_eq) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.ordered_ring_abs_class.abs_eq_mult,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.conj @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ (cGroups.abs_class.abs @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cGroups.times_class.times @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1)))))))))
(TRings.semiring_0_class.semiring_0_axioms,(((cRings.class.semiring_0 @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.semiring_1_class.semiring_1_axioms,((((cRings.class.semiring_1 @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TSMT.term_of_pattern_inst.term_of_pattern,((c== @ cSMT.term_of_pattern_inst.term_of_pattern) @ cSMT.term_of_pattern_inst.term_of_pattern))
(TSMT.typerep_pattern_inst.typerep_pattern,((c== @ cSMT.typerep_pattern_inst.typerep_pattern) @ cSMT.typerep_pattern_inst.typerep_pattern))
(TSet_Interval.atLeastAtMostPlus1_int_conv,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ V0) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ V1))) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ V1))) @ ((cSet.insert @ ((cInt.plus_int_inst.plus_int @ cInt.one_int_inst.one_int) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)))))))))
(TSet_Interval.complete_lattice.Inf_atMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ ((cSet_Interval.ord.atMost @ V3) @ V8))) @ V6)))))))))))))))))))))
(TSet_Interval.complete_lattice.Sup_atMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ ((cSet_Interval.ord.atMost @ V3) @ V8))) @ V8)))))))))))))))))))))
(TSet_Interval.dvd.atLeastAtMost_singleton,(call @ (^[V0]: ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V0)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TSet_Interval.dvd.atLeastatMost_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))))))))
(TSet_Interval.dvd.greaterThanAtMost_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((((cSet_Interval.ord.greaterThanAtMost @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TSet_Interval.dvd.greaterThanLessThan_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ (((cSet_Interval.ord.greaterThanLessThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.greaterThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0)) @ ((cSet_Interval.ord.lessThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1))))))))
(TSet_Interval.dvd.greaterThanLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ (((cSet_Interval.ord.greaterThanLessThan @ (^[V3]: (^[V4]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V3) @ V4)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V4) @ V3)))))) @ V1) @ V2))) @ ((cHOL.conj @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V2) @ V0))))))))))))
(TSet_Interval.no_bot_class.not_Icc_eq_Iic,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.atMost @ V2))))))))))
(TSet_Interval.no_bot_class.not_Iic_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))))))))))
(TSet_Interval.no_bot_class.not_Iic_le_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))))))))))
(TSet_Interval.no_bot_class.not_Iic_le_Ici,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.atMost @ V0)) @ (cSet_Interval.ord_class.atLeast @ V1))))))))
(TSet_Interval.no_top_class.not_Icc_eq_Ici,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V2))))))))))
(TSet_Interval.no_top_class.not_Ici_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))))))))))
(TSet_Interval.no_top_class.not_Ici_eq_Iic,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.no_top_class.not_Ici_le_Icc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))))))))))
(TSet_Interval.no_top_class.not_Ici_le_Iic,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.no_top_class.not_Iic_eq_Ici,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ (cSet_Interval.ord_class.atLeast @ V1))))))))
(TSet_Interval.ord.greaterThanLessThan_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cSet_Interval.ord.greaterThanLessThan @ V0) @ V1) @ V2)) @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.greaterThan @ V0) @ V1)) @ ((cSet_Interval.ord.lessThan @ V0) @ V2))))))))))
(TSet_Interval.ord.greaterThanLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cSet.member @ V0) @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V2) @ V3))) @ ((cHOL.conj @ ((V1 @ V2) @ V0)) @ ((V1 @ V0) @ V3))))))))))))
(TSet_Interval.ord_class.atLeastAtMost_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atLeast @ V0)) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.ord_class.atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet_Interval.order.atLeastLessThan_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V3) @ V2)) @ cOrderings.bot_class.bot))))))))))))
(TSet_Interval.setsum_shift_bounds_Suc_ivl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ (cNat.Suc @ V1)) @ (cNat.Suc @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V0 @ (cNat.Suc @ V3)))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))))))))))
(TSet_Interval.setsum_shift_bounds_nat_ivl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (V0 @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V2)))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V3))))))))))))
(TString.nibble.nibble_size_overloaded_def,((c== @ cString.nibble.size_nibble_inst.size_nibble) @ ((((((((((((((((cString.nibble.nibble_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TTransitive_Closure.relpow_finite_bounded,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cNat.compow @ V1) @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V2]: ((cNat.ord_nat_inst.less_eq_nat @ V2) @ (cFinite_Set.card @ V0))))) @ (^[V2]: ((cNat.compow @ V2) @ V0))))))))))
(TTransitive_Closure.rtrancl_Un_separatorE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ ((cLattices.sup_class.sup @ V2) @ V3)))) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V4)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V3)) @ ((cHOL.eq @ V4) @ V5)))))))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.rtrancl_imp_UN_relpow,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cTransitive_Closure.rtrancl @ V1))) @ ((cSet.member @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: ((cNat.compow @ V2) @ V1))))))))))
(TTransitive_Closure.rtrancl_reflcl_absorb,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cTransitive_Closure.rtrancl @ V0)) @ cRelation.Id)) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.rtrancl_trancl_absorb,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.trancl @ (cTransitive_Closure.rtrancl @ V0))) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.rtrancl_trancl_reflcl,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ V0)) @ ((cLattices.sup_class.sup @ (cTransitive_Closure.trancl @ V0)) @ cRelation.Id)))))
(TTransitive_Closure.rtrancl_trancl_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.rtranclp.rtrancl_refl,(call @ (^[V0]: (call @ (^[V1]: (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V1))))))
(TTransitive_Closure.rtranclp_sup_rtranclp,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cTransitive_Closure.rtranclp @ ((cLattices.sup_class.sup @ (cTransitive_Closure.rtranclp @ V0)) @ (cTransitive_Closure.rtranclp @ V1)))) @ (cTransitive_Closure.rtranclp @ ((cLattices.sup_class.sup @ V0) @ V1))))))))
(TTransitive_Closure.trancl_rtrancl_absorb,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtrancl @ (cTransitive_Closure.trancl @ V0))) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.trancl_rtrancl_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.tranclp.r_into_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)))))))))
(TTransitive_Closure.tranclp_into_rtranclp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)))))))))
(TTransitive_Closure.tranclp_into_tranclp2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTyperep.equal_typerep_inst.equal_typerep,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TBig_Operators.comm_monoid_add.setsum_Plus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V4) @ ((cSum_Type.Plus @ V2) @ V3))) @ ((V0 @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ ((cFun.comp @ V4) @ cSum_Type.Inl)) @ V2)) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ ((cFun.comp @ V4) @ cSum_Type.Inr)) @ V3)))))))))))))))))
(TBig_Operators.comm_monoid_set.strong_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V3)) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V6]: (V4 @ V6))) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V6]: (V5 @ V6))) @ V3))))))))))))))))))
(TBig_Operators.comm_monoid_set.subset_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V3)) @ ((V0 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cGroups.minus_class.minus @ V3) @ V2))) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)))))))))))))))))
(TBig_Operators.comm_monoid_set.union_inter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((cHOL.eq @ ((V0 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cLattices.sup_class.sup @ V2) @ V3))) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cLattices.inf_class.inf @ V2) @ V3)))) @ ((V0 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V3)))))))))))))))))
(TBig_Operators.linorder_class.Max.antimono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Max @ V0)) @ (cBig_Operators.linorder_class.Max @ V1))))))))))
(TBig_Operators.linorder_class.Max.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Max @ V0)) @ V1)) @ ((c==> @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V3) @ V1))))) @ V2)) @ V2)))))))))))
(TBig_Operators.linorder_class.Max.boundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Max @ V0)) @ V1)))))))))
(TBig_Operators.linorder_class.Max.eq_fold',(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ V0)) @ (cOption.the @ (((cFinite_Set.fold @ (^[V1]: (^[V2]: (cOption.option.Some @ (((cOption.option.option_case @ V1) @ (^[V3]: ((cOrderings.ord_class.max @ V1) @ V3))) @ V2))))) @ cOption.option.None) @ V0))))))
(TBig_Operators.linorder_class.Max_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (cBig_Operators.linorder_class.Max @ V0)) @ V1)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less @ V2) @ V1)))))))))))
(TBig_Operators.linorder_class.Min.antimono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Min @ V1)) @ (cBig_Operators.linorder_class.Min @ V0))))))))))
(TBig_Operators.linorder_class.Min.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ ((c==> @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3))))) @ V2)) @ V2)))))))))))
(TBig_Operators.linorder_class.Min.boundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.linorder_class.Min @ V0))))))))))
(TBig_Operators.linorder_class.Min.eq_fold',(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ V0)) @ (cOption.the @ (((cFinite_Set.fold @ (^[V1]: (^[V2]: (cOption.option.Some @ (((cOption.option.option_case @ V1) @ (^[V3]: ((cOrderings.ord_class.min @ V1) @ V3))) @ V2))))) @ cOption.option.None) @ V0))))))
(TBig_Operators.linorder_class.Min_antimono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Min @ V1)) @ (cBig_Operators.linorder_class.Min @ V0))))))))))
(TBig_Operators.linorder_class.Min_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (cBig_Operators.linorder_class.Min @ V0)) @ V1)) @ ((cSet.Bex @ V0) @ (^[V2]: ((cOrderings.ord_class.less @ V2) @ V1)))))))))))
(TBig_Operators.semilattice_inf.Inf_fin_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf.Inf_fin @ V0)) @ (cBig_Operators.semilattice_set.F @ V0))))))))))
(TBig_Operators.semilattice_neutr_set.empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((cHOL.eq @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ cOrderings.bot_class.bot)) @ V1)))))))
(TBig_Operators.semilattice_neutr_set.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cLattices.semilattice_neutr @ V0) @ V1)) @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)))))))
(TBig_Operators.semilattice_neutr_set.union,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((cHOL.eq @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ ((cLattices.sup_class.sup @ V2) @ V3))) @ ((V0 @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2)) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V3)))))))))))))))
(TBig_Operators.semilattice_order_set.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2))))))))))
(TBig_Operators.semilattice_set.hom_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V1 @ ((V0 @ V3) @ V4))) @ ((V0 @ (V1 @ V3)) @ (V1 @ V4)))))))) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V1 @ ((cBig_Operators.semilattice_set.F @ V0) @ V2))) @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cSet.image @ V1) @ V2))))))))))))))
(TBig_Operators.semilattice_sup.Sup_fin_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup.Sup_fin @ V0)) @ (cBig_Operators.semilattice_set.F @ V0))))))))))
(TBig_Operators.setprod_dvd_setprod_subset2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V4]: ((cRings.dvd_class.dvd @ (V2 @ V4)) @ (V3 @ V4))))) @ ((cRings.dvd_class.dvd @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V0))))))))))))))
(TBig_Operators.setprod_mono_one_cong_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.one_class.one)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)))))))))))))))
(TBig_Operators.setsum_mono_zero_cong_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.zero_class.zero)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1)))))))))))))))
(TCode_Evaluation.term.term_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cCode_Evaluation.term.term_rep_set @ V0)) @ ((c==> @ (V1 @ cHOL.undefined)) @ (V1 @ V0))))))))
(TCode_Evaluation.typerep_lazy_sequence_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TCode_Numeral.abs_integer_inst.abs_integer,((c== @ cCode_Numeral.abs_integer_inst.abs_integer) @ cCode_Numeral.abs_integer_inst.abs_integer))
(TCode_Numeral.div_integer_inst.div_integer,((c== @ cCode_Numeral.div_integer_inst.div_integer) @ cCode_Numeral.div_integer_inst.div_integer))
(TCode_Numeral.div_integer_inst.mod_integer,((c== @ cCode_Numeral.div_integer_inst.mod_integer) @ cCode_Numeral.div_integer_inst.mod_integer))
(TCode_Numeral.div_natural_inst.div_natural,((c== @ cCode_Numeral.div_natural_inst.div_natural) @ cCode_Numeral.div_natural_inst.div_natural))
(TCode_Numeral.div_natural_inst.mod_natural,((c== @ cCode_Numeral.div_natural_inst.mod_natural) @ cCode_Numeral.div_natural_inst.mod_natural))
(TCode_Numeral.integer.int_of_integer_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cCode_Numeral.int_of_integer @ V2))) @ V1)))) @ V1)))))))
(TCode_Numeral.integer.integer_of_int_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cCode_Numeral.integer_of_int @ V2))) @ ((c==> @ ((cSet.member @ V2) @ cOrderings.top_class.top)) @ V1))))) @ V1))))))
(TCode_Numeral.natural.nat_of_natural_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cCode_Numeral.nat_of_natural @ V2))) @ V1)))) @ V1)))))))
(TCode_Numeral.natural.natural_of_nat_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cCode_Numeral.natural_of_nat @ V2))) @ ((c==> @ ((cSet.member @ V2) @ cOrderings.top_class.top)) @ V1))))) @ V1))))))
(TCode_Numeral.one_integer_inst.one_integer,((c== @ cCode_Numeral.one_integer_inst.one_integer) @ cCode_Numeral.one_integer_inst.one_integer))
(TCode_Numeral.one_natural_inst.one_natural,((c== @ cCode_Numeral.one_natural_inst.one_natural) @ cCode_Numeral.one_natural_inst.one_natural))
(TCode_Numeral.sgn_integer_inst.sgn_integer,((c== @ cCode_Numeral.sgn_integer_inst.sgn_integer) @ cCode_Numeral.sgn_integer_inst.sgn_integer))
(TComplete_Lattices.not_False_in_image_Ball,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cSet.member @ cHOL.False) @ ((cSet.image @ V0) @ V1)))) @ ((cSet.Ball @ V1) @ V0)))))))
(TComplete_Partial_Order.ccpo.iterates.step,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((cSet.member @ (V4 @ V3)) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4)))))))))))))))
(TComplete_Partial_Order.ccpo.iterates_fixp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ (((cComplete_Partial_Order.monotone @ V1) @ V1) @ V3)) @ ((cSet.member @ (((cComplete_Partial_Order.ccpo.fixp @ V0) @ V1) @ V3)) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V3)))))))))))))
(TComplete_Partial_Order.ccpo.iterates_le_f,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((c==> @ (((cComplete_Partial_Order.monotone @ V1) @ V1) @ V4)) @ ((V1 @ V3) @ (V4 @ V3))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp.Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V5]: ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V4) @ V5)))) @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V4) @ (V0 @ V3))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c== @ ((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1)) @ (^[V3]: (cInductive.complete_lattice_class.lfp @ (^[V4]: (^[V5]: ((cHOL.disj @ (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V5) @ (V3 @ V6))) @ (V4 @ V6))))) @ (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V5) @ (V0 @ V6))) @ ((cHOL.conj @ ((cComplete_Partial_Order.chain @ V1) @ V6)) @ ((cSet.Ball @ V6) @ (^[V7]: (V4 @ V7)))))))))))))))))))))
(TDivides.class.semiring_numeral_div.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ (((((((((cDivides.class.semiring_numeral_div_axioms @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)))))))))))))))))))))
(TDivides.class.semiring_numeral_div.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((((((cRings.class.linordered_semidom @ V3) @ V4) @ V0) @ V5) @ V7) @ V8)))))))))))))))))))))
(TDivides.class.semiring_numeral_div.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))))))))
(TDivides.semiring_div.div_mult_self1_is_id,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V0 @ V6) @ V7)) @ V6)) @ V7))))))))))))))))))))
(TDivides.semiring_div.div_mult_self2_is_id,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cDivides.class.semiring_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V4))) @ ((cHOL.eq @ ((V1 @ ((V0 @ V7) @ V6)) @ V6)) @ V7))))))))))))))))))))
(TDivides.semiring_div_class.div_mult_mult1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cDivides.div_class.div @ V1) @ V2))))))))))
(TDivides.semiring_div_class.div_mult_mult2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V1) @ V0)) @ ((cGroups.times_class.times @ V2) @ V0))) @ ((cDivides.div_class.div @ V1) @ V2))))))))))
(TDivides.semiring_div_class.div_mult_self1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.times_class.times @ V2) @ V0))) @ V0)) @ ((cGroups.plus_class.plus @ V2) @ ((cDivides.div_class.div @ V1) @ V0)))))))))))
(TDivides.semiring_div_class.div_mult_self2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.times_class.times @ V0) @ V2))) @ V0)) @ ((cGroups.plus_class.plus @ V2) @ ((cDivides.div_class.div @ V1) @ V0)))))))))))
(TDivides.semiring_div_class.mod_div_decomp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V3) @ ((cDivides.div_class.div @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ V4) @ ((cDivides.div_class.mod @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V1)) @ V4))) @ V2)))))))) @ V2))))))))
(TDivides.semiring_div_class.mod_mod_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_class.mod @ ((cDivides.div_class.mod @ V2) @ V1)) @ V0)) @ ((cDivides.div_class.mod @ V2) @ V0))))))))))
(TDivides.semiring_div_class.mod_mult_mult1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))))))))))
(TDivides.semiring_div_class.mod_mult_mult2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cGroups.times_class.times @ ((cDivides.div_class.mod @ V0) @ V2)) @ V1)))))))))
(TDivides.semiring_div_class.mod_mult_self1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ V2)) @ ((cDivides.div_class.mod @ V0) @ V2)))))))))
(TDivides.semiring_div_class.mod_mult_self2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ V1)) @ ((cDivides.div_class.mod @ V0) @ V1)))))))))
(TDivides.semiring_div_class.mult_mod_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TDivides.semiring_numeral_div.div_mult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V4) @ V9)) @ ((cHOL.eq @ ((V1 @ V10) @ ((V0 @ V11) @ V9))) @ ((V1 @ ((V1 @ V10) @ V11)) @ V9)))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.div_positive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V8 @ V4) @ V9)) @ ((c==> @ ((V7 @ V9) @ V10)) @ ((V8 @ V4) @ ((V1 @ V10) @ V9))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.mod_mult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V4) @ V9)) @ ((cHOL.eq @ ((V2 @ V10) @ ((V0 @ V11) @ V9))) @ ((V3 @ ((V0 @ V11) @ ((V2 @ ((V1 @ V10) @ V11)) @ V9))) @ ((V2 @ V10) @ V11))))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.pos_mod_sign,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V8 @ V4) @ V9)) @ ((V7 @ V4) @ ((V2 @ V10) @ V9)))))))))))))))))))))))))))
(TDivides.semiring_numeral_div_class.axioms,(((((((((cDivides.class.semiring_numeral_div_axioms @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cGroups.minus_class.minus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TDivides.semiring_numeral_div_class.parity,(call @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.one_class.one)))))
(TEnum.enum_finite_1_inst.enum_all_finite_1,((c== @ cEnum.enum_finite_1_inst.enum_all_finite_1) @ cEnum.enum_finite_1_inst.enum_all_finite_1))
(TEnum.enum_finite_2_inst.enum_all_finite_2,((c== @ cEnum.enum_finite_2_inst.enum_all_finite_2) @ cEnum.enum_finite_2_inst.enum_all_finite_2))
(TEnum.enum_finite_3_inst.enum_all_finite_3,((c== @ cEnum.enum_finite_3_inst.enum_all_finite_3) @ cEnum.enum_finite_3_inst.enum_all_finite_3))
(TEnum.enum_finite_4_inst.enum_all_finite_4,((c== @ cEnum.enum_finite_4_inst.enum_all_finite_4) @ cEnum.enum_finite_4_inst.enum_all_finite_4))
(TEnum.enum_finite_5_inst.enum_all_finite_5,((c== @ cEnum.enum_finite_5_inst.enum_all_finite_5) @ cEnum.enum_finite_5_inst.enum_all_finite_5))
(TExtraction.sumbool.sumbool_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TExtraction.sumbool.sumbool_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((((cExtraction.sumbool.sumbool_rec_set @ V0) @ V1) @ cExtraction.sumbool.Right) @ V1))))))
(TExtraction.sumbool.sumbool_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cExtraction.sumbool.sumbool_rec_set @ V0) @ V1) @ cExtraction.sumbool.Left) @ V0))))))
(TExtraction.sumbool.sumbool_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cExtraction.sumbool.sumbool_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (V1 @ (cDatatype.In1 @ cHOL.undefined))) @ (V1 @ V0)))))))))
(TExtraction.sumbool.sumbool_rep_set.intros_2,(cExtraction.sumbool.sumbool_rep_set @ (cDatatype.In1 @ cHOL.undefined)))
(TExtraction.sumbool.sumbool_rep_set.intros_1,(cExtraction.sumbool.sumbool_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TFields.division_ring.nonzero_divide_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V9) @ V8)) @ V10)) @ ((cHOL.eq @ V9) @ ((V3 @ V10) @ V8))))))))))))))))))))))))))))
(TFields.division_ring.nonzero_eq_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((cHOL.eq @ V9) @ ((V1 @ V10) @ V8))) @ ((cHOL.eq @ ((V3 @ V9) @ V8)) @ V10)))))))))))))))))))))))))))
(TFields.division_ring_class.divide_inverse,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ (cFields.inverse_class.inverse @ V1))))))))
(TFields.division_ring_class.inverse_unique,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ V1)))))))
(TFields.field_inverse_zero.divide_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ V5)) @ ((cHOL.disj @ ((cHOL.eq @ V8) @ V5)) @ ((cHOL.eq @ V9) @ V5)))))))))))))))))))))))))
(TFields.field_inverse_zero.divide_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ V3)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ V8) @ V9)))))))))))))))))))))))))
(TFields.linordered_field.divide_nonneg_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V5) @ V12)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V9 @ ((V1 @ V12) @ V13)) @ V5)))))))))))))))))))))))))))))))))
(TFields.linordered_field.divide_nonneg_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V5) @ V12)) @ ((c==> @ ((V10 @ V5) @ V13)) @ ((V9 @ V5) @ ((V1 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.divide_nonpos_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V5)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V9 @ V5) @ ((V1 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field.divide_nonpos_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V5)) @ ((c==> @ ((V10 @ V5) @ V13)) @ ((V9 @ ((V1 @ V12) @ V13)) @ V5)))))))))))))))))))))))))))))))))
(TFields.linordered_field.inverse_le_iff_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V10 @ V5) @ V13)) @ ((cHOL.eq @ ((V9 @ (V0 @ V12)) @ (V0 @ V13))) @ ((V9 @ V13) @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field.inverse_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ (V0 @ V12)) @ (V0 @ V13))) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((V9 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field.le_imp_inverse_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((V9 @ (V0 @ V13)) @ (V0 @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.gt_half_sum,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ cGroups.one_class.one))) @ V1)))))))
(TFinite_Set.comp_fun_commute.fold_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V1) @ V2)) @ V3))))))))))))
(TFinite_Set.comp_fun_commute.fun_left_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ V2) @ ((V0 @ V1) @ V3)))))))))))))
(TFinite_Set.comp_fun_idem.fold_insert_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V2) @ ((cSet.insert @ V3) @ V1))) @ ((V0 @ V3) @ (((cFinite_Set.fold @ V0) @ V2) @ V1))))))))))))))
(TFun.linorder_class.strict_mono_imp_inj_on,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.strict_mono @ V0)) @ ((cFun.inj_on @ V0) @ V1)))))))
(TFun.ordered_ab_group_add_class.inj_uminus,(call @ (^[V0]: ((cFun.inj_on @ cGroups.uminus_class.uminus) @ V0))))
(TGroups.ab_semigroup_add_class.add.commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TGroups.ab_semigroup_add_class.add_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TGroups.cancel_ab_semigroup_add.add_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TGroups.cancel_comm_monoid_add_class.intro,((c==> @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ (cGroups.cancel_comm_monoid_add_class @ cTYPE))))
(TGroups.cancel_comm_monoid_add_class.super_2,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TGroups.cancel_comm_monoid_add_class.super_1,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)))
(TGroups.class.ab_semigroup_mult_axioms_def,(call @ (^[V0]: ((c== @ (cGroups.class.ab_semigroup_mult_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TGroups.class.cancel_comm_monoid_add.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1))))))))
(TGroups.class.comm_monoid_add_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))) @ ((cGroups.class.comm_monoid_add_axioms @ V0) @ V1)))))))
(TGroups.class.ordered_ab_group_add_abs_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c== @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.conj @ ((((((cGroups.class.ordered_ab_group_add @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (((((cGroups.class.ordered_ab_group_add_abs_axioms @ V0) @ V1) @ V2) @ V4) @ V5))))))))))))))))))
(TGroups.class.ordered_ab_semigroup_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cGroups.class.ab_semigroup_add @ V0)) @ ((cHOL.conj @ ((cOrderings.class.order @ V1) @ V2)) @ ((cGroups.class.ordered_ab_semigroup_add_axioms @ V0) @ V1)))))))))))
(TGroups.comm_monoid_diff_class.diff_cancel,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V0)) @ cGroups.zero_class.zero))))
(TGroups.group_add_class.equation_minus_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cHOL.eq @ V1) @ (cGroups.uminus_class.uminus @ V0))))))))
(TGroups.group_add_class.minus_equation_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V1)) @ V0)))))))
(TGroups.monoid_add_class.add.monoid_axioms,((cGroups.monoid @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.monoid_add_class.add.right_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TGroups.monoid_add_class.monoid_add_axioms,((cGroups.class.monoid_add @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.ordered_ab_group_add.le_imp_neg_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V4 @ V6) @ V7)) @ ((V4 @ (V3 @ V7)) @ (V3 @ V6)))))))))))))))))))))
(TGroups.ordered_ab_group_add.neg_le_iff_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (V3 @ V6)) @ (V3 @ V7))) @ ((V4 @ V7) @ V6))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_le_D1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V5 @ (V0 @ V7)) @ V8)) @ ((V5 @ V7) @ V8))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_le_D2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V5 @ (V0 @ V7)) @ V8)) @ ((V5 @ (V4 @ V7)) @ V8))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class_def,((c== @ (cGroups.ordered_ab_group_add_abs_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.abs_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ (((((cGroups.class.ordered_ab_group_add_abs_axioms @ cGroups.abs_class.abs) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus) @ cOrderings.ord_class.less_eq)))))
(TGroups.ordered_ab_semigroup_add_class_def,((c== @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.order_class @ cTYPE)) @ ((cGroups.class.ordered_ab_semigroup_add_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq)))))
(THilbert_Choice.wf_no_infinite_down_chainE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cSet.member @ ((cProduct_Type.Pair @ (V1 @ (cNat.Suc @ V3))) @ (V1 @ V3))) @ V0))) @ V2)))) @ V2)))))))))
(TInductive.complete_lattice.lfp_lowerbound,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V3 @ (V8 @ V9)) @ V9)) @ ((V3 @ (((cInductive.complete_lattice.lfp @ V0) @ V3) @ V8)) @ V9))))))))))))))))))))))))
(TInt.linordered_idom_class.of_int_0_le_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cInt.ring_1_class.of_int @ V0))) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)))))
(TInt.linordered_idom_class.of_int_le_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cInt.ring_1_class.of_int @ V0)) @ cGroups.zero_class.zero)) @ ((cInt.ord_int_inst.less_eq_int @ V0) @ cInt.zero_int_inst.zero_int)))))
(TInt.linordered_idom_class.of_int_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cInt.ring_1_class.of_int @ V0)) @ (cInt.ring_1_class.of_int @ V1))) @ ((cInt.ord_int_inst.less_int @ V0) @ V1)))))))
(TInt.ring_1_class.ring_1_class.of_int_dict,((c== @ cInt.ring_1_class.of_int) @ ((((cInt.ring_1.of_int @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus)))
(TLattices.boolean_algebra.compl_less_swap1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ V8) @ (V1 @ V9))) @ ((V4 @ V9) @ (V1 @ V8)))))))))))))))))))))))))
(TLattices.boolean_algebra.compl_less_swap2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ (V1 @ V8)) @ V9)) @ ((V4 @ (V1 @ V9)) @ V8))))))))))))))))))))))))
(TLattices.boolean_algebra_class.compl_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TLattices.bounded_lattice_bot.inf_bot_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ V4)))))))))))))))
(TLattices.bounded_lattice_bot.sup_bot_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V3 @ V4) @ V5)) @ V5)))))))))))))))
(TLattices.bounded_lattice_top.inf_top_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ V5)))))))))))))))
(TLattices.bounded_lattice_top.sup_top_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V3 @ V4) @ V5)) @ V4)))))))))))))))
(TLattices.class.boolean_algebra_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cLattices.class.boolean_algebra_axioms @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ (cHOL.All @ (^[V6]: ((cHOL.eq @ ((V2 @ V6) @ (V1 @ V6))) @ V4)))) @ ((cHOL.conj @ (cHOL.All @ (^[V6]: ((cHOL.eq @ ((V3 @ V6) @ (V1 @ V6))) @ V5)))) @ (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.eq @ ((V0 @ V6) @ V7)) @ ((V2 @ V6) @ (V1 @ V7)))))))))))))))))))))))
(TLattices.class.bounded_lattice_bot.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cOrderings.class.order_bot @ V4) @ V1) @ V2)))))))))))))
(TLattices.class.bounded_lattice_bot.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)))))))))))))
(TLattices.class.bounded_lattice_top.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cOrderings.class.order_top @ V1) @ V2) @ V4)))))))))))))
(TLattices.class.bounded_lattice_top.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)))))))))))))
(TLattices.class.distrib_lattice_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLattices.class.distrib_lattice_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.eq @ ((V1 @ V2) @ ((V0 @ V3) @ V4))) @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V1 @ V2) @ V4)))))))))))))))
(TLattices.class.semilattice_inf_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLattices.class.semilattice_inf_axioms @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((V1 @ ((V0 @ V2) @ V3)) @ V2)))))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((V1 @ ((V0 @ V2) @ V3)) @ V3)))))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((cHOL.implies @ ((V1 @ V2) @ V4)) @ ((V1 @ V2) @ ((V0 @ V3) @ V4))))))))))))))))))
(TLattices.class.semilattice_sup_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cLattices.class.semilattice_sup_axioms @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((V1 @ V2) @ ((V0 @ V2) @ V3))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((V1 @ V2) @ ((V0 @ V3) @ V2))))))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((cHOL.implies @ ((V1 @ V4) @ V3)) @ ((V1 @ ((V0 @ V2) @ V4)) @ V3)))))))))))))))))
(TLattices.distrib_lattice.inf_sup_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V3 @ V5) @ V6))) @ ((V3 @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.inf_sup_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V3 @ V4) @ V5)) @ V6)) @ ((V3 @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.sup_inf_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V3 @ V4) @ V5)) @ ((V3 @ V4) @ V6)))))))))))))))))))
(TLattices.distrib_lattice.sup_inf_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V3 @ ((V0 @ V4) @ V5)) @ V6)) @ ((V0 @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))))))))))))
(TLattices.semilattice_inf.inf_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V4) @ V5))) @ ((V0 @ V4) @ ((V0 @ V3) @ V5)))))))))))))))))
(TLattices.semilattice_inf_class.inf.orderE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ V2)) @ V2)))))))))
(TLattices.semilattice_inf_class.inf.orderI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TLattices.semilattice_inf_class.inf_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ ((V0 @ V3) @ V4)) @ V3)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ ((V0 @ V3) @ V4)) @ V4)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V4)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V5)) @ ((cOrderings.ord_class.less_eq @ V3) @ ((V0 @ V4) @ V5))))))))))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))))
(TLattices.semilattice_inf_class.le_iff_inf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0)))))))
(TLattices.semilattice_inf_class.le_inf_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TLattices.semilattice_inf_class.less_infI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cLattices.inf_class.inf @ V0) @ V2)) @ V1)))))))))
(TLattices.semilattice_inf_class.less_infI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cLattices.inf_class.inf @ V2) @ V0)) @ V1)))))))))
(TLattices.semilattice_sup.dual_semilattice,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ (((cLattices.class.semilattice_inf @ V0) @ (^[V3]: (^[V4]: ((V1 @ V4) @ V3)))) @ (^[V3]: (^[V4]: ((V2 @ V4) @ V3))))))))))))
(TLattices.semilattice_sup.sup_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ ((V0 @ V4) @ V5))) @ ((V0 @ V4) @ ((V0 @ V3) @ V5)))))))))))))))))
(TLattices.semilattice_sup_class.le_iff_sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V1)))))))
(TLattices.semilattice_sup_class.le_sup_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.less_supI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.less_supI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cLattices.sup_class.sup @ V2) @ V1))))))))))
(TLattices.semilattice_sup_class.sup.orderE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ ((cLattices.sup_class.sup @ V1) @ V0))) @ V2)) @ V2)))))))))
(TLattices.semilattice_sup_class.sup.orderI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TLattices.semilattice_sup_class.sup_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ V3) @ ((V0 @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ V4) @ ((V0 @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((V0 @ V4) @ V5)) @ V3)))))))))) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))))
(TLazy_Sequence.list_of_lazy_sequence.simps,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V0))) @ V0))))
(TLazy_Sequence.list_of_lazy_sequence_empty,((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ cLazy_Sequence.empty)) @ cList.list.Nil))
(TLazy_Sequence.small_lazy_list.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ V0))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cLazy_Sequence.small_lazy_list_rel) @ V1))))))))
(TLazy_Sequence.small_lazy_list_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy_list_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (cLazy_Sequence.single @ ((cList.list.Cons @ V5) @ V6))))))) @ cLazy_Sequence.empty)))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((cLazy_Sequence.small_lazy_list_graph @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ V2)))))))) @ V2)))))))))
(TLazy_Sequence.small_lazy_list_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLazy_Sequence.small_lazy_list_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (cLazy_Sequence.single @ ((cList.list.Cons @ V4) @ V5))))))) @ cLazy_Sequence.empty)))) @ ((cHOL.implies @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)) @ ((cLazy_Sequence.small_lazy_list_graph @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V2 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))))
(TLazy_Sequence.small_lazy_list_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy_list_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V3)) @ ((V2 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ V3))))) @ ((V2 @ V0) @ V1))))))))))
(TList.ab_group_add_class.listsum_subtractf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ (^[V3]: ((cGroups.minus_class.minus @ (V0 @ V3)) @ (V1 @ V3)))) @ V2))) @ ((cGroups.minus_class.minus @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ V2))) @ (cList.monoid_add_class.listsum @ ((cList.map @ V1) @ V2)))))))))))
(TList.linorder.distinct_sorted_list_of_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ (cList.distinct @ ((cList.linorder.sorted_list_of_set @ V0) @ V2))))))))))
(TList.linorder_class.insort_insert_key_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cList.linorder_class.insort_insert_key @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cSet.member @ (V0 @ V1)) @ ((cSet.image @ V0) @ (cList.set @ V2)))) @ V2) @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2))))))))))
(TList.ordered_ab_group_add_abs.listsum_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ (V0 @ (((cList.monoid_add.listsum @ V1) @ V2) @ V7))) @ (((cList.monoid_add.listsum @ V1) @ V2) @ ((cList.map @ V0) @ V7)))))))))))))))))))))
(TMain.term_of_sumbool_inst.term_of_sumbool,((c== @ cMain.term_of_sumbool_inst.term_of_sumbool) @ cMain.term_of_sumbool_inst.term_of_sumbool))
(TMain.typerep_sumbool_inst.typerep_sumbool,((c== @ cMain.typerep_sumbool_inst.typerep_sumbool) @ cMain.typerep_sumbool_inst.typerep_sumbool))
(TNat.dvd.order.not_eq_order_implies_strict,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))))
(TNat.semiring_char_0_class.of_nat_0_eq_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNat.semiring_1_class.of_nat @ V0))) @ ((cHOL.eq @ cNat.zero_nat_inst.zero_nat) @ V0)))))
(TNat.semiring_char_0_class.of_nat_eq_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNat.semiring_1_class.of_nat @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TNat_Transfer.transfer_int_nat_quantifiers_2,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ V1))))) @ (cHOL.Ex @ (^[V1]: (V0 @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TNat_Transfer.transfer_int_nat_quantifiers_1,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ V1))))) @ (cHOL.All @ (^[V1]: (V0 @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TNat_Transfer.transfer_nat_int_quantifiers_2,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Ex @ (^[V1]: (V0 @ V1)))) @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ (cInt.nat @ V1)))))))))
(TNat_Transfer.transfer_nat_int_quantifiers_1,(call @ (^[V0]: ((cHOL.eq @ (cHOL.All @ (^[V1]: (V0 @ V1)))) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ (cInt.nat @ V1)))))))))
(TNitpick.pair_box.narrowing_pair_box.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cNitpick.pair_box.PairBox)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)))
(TNitpick.pair_box.pair_box_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNitpick.pair_box.pair_box_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))) @ (V1 @ V0))))))))
(TNum.linordered_idom.neg_numeral_less_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V3)))))))))))))))))))))))))
(TNum.linordered_idom_class.abs_neg_numeral,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.linordered_semidom.less_numeral_extra_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ V3) @ V3))))))))))))))))
(TNum.linordered_semidom.less_numeral_extra_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ V1) @ V1))))))))))))))))
(TNum.linordered_semidom.less_numeral_extra_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ V3) @ V1))))))))))))))))
(TNum.linordered_semidom.less_numeral_extra_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V5 @ V1) @ V3)))))))))))))))
(TNum.linordered_semidom.less_numeral_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V1))))))))))))))))))
(TNum.linordered_semidom.less_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((V5 @ V1) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))))))))))))))))))
(TNum.linordered_semidom.less_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V3))))))))))))))))))
(TNum.linordered_semidom.less_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V3) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))) @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ V6))))))))))))))))))
(TNum.linordered_semidom.less_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ (((cNum.numeral.numeral @ V3) @ V0) @ V7))) @ ((cNum.ord_num_inst.less_num @ V6) @ V7))))))))))))))))))))
(TNum.linordered_semidom.numeral_le_one_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V3)) @ ((cNum.ord_num_inst.less_eq_num @ V6) @ cNum.num.One))))))))))))))))))
(TNum.neg_numeral_class.minus_numeral_simps_3,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.neg_numeral_class.minus_numeral_simps_2,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cNum.numeral_class.numeral @ V0))) @ (cNum.neg_numeral_class.neg_numeral @ V0)))))
(TNum.neg_numeral_class.minus_numeral_simps_1,((cHOL.eq @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ cNum.num.One)))
(TNum.ring_1_class.ring_1_class.iszero_dict,((c== @ cNum.ring_1_class.iszero) @ (cNum.ring_1.iszero @ cGroups.zero_class.zero)))
(TNum.ring_char_0_class.neg_numeral_neq_one,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.ring_char_0_class.one_neq_neg_numeral,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNumeral_Simprocs.nat_mult_div_cancel_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_nat_inst.div_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat) @ ((cDivides.div_nat_inst.div_nat @ V1) @ V2))))))))))
(TNumeral_Simprocs.nat_mult_dvd_cancel_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)) @ ((cRings.dvd_class.dvd @ V1) @ V2))))))))))
(TOrderings.dense_linorder.dense_ge_bounded,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((V1 @ V2) @ V5)) @ ((c==> @ ((V1 @ V5) @ V3)) @ ((V0 @ V4) @ V5)))))) @ ((V0 @ V4) @ V2)))))))))))))))
(TOrderings.dense_linorder.dense_le_bounded,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((c==> @ ((V1 @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((V1 @ V2) @ V5)) @ ((c==> @ ((V1 @ V5) @ V3)) @ ((V0 @ V5) @ V4)))))) @ ((V0 @ V3) @ V4)))))))))))))))
(TOrderings.linorder_class.strict_mono_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.strict_mono @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (V0 @ V1)) @ (V0 @ V2))) @ ((cOrderings.ord_class.less @ V1) @ V2))))))))))
(TOrderings.order_class.order.strict_trans1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.order_class.order.strict_trans2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.wellorder.wellorder_Least_lemma_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ ((V0 @ ((cOrderings.ord.Least @ V0) @ (^[V4]: (V2 @ V4)))) @ V3))))))))))))
(TOrderings.wellorder.wellorder_Least_lemma_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.wellorder @ V0) @ V1)) @ ((c==> @ (V2 @ V3)) @ (V2 @ ((cOrderings.ord.Least @ V0) @ (^[V4]: (V2 @ V4)))))))))))))))
(TPower.comm_monoid_mult.power_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ ((V0 @ V2) @ V3)) @ V4)) @ ((V0 @ ((((cPower.power.power @ V1) @ V0) @ V2) @ V4)) @ ((((cPower.power.power @ V1) @ V0) @ V3) @ V4)))))))))))))))
(TPower.division_ring.nonzero_power_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ (V0 @ ((((cPower.power.power @ V2) @ V3) @ V8) @ V9))) @ ((((cPower.power.power @ V2) @ V3) @ (V0 @ V8)) @ V9)))))))))))))))))))))))))
(TPower.linordered_idom.odd_power_less_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V5 @ V10) @ V3)) @ ((V5 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V11)))) @ V3))))))))))))))))))))))))))))
(TPower.linordered_idom.zero_le_even_power',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ V3) @ ((((cPower.power.power @ V7) @ V9) @ V10) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V11)))))))))))))))))))))))))))))
(TPower.linordered_idom_class.power2_less_0,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.zero_class.zero)))))
(TPower.linordered_ring.sum_squares_ge_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((V4 @ V3) @ ((V6 @ ((V7 @ V8) @ V8)) @ ((V7 @ V9) @ V9)))))))))))))))))))))))))
(TPower.linordered_semidom.power2_eq_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cHOL.eq @ ((((cPower.power.power @ V3) @ V2) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V3) @ V2) @ V7) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((c==> @ ((V4 @ V1) @ V6)) @ ((c==> @ ((V4 @ V1) @ V7)) @ ((cHOL.eq @ V6) @ V7))))))))))))))))))))))
(TPower.linordered_semidom.power2_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V3) @ V2) @ V7) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((c==> @ ((V4 @ V1) @ V7)) @ ((V4 @ V6) @ V7)))))))))))))))))))))
(TPower.linordered_semidom.power_decreasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V6) @ V7)) @ ((c==> @ ((V4 @ V1) @ V8)) @ ((cHOL.implies @ ((V4 @ V8) @ V3)) @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V6)))))))))))))))))))))))))
(TPower.linordered_semidom.power_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V6) @ V7)) @ ((c==> @ ((V4 @ V3) @ V8)) @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V6)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V7))))))))))))))))))))))))
(TPower.linordered_semidom.power_inject_exp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V8))) @ ((cHOL.eq @ V7) @ V8)))))))))))))))))))))))
(TPower.linordered_semidom_class.power_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V1) @ V2)))))))))))
(TPower.monoid_mult_class.power_numeral_odd,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V1)))) @ ((cHOL.Let @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ V1))) @ (^[V2]: ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V2)) @ V2)))))))))
(TPower.ring_1_class.power_neg_numeral_Bit0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ (cNum.numeral_class.numeral @ ((cNum.pow @ V0) @ (cNum.num.Bit0 @ V1)))))))))
(TPower.ring_1_class.power_neg_numeral_Bit1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ V1)))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.pow @ V0) @ (cNum.num.Bit1 @ V1)))))))))
(TPower.semiring_1_class.power_zero_numeral,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ cGroups.zero_class.zero))))
(TQuickcheck_Exhaustive.arity_check_all_fun,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_set,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_sum,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_equal_unknown,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_class_def,((c== @ (cQuickcheck_Exhaustive.check_all_class @ cTYPE)) @ ((cPure.conjunction @ (cCode_Evaluation.term_of_class @ cTYPE)) @ (cEnum.enum_class @ cTYPE))))
(TQuickcheck_Exhaustive.class.check_all_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cQuickcheck_Exhaustive.class.check_all @ V0) @ V1) @ V2)) @ (((cEnum.class.enum @ V0) @ V1) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_def,((c== @ cQuickcheck_Exhaustive.exhaustive_fun') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.exhaustive_fun'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_def,((c== @ cQuickcheck_Exhaustive.exhaustive_int') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.exhaustive_int'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.exhaustive_prod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ V0) @ V1)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V2]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V3]: (V0 @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V1))) @ V1)))))))
(TQuickcheck_Exhaustive.termify_fun_upd_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((((cQuickcheck_Exhaustive.term_syntax.termify_fun_upd @ cTYPE) @ cTYPE) @ V0) @ V1) @ V2)) @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ V0)) @ V1)) @ V2)))))))))
(TQuickcheck_Exhaustive.three_valued.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Exhaustive.three_valued.Value @ V2))))) @ ((c==> @ (V0 @ cQuickcheck_Exhaustive.three_valued.No_value)) @ (V0 @ V1)))))))))
(TQuickcheck_Exhaustive.three_valued.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ (cQuickcheck_Exhaustive.three_valued.Value @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.three_valued.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cQuickcheck_Exhaustive.three_valued.Value @ V5))) @ (cHOL.Not @ (V0 @ (V2 @ V5))))))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ (cHOL.Not @ (V0 @ V3))))))))))))))))))
(TQuickcheck_Exhaustive.three_valued.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V1) @ V2) @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ (V0 @ V1))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V4) @ (cQuickcheck_Exhaustive.three_valued.Value @ V5))) @ (V0 @ (V2 @ V5)))))) @ ((cHOL.implies @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ (V0 @ V3))))))))))))))))
(TQuickcheck_Exhaustive.typerep_unknown_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TQuickcheck_Exhaustive.unknown.Rep_unknown,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Exhaustive.Rep_unknown @ V0)) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set)))))
(TQuickcheck_Exhaustive.unknown.Unknown_def,((c== @ cQuickcheck_Exhaustive.unknown.Unknown) @ (cQuickcheck_Exhaustive.Abs_unknown @ (cDatatype.In0 @ cHOL.undefined))))
(TQuickcheck_Exhaustive.valtermify_pair_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.valtermify_pair @ V0) @ V1)) @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cProduct_Type.Pair) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)) @ V1)))))))
(TQuickcheck_Narrowing.arity_equal_property,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_bool,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_cfun,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_char,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_ffun,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_list,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_prod,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_term,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_unit,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero_sumC_def,((c== @ cQuickcheck_Narrowing.around_zero_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Narrowing.around_zero_graph @ V0) @ V1))))))
(TQuickcheck_Narrowing.cfun.Abs_cfun_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set))) @ (V0 @ (cQuickcheck_Narrowing.Abs_cfun @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.cfun.Abs_cfun_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_cfun @ V0)) @ (cQuickcheck_Narrowing.Abs_cfun @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.cfun.Rep_cfun_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Narrowing.Rep_cfun @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.cfun.Rep_cfun_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_cfun @ V0)) @ (cQuickcheck_Narrowing.Rep_cfun @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.cfun.arity_size_cfun,(cNat.size_class @ cTYPE))
(TQuickcheck_Narrowing.ffun.Abs_ffun_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set))) @ (V0 @ (cQuickcheck_Narrowing.Abs_ffun @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.ffun.Abs_ffun_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_ffun @ V0)) @ (cQuickcheck_Narrowing.Abs_ffun @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.ffun.Rep_ffun_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Narrowing.Rep_ffun @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.ffun.Rep_ffun_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_ffun @ V0)) @ (cQuickcheck_Narrowing.Rep_ffun @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.ffun.arity_size_ffun,(cNat.size_class @ cTYPE))
(TQuickcheck_Narrowing.narrowing_cons.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_cons.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_cons.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_cons.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_cons.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.cases_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V0) @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))) @ ((V1 @ V2) @ V3)))))))))))
(TQuickcheck_Narrowing.narrowing_term.cases_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V0) @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))) @ ((V0 @ V2) @ V3)))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ ((cList.list.Cons @ V4) @ V5))) @ ((((V3 @ V4) @ V5) @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ V5))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ cList.list.Nil)) @ V2))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ V0) @ V1) @ V2) @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5))) @ (((V1 @ V4) @ V5) @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2 @ V0) @ V1) @ V2) @ V3) @ V5))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ V0) @ V1) @ V2) @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))) @ ((V0 @ V4) @ V5)))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V0) @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))) @ ((V1 @ V2) @ V3)))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V0) @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))) @ ((V0 @ V2) @ V3)))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))) @ (V0 @ ((V1 @ V4) @ V5)))))))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5))) @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.cases,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V1))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ ((((V4 @ V5) @ V6) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ cList.list.Nil)) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_type.simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ ((((V2 @ V5) @ V6) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ cList.list.Nil)) @ V1))))))))))))
(TQuickcheck_Narrowing.narrowing_type.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V5))) @ ((V0 @ V5) @ ((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V1))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0)) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.split,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TQuickcheck_Narrowing.non_empty_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.non_empty_rel @ V0) @ V1)) @ ((V2 @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.type_definition_cfun,(((cTypedef.type_definition @ cQuickcheck_Narrowing.Rep_cfun) @ cQuickcheck_Narrowing.Abs_cfun) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set)))
(TQuickcheck_Narrowing.type_definition_ffun,(((cTypedef.type_definition @ cQuickcheck_Narrowing.Rep_ffun) @ cQuickcheck_Narrowing.Abs_ffun) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set)))
(TQuickcheck_Narrowing.typerep_property_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.typerep_property_inst.typerep_property @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)))))
(TQuickcheck_Random.nibble.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_nibble @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble0) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble4) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble5) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble6) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble7) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble8) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.Nibble9) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleA) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleB) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleC) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleD) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleE) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cString.nibble.NibbleF) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))))))))))))))))) @ V2)))))))))
(TQuickcheck_Random.option.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_option @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cOption.option.None) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cOption.option.Some) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Random.random_aux_finite_1_def,((c== @ cQuickcheck_Random.random_aux_finite_1) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_1.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_1.a\<__caret__sub>1) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_finite_2_def,((c== @ cQuickcheck_Random.random_aux_finite_2) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>1) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>2) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_finite_3_def,((c== @ cQuickcheck_Random.random_aux_finite_3) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>1) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>2) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>3) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_finite_4_def,((c== @ cQuickcheck_Random.random_aux_finite_4) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>4) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>1) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>2) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>3) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>4) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_aux_finite_5_def,((c== @ cQuickcheck_Random.random_aux_finite_5) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>4) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>5) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>1) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>2) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>3) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>4) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>5) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))))) @ V4)))))) @ V0))))
(TRecord.iso_tuple_surjective_proof_assistI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ V2)) @ (((cRecord.iso_tuple_surjective_proof_assist @ V1) @ V2) @ V0)))))))))
(TRecord.tuple_isomorphism.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRecord.random_aux_tuple_isomorphism @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cRecord.tuple_isomorphism.Tuple_Isomorphism) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))))))))
(TRecord.update_accessor_congruence_unfoldE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ (V1 @ V3)) @ V4)) @ ((c==> @ (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V7) @ V4)) @ ((cHOL.eq @ (V5 @ V7)) @ (V6 @ V7)))))) @ ((cHOL.eq @ ((V0 @ V5) @ V2)) @ ((V0 @ V6) @ V3)))))))))))))))))))))
(TRings.class.comm_semiring_0_cancel.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.comm_semiring_0_cancel @ V0) @ V1) @ V2)) @ ((cRings.class.comm_semiring @ V0) @ V2)))))))))
(TRings.class.comm_semiring_0_cancel.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cRings.class.comm_semiring_0_cancel @ V0) @ V1) @ V2)) @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)))))))))
(TRings.class.comm_semiring_1_cancel.axioms_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.zero_neq_one @ V3) @ V1)))))))))))
(TRings.class.comm_semiring_1_cancel.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cRings.class.comm_semiring @ V0) @ V2)))))))))))
(TRings.class.comm_semiring_1_cancel.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.comm_monoid_mult @ V2) @ V3)))))))))))
(TRings.class.comm_semiring_1_cancel.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)))))))))))
(TRings.class.linordered_ring_strict.axioms_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cRings.class.ring @ V6) @ V3) @ V1) @ V2) @ V7)))))))))))))))))))
(TRings.class.linordered_ring_strict.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cRings.class.linordered_semiring_strict @ V6) @ V3) @ V4) @ V5) @ V7)))))))))))))))))))
(TRings.class.linordered_ring_strict.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((cGroups.class.ordered_ab_group_add @ V6) @ V3) @ V1) @ V2) @ V4) @ V5)))))))))))))))))))
(TRings.class.linordered_ring_strict.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((cGroups.class.abs_if @ V0) @ V2) @ V3) @ V5)))))))))))))))))))
(TRings.class.linordered_semidom_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.linordered_semidom_axioms @ V0) @ V1) @ V2)) @ ((V2 @ V0) @ V1)))))))))
(TRings.class.ordered_cancel_semiring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((c==> @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TRings.class.ordered_ring_abs_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.conj @ ((cHOL.disj @ ((V0 @ V1) @ V4)) @ ((V0 @ V4) @ V1))) @ ((cHOL.disj @ ((V0 @ V1) @ V5)) @ ((V0 @ V5) @ V1)))) @ ((cHOL.eq @ (V2 @ ((V3 @ V4) @ V5))) @ ((V3 @ (V2 @ V4)) @ (V2 @ V5))))))))) @ ((((cRings.class.ordered_ring_abs_axioms @ V2) @ V1) @ V0) @ V3)))))))))))
(TRings.class.ordered_semiring_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V5))))))))))) @ (((cRings.class.ordered_semiring_axioms @ V1) @ V0) @ V2))))))))))
(TRings.class.ring_1_no_zero_divisors.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((((cRings.class.ring_no_zero_divisors @ V1) @ V3) @ V2) @ V4) @ V5)) @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TRings.classrel_comm_semiring_0_semiring_0,(cRings.semiring_0_class @ cTYPE))
(TRings.classrel_comm_semiring_1_semiring_1,(cRings.semiring_1_class @ cTYPE))
(TRings.comm_semiring_1_class.dvd_mult_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V2)))))))))
(TRings.comm_semiring_1_class.dvd_triv_left,(call @ (^[V0]: (call @ (^[V1]: ((cRings.dvd_class.dvd @ V0) @ ((cGroups.times_class.times @ V0) @ V1)))))))
(TRings.comm_semiring_1_class.mult_dvd_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ ((cRings.dvd_class.dvd @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))
(TRings.linordered_idom.less_minus_self_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V10) @ (V2 @ V10))) @ ((V5 @ V10) @ V3))))))))))))))))))))))))))
(TRings.linordered_idom.mult_left_le_one_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V4 @ V3) @ V10)) @ ((c==> @ ((V4 @ V3) @ V11)) @ ((c==> @ ((V4 @ V11) @ V7)) @ ((V4 @ ((V9 @ V11) @ V10)) @ V10))))))))))))))))))))))))))))))
(TRings.linordered_idom_class.abs_mult_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ (cGroups.abs_class.abs @ V0)) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ (cGroups.abs_class.abs @ V2)) @ V3)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V2))) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))
(TRings.linordered_idom_class.abs_mult_self,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V0))) @ ((cGroups.times_class.times @ V0) @ V0)))))
(TRings.linordered_idom_class.dvd_if_abs_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))) @ ((cRings.dvd_class.dvd @ V0) @ V1)))))))
(TRings.linordered_ring_strict.mult_neg_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V5 @ V8) @ V3)) @ ((c==> @ ((V5 @ V9) @ V3)) @ ((V5 @ V3) @ ((V7 @ V8) @ V9))))))))))))))))))))))))))
(TRings.ordered_cancel_semiring_class.intro,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cRings.ordered_semiring_class @ cTYPE)) @ (cRings.ordered_cancel_semiring_class @ cTYPE))))
(TRings.ordered_cancel_semiring_class.super_2,((c==> @ (cRings.ordered_cancel_semiring_class @ cTYPE)) @ (cRings.ordered_semiring_class @ cTYPE)))
(TRings.ordered_cancel_semiring_class.super_1,((c==> @ (cRings.ordered_cancel_semiring_class @ cTYPE)) @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)))
(TRings.ring_1_no_zero_divisors_class.intro,((c==> @ (cRings.ring_1_class @ cTYPE)) @ ((c==> @ (cRings.ring_no_zero_divisors_class @ cTYPE)) @ (cRings.ring_1_no_zero_divisors_class @ cTYPE))))
(TRings.ring_1_no_zero_divisors_class.super_2,((c==> @ (cRings.ring_1_no_zero_divisors_class @ cTYPE)) @ (cRings.ring_no_zero_divisors_class @ cTYPE)))
(TRings.ring_1_no_zero_divisors_class.super_1,((c==> @ (cRings.ring_1_no_zero_divisors_class @ cTYPE)) @ (cRings.ring_1_class @ cTYPE)))
(TRings.ring_no_zero_divisors.mult_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ring_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V5) @ V6)) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V5) @ V1)) @ ((cHOL.eq @ V6) @ V1)))))))))))))))))))
(TSMT.pattern.full_exhaustive_pattern.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSMT.full_exhaustive_pattern_inst.full_exhaustive_pattern @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ (V0 @ ((cProduct_Type.Pair @ cSMT.pattern.Pattern) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))) @ cList.list.Nil)))))) @ cOption.option.None)))))))
(TSet_Interval.card_atLeastZeroLessThan_int,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.atLeastLessThan @ cInt.zero_int_inst.zero_int) @ V0))) @ (cInt.nat @ V0)))))
(TSet_Interval.card_greaterThanLessThan_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ (cInt.nat @ ((cInt.minus_int_inst.minus_int @ V1) @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)))))))))
(TSet_Interval.complete_lattice.Inf_atLeast,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ ((cSet_Interval.ord.atLeast @ V3) @ V8))) @ V8)))))))))))))))))))))
(TSet_Interval.complete_lattice.Sup_atLeast,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ ((cSet_Interval.ord.atLeast @ V3) @ V8))) @ V7)))))))))))))))))))))
(TSet_Interval.dvd.atLeastAtMost_singleton',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.dvd.atLeastatMost_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1))) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))))))))
(TSet_Interval.dvd.atLeastatMost_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V2) @ V3))) @ ((cHOL.disj @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V0)) @ ((cRings.dvd_class.dvd @ V1) @ V3)))))))))))))
(TSet_Interval.finite_greaterThanAtMost_int,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)))))))
(TSet_Interval.linorder.Int_atLeastAtMostL1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet_Interval.ord.atMost @ V0) @ V4))) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ (((cOrderings.ord.min @ V0) @ V3) @ V4)))))))))))))))
(TSet_Interval.linorder.Int_atLeastAtMostL2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet_Interval.ord.atLeast @ V0) @ V4))) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ (((cOrderings.ord.max @ V0) @ V2) @ V4)) @ V3))))))))))))))
(TSet_Interval.linorder.Int_atLeastAtMostR1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.atMost @ V0) @ V2)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ V4))) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ (((cOrderings.ord.min @ V0) @ V2) @ V4)))))))))))))))
(TSet_Interval.linorder.Int_atLeastAtMostR2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.atLeast @ V0) @ V2)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V3) @ V4))) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ (((cOrderings.ord.max @ V0) @ V2) @ V3)) @ V4))))))))))))))
(TSet_Interval.linorder.Int_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V2) @ V3)) @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V4) @ V5))) @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ (((cOrderings.ord.max @ V0) @ V2) @ V4)) @ (((cOrderings.ord.min @ V0) @ V3) @ V5)))))))))))))))))
(TSet_Interval.no_bot_class.not_Ici_eq_UNIV,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ cOrderings.top_class.top)))))
(TSet_Interval.no_bot_class.not_UNIV_eq_Ici,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOrderings.top_class.top) @ (cSet_Interval.ord_class.atLeast @ V0))))))
(TSet_Interval.no_bot_class.not_UNIV_le_Ici,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ (cSet_Interval.ord_class.atLeast @ V0))))))
(TSet_Interval.no_top.greaterThan_non_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord.greaterThan @ V1) @ V2)) @ cOrderings.bot_class.bot))))))))))
(TSet_Interval.no_top_class.not_Icc_eq_UNIV,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ cOrderings.top_class.top)))))))
(TSet_Interval.no_top_class.not_Iic_eq_UNIV,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ cOrderings.top_class.top)))))
(TSet_Interval.no_top_class.not_UNIV_eq_Icc,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ cOrderings.top_class.top) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.no_top_class.not_UNIV_eq_Iic,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOrderings.top_class.top) @ (cSet_Interval.ord_class.atMost @ V0))))))
(TSet_Interval.no_top_class.not_UNIV_le_Icc,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.no_top_class.not_UNIV_le_Iic,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ (cSet_Interval.ord_class.atMost @ V0))))))
(TSet_Interval.order_class.not_Ici_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ cOrderings.bot_class.bot)))))
(TSet_Interval.order_class.not_Iic_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ cOrderings.bot_class.bot)))))
(TSet_Interval.order_top.atMost_eq_UNIV_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_top @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord.atMost @ V0) @ V3)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ V3) @ V2))))))))))))
(TTransitive_Closure.converse_trancl_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V1)) @ V2)) @ (V3 @ V4))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ (V3 @ V5)) @ (V3 @ V4))))))))) @ (V3 @ V0)))))))))))))
(TTransitive_Closure.relpow_finite_bounded1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cNat.compow @ V1) @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ (cFinite_Set.card @ V0)))))) @ (^[V2]: ((cNat.compow @ V2) @ V0)))))))))))
(TTransitive_Closure.rtrancl_subset_rtrancl,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (cTransitive_Closure.rtrancl @ V1))) @ ((cOrderings.ord_class.less_eq @ (cTransitive_Closure.rtrancl @ V0)) @ (cTransitive_Closure.rtrancl @ V1))))))))
(TTransitive_Closure.rtranclp_into_tranclp1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.rtranclp_into_tranclp2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TBig_Operators.comm_monoid_add.setsum_cong2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V2)) @ ((cHOL.eq @ (V3 @ V5)) @ (V4 @ V5)))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V3) @ V2)) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V4) @ V2)))))))))))))))
(TBig_Operators.comm_monoid_mult.setprod_Un2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ ((cLattices.sup_class.sup @ V2) @ V3))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V4) @ ((cLattices.sup_class.sup @ V2) @ V3))) @ ((V0 @ ((V0 @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V4) @ ((cGroups.minus_class.minus @ V2) @ V3))) @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V4) @ ((cGroups.minus_class.minus @ V3) @ V2)))) @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V4) @ ((cLattices.inf_class.inf @ V2) @ V3)))))))))))))))))
(TBig_Operators.comm_monoid_mult.setprod_def,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_set.F @ V0) @ V1))))))))
(TBig_Operators.complete_lattice.Inf_fin_Inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.semilattice_inf.Inf_fin @ V2) @ V8)) @ (V0 @ V8))))))))))))))))))))))))
(TBig_Operators.complete_lattice.Sup_fin_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.semilattice_sup.Sup_fin @ V5) @ V8)) @ (V1 @ V8))))))))))))))))))))))))
(TBig_Operators.lattice_class.inf_Sup_absorb,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0))) @ V1))))))))
(TBig_Operators.lattice_class.sup_Inf_absorb,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))) @ V1))))))))
(TBig_Operators.linorder_class.Max.singleton,(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0))))
(TBig_Operators.linorder_class.Max_singleton,(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0))))
(TBig_Operators.linorder_class.Min.singleton,(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0))))
(TBig_Operators.linorder_class.Min_singleton,(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0))))
(TBig_Operators.semilattice_neutr_set.axioms,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((cLattices.semilattice_neutr @ V0) @ V1)))))))
(TBig_Operators.semilattice_neutr_set.closed,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cSet.member @ ((V0 @ V3) @ V4)) @ ((cSet.insert @ V3) @ ((cSet.insert @ V4) @ cOrderings.bot_class.bot)))))))) @ ((cSet.member @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2)) @ V2))))))))))))
(TBig_Operators.semilattice_neutr_set.insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ ((cSet.insert @ V3) @ V2))) @ ((V0 @ V3) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2))))))))))))))
(TBig_Operators.semilattice_neutr_set.remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((cHOL.eq @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2)) @ ((V0 @ V3) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot)))))))))))))))))
(TBig_Operators.semilattice_neutr_set.subset,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((cHOL.eq @ ((V0 @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V3)) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2))) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2))))))))))))))
(TBig_Operators.semilattice_order_set.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ (cBig_Operators.semilattice_set @ V0)))))))))
(TBig_Operators.semilattice_order_set.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)))))))))
(TCode_Evaluation.equal_term_inst.equal_term,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TCode_Evaluation.term_of_lazy_sequence_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TCode_Numeral.arity_linordered_idom_integer,(cRings.linordered_idom_class @ cTYPE))
(TCode_Numeral.int_of_integer_integer_of_int,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_int @ V0))) @ V0))))
(TCode_Numeral.int_of_integer_integer_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_nat @ V0))) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TCode_Numeral.integer.int_of_integer_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cCode_Numeral.int_of_integer @ V2))))) @ (V1 @ V0))))))))
(TCode_Numeral.integer.int_of_integer_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cCode_Numeral.int_of_integer @ V0)) @ (cCode_Numeral.int_of_integer @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TCode_Numeral.integer.integer_of_int_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ cOrderings.top_class.top)) @ (V0 @ (cCode_Numeral.integer_of_int @ V2)))))) @ (V0 @ V1)))))))
(TCode_Numeral.integer.integer_of_int_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cSet.member @ V1) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHOL.eq @ (cCode_Numeral.integer_of_int @ V0)) @ (cCode_Numeral.integer_of_int @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TCode_Numeral.integer_of_int_int_of_integer,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_int @ (cCode_Numeral.int_of_integer @ V0))) @ V0))))
(TCode_Numeral.integer_of_natural_of_integer,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_natural @ (cCode_Numeral.natural_of_integer @ V0))) @ ((cOrderings.ord_class.max @ cCode_Numeral.zero_integer_inst.zero_integer) @ V0)))))
(TCode_Numeral.nat_of_integer_integer_of_nat,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_integer @ (cCode_Numeral.integer_of_nat @ V0))) @ V0))))
(TCode_Numeral.nat_of_natural_of_nat_inverse,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ (cCode_Numeral.natural_of_nat @ V0))) @ V0))))
(TCode_Numeral.natural.nat_of_natural_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cCode_Numeral.nat_of_natural @ V2))))) @ (V1 @ V0))))))))
(TCode_Numeral.natural.nat_of_natural_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ V0)) @ (cCode_Numeral.nat_of_natural @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TCode_Numeral.natural.natural_of_nat_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ cOrderings.top_class.top)) @ (V0 @ (cCode_Numeral.natural_of_nat @ V2)))))) @ (V0 @ V1)))))))
(TCode_Numeral.natural.natural_of_nat_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((c==> @ ((cSet.member @ V1) @ cOrderings.top_class.top)) @ ((cHOL.eq @ ((cHOL.eq @ (cCode_Numeral.natural_of_nat @ V0)) @ (cCode_Numeral.natural_of_nat @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TCode_Numeral.natural.natural_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V2) @ (cCode_Numeral.Suc @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ ((V1 @ V5) @ V6))) @ ((c==> @ ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ V5) @ V6)) @ V4)))))))) @ V4))))))))))))))
(TCode_Numeral.natural.natural_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((cHOL.eq @ V3) @ V0))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cCode_Numeral.Suc @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((V1 @ V4) @ V5))) @ ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ V4) @ V5))))))))))))))))))
(TCode_Numeral.natural_of_integer_of_natural,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.natural_of_integer @ (cCode_Numeral.integer_of_natural @ V0))) @ V0))))
(TCode_Numeral.ord_integer_inst.less_integer,((c== @ cCode_Numeral.ord_integer_inst.less_integer) @ cCode_Numeral.ord_integer_inst.less_integer))
(TCode_Numeral.ord_natural_inst.less_natural,((c== @ cCode_Numeral.ord_natural_inst.less_natural) @ cCode_Numeral.ord_natural_inst.less_natural))
(TComplete_Lattices.complete_lattice.INFI_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((cSet.Bex @ V9) @ (^[V13]: ((V3 @ (V10 @ V13)) @ (V11 @ V12)))))))) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V9)) @ ((cSet.Bex @ V8) @ (^[V13]: ((V3 @ (V11 @ V13)) @ (V10 @ V12)))))))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V12]: (V11 @ V12)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V12]: (V10 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ V9)) @ (V0 @ ((cSet.image @ V9) @ V8)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V11]: ((c==> @ ((cSet.member @ V11) @ V8)) @ ((V3 @ V9) @ (V10 @ V11)))))) @ ((c==> @ (call @ (^[V11]: ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((V3 @ V11) @ (V10 @ V12)))))) @ ((V3 @ V11) @ V9))))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (V10 @ V11)))) @ V9)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_top,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V9]: V7))) @ V7)))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ V8)) @ (V1 @ (cSet.Collect @ (^[V9]: ((cSet.Ball @ V8) @ (^[V10]: ((V3 @ V9) @ V10)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((V3 @ V9) @ V10))))) @ ((c==> @ (call @ (^[V10]: ((c==> @ (call @ (^[V11]: ((c==> @ ((cSet.member @ V11) @ V8)) @ ((V3 @ V10) @ V11))))) @ ((V3 @ V10) @ V9))))) @ ((cHOL.eq @ (V0 @ V8)) @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUPR_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((cSet.Bex @ V9) @ (^[V13]: ((V3 @ (V10 @ V12)) @ (V11 @ V13)))))))) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V9)) @ ((cSet.Bex @ V8) @ (^[V13]: ((V3 @ (V11 @ V12)) @ (V10 @ V13)))))))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: (V10 @ V12)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V12]: (V11 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_bot,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V9]: V6))) @ V6)))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ V9)) @ (V1 @ ((cSet.image @ V9) @ V8)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V11]: ((c==> @ ((cSet.member @ V11) @ V8)) @ ((V3 @ (V9 @ V11)) @ V10))))) @ ((c==> @ (call @ (^[V11]: ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((V3 @ (V9 @ V12)) @ V11))))) @ ((V3 @ V10) @ V11))))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (V9 @ V11)))) @ V10)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_Inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ V8)) @ (V0 @ (cSet.Collect @ (^[V9]: ((cSet.Ball @ V8) @ (^[V10]: ((V3 @ V10) @ V9)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((V3 @ V10) @ V9))))) @ ((c==> @ (call @ (^[V10]: ((c==> @ (call @ (^[V11]: ((c==> @ ((cSet.member @ V11) @ V8)) @ ((V3 @ V11) @ V10))))) @ ((V3 @ V9) @ V10))))) @ ((cHOL.eq @ (V1 @ V8)) @ V9)))))))))))))))))))))))))
(TComplete_Partial_Order.ccpo.admissible_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((cHOL.implies @ ((cSet.Ball @ V3) @ (^[V4]: (V2 @ V4)))) @ (V2 @ (V0 @ V3))))))))))))))
(TComplete_Partial_Order.ccpo.ccpo_Sup_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V3)) @ ((V1 @ V5) @ V4))))) @ ((V1 @ (V0 @ V3)) @ V4)))))))))))))))
(TComplete_Partial_Order.ccpo.ccpo_Sup_upper,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ V3)) @ ((V1 @ V4) @ (V0 @ V3))))))))))))))))
(TComplete_Partial_Order.ccpo.chain_iterates,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ (((cComplete_Partial_Order.monotone @ V1) @ V1) @ V3)) @ ((cComplete_Partial_Order.chain @ V1) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V3)))))))))))))
(TComplete_Partial_Order.ccpo.iterates.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V3) @ (V4 @ V6))) @ ((c==> @ ((cSet.member @ V6) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ V5))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V3) @ (V0 @ V6))) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V6)) @ ((c==> @ ((cSet.Ball @ V6) @ (^[V7]: ((cSet.member @ V7) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))))) @ V5)))))) @ V5)))))))))))))))))
(TComplete_Partial_Order.ccpo.iterates.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cSet.member @ V3) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (V4 @ V5))) @ ((cSet.member @ V5) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4)))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (V0 @ V5))) @ ((cHOL.conj @ ((cComplete_Partial_Order.chain @ V1) @ V5)) @ ((cSet.Ball @ V5) @ (^[V6]: ((cSet.member @ V6) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))))))))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp.step,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V4)) @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ (V3 @ V4)))))))))))))))
(TComplete_Partial_Order.ccpo_class.fixp_def,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Partial_Order.ccpo_class.fixp @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ (cComplete_Partial_Order.ccpo_class.iterates @ V0))))))
(TDivides.semiring_div_class.dvd_div_eq_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_class.div @ V1) @ V0)) @ V2)) @ ((cHOL.eq @ V1) @ ((cGroups.times_class.times @ V2) @ V0))))))))))))
(TDivides.semiring_div_class.dvd_eq_mod_eq_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_class.mod @ V1) @ V0)) @ cGroups.zero_class.zero)))))))
(TDivides.semiring_div_class.dvd_mod_imp_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((cRings.dvd_class.dvd @ V0) @ V1))))))))))
(TDivides.semiring_div_class.mod_add_left_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ ((cDivides.div_class.mod @ V0) @ V2)) @ V1)) @ V2)))))))))
(TDivides.semiring_div_class.mod_div_trivial,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.div @ ((cDivides.div_class.mod @ V0) @ V1)) @ V1)) @ cGroups.zero_class.zero))))))
(TDivides.semiring_div_class.mod_mod_trivial,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cDivides.div_class.mod @ V0) @ V1)) @ V1)) @ ((cDivides.div_class.mod @ V0) @ V1)))))))
(TDivides.semiring_numeral_div.divmod_cancel_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ (cNum.num.Bit1 @ V9)) @ (cNum.num.Bit0 @ V10))) @ ((cProduct_Type.prod.prod_case @ (^[V11]: (^[V12]: ((cProduct_Type.Pair @ V11) @ ((V3 @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V12)) @ V5))))) @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ V9) @ V10)))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.divmod_cancel_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ (cNum.num.Bit0 @ V9)) @ (cNum.num.Bit0 @ V10))) @ ((cProduct_Type.prod.prod_case @ (^[V11]: (^[V12]: ((cProduct_Type.Pair @ V11) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V12))))) @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ V9) @ V10)))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.pos_mod_bound,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V8 @ V4) @ V9)) @ ((V8 @ ((V2 @ V10) @ V9)) @ V9))))))))))))))))))))))))))
(TDivides.transfer_int_nat_function_closures_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ ((c==> @ (cNat_Transfer.is_nat @ V1)) @ (cNat_Transfer.is_nat @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)))))))))
(TDivides.transfer_int_nat_function_closures_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ ((c==> @ (cNat_Transfer.is_nat @ V1)) @ (cNat_Transfer.is_nat @ ((cDivides.div_int_inst.div_int @ V0) @ V1)))))))))
(TDivides.transfer_nat_int_function_closures_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.mod_int @ V0) @ V1)))))))))
(TDivides.transfer_nat_int_function_closures_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cDivides.div_int_inst.div_int @ V0) @ V1)))))))))
(TEnum.finite_1.finite_1_size_overloaded_def,((c== @ cEnum.finite_1.size_finite_1_inst.size_finite_1) @ (cEnum.finite_1.finite_1_rec @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_2.finite_2_size_overloaded_def,((c== @ cEnum.finite_2.size_finite_2_inst.size_finite_2) @ ((cEnum.finite_2.finite_2_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_3.finite_3_size_overloaded_def,((c== @ cEnum.finite_3.size_finite_3_inst.size_finite_3) @ (((cEnum.finite_3.finite_3_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_4.finite_4_size_overloaded_def,((c== @ cEnum.finite_4.size_finite_4_inst.size_finite_4) @ ((((cEnum.finite_4.finite_4_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEnum.finite_5.finite_5_size_overloaded_def,((c== @ cEnum.finite_5.size_finite_5_inst.size_finite_5) @ (((((cEnum.finite_5.finite_5_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TEquiv_Relations.equivp_implies_part_equivp,(call @ (^[V0]: ((c==> @ (cEquiv_Relations.equivp @ V0)) @ (cEquiv_Relations.part_equivp @ V0)))))
(TExtraction.sumbool.sumbool_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cExtraction.sumbool.sumbool_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (V1 @ (cDatatype.In1 @ cHOL.undefined))) @ (V1 @ V0)))))))))
(TFields.class.field_inverse_zero_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cFields.class.field_inverse_zero_axioms @ V0) @ V1)) @ ((cHOL.eq @ (V0 @ V1)) @ V1)))))))
(TFields.division_ring.inverse_zero_imp_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ (V0 @ V8)) @ V5)) @ ((cHOL.eq @ V8) @ V5))))))))))))))))))))))
(TFields.division_ring.times_divide_eq_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ V8) @ ((V1 @ V9) @ V10))) @ ((V1 @ ((V3 @ V8) @ V9)) @ V10))))))))))))))))))))))))))
(TFields.field_inverse_zero.inverse_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V8)) @ V3)) @ ((cHOL.eq @ V8) @ V3))))))))))))))))))))))
(TFields.linordered_field.neg_divide_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V13) @ V12)) @ V14)) @ ((V10 @ ((V2 @ V14) @ V12)) @ V13)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.neg_less_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V10 @ V13) @ ((V1 @ V14) @ V12))) @ ((V10 @ V14) @ ((V2 @ V13) @ V12))))))))))))))))))))))))))))))))))))
(TFields.linordered_field.nonzero_abs_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V12) @ V5))) @ ((cHOL.eq @ (V8 @ ((V1 @ V13) @ V12))) @ ((V1 @ (V8 @ V13)) @ (V8 @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field.pos_divide_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V13) @ V12)) @ V14)) @ ((V10 @ V13) @ ((V2 @ V14) @ V12))))))))))))))))))))))))))))))))))))
(TFields.linordered_field.pos_less_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V10 @ V13) @ ((V1 @ V14) @ V12))) @ ((V10 @ ((V2 @ V13) @ V12)) @ V14)))))))))))))))))))))))))))))))))))
(TFinite_Set.comp_fun_idem.fold_insert_idem2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V2) @ ((cSet.insert @ V3) @ V1))) @ (((cFinite_Set.fold @ V0) @ ((V0 @ V3) @ V2)) @ V1)))))))))))))
(TFinite_Set.finite_imp_nat_seg_image_inj_on,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cSet.image @ V2) @ (cSet.Collect @ (^[V3]: ((cNat.ord_nat_inst.less_nat @ V3) @ V1)))))) @ ((cFun.inj_on @ V2) @ (cSet.Collect @ (^[V3]: ((cNat.ord_nat_inst.less_nat @ V3) @ V1)))))))))))))
(TGroups.ab_group_add_class.diff_eq_0_iff_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ V1)))))))
(TGroups.ab_semigroup_mult.mult_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.ab_semigroup_mult @ V0)) @ ((cHOL.eq @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ V2) @ ((V0 @ V1) @ V3)))))))))))))
(TGroups.cancel_ab_semigroup_add_class.intro,((c==> @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.class.cancel_ab_semigroup_add_axioms @ cGroups.plus_class.plus)) @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE))))
(TGroups.cancel_ab_semigroup_add_class.super,((c==> @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ab_semigroup_add_class @ cTYPE)))
(TGroups.class.ab_semigroup_add_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (cGroups.class.ab_semigroup_add_axioms @ V0)))))
(TGroups.class.cancel_ab_semigroup_add.intro,(call @ (^[V0]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((c==> @ (cGroups.class.cancel_ab_semigroup_add_axioms @ V0)) @ (cGroups.class.cancel_ab_semigroup_add @ V0))))))
(TGroups.class.cancel_comm_monoid_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))
(TGroups.class.cancel_comm_monoid_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ (cGroups.class.cancel_ab_semigroup_add @ V0)))))))
(TGroups.class.comm_monoid_diff_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((cHOL.eq @ ((V0 @ V3) @ V1)) @ V3)))) @ ((c==> @ (call @ (^[V3]: ((cHOL.eq @ ((V0 @ V1) @ V3)) @ V1)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((V0 @ ((V2 @ V3) @ V4)) @ ((V2 @ V3) @ V5))) @ ((V0 @ V4) @ V5))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((V0 @ ((V0 @ V3) @ V4)) @ V5)) @ ((V0 @ V3) @ ((V2 @ V4) @ V5)))))))))) @ (((cGroups.class.comm_monoid_diff_axioms @ V2) @ V1) @ V0))))))))))))
(TGroups.class.comm_monoid_mult_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ V2)))) @ ((cGroups.class.comm_monoid_mult_axioms @ V0) @ V1)))))))
(TGroups.class.linordered_ab_group_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cOrderings.class.linorder @ V4) @ V5)) @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TGroups.class.ordered_comm_monoid_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V2) @ V3)) @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3))))))))))))
(TGroups.classrel_comm_monoid_add_monoid_add,(cGroups.monoid_add_class @ cTYPE))
(TGroups.comm_monoid_diff.diff_right_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V3) @ V4)) @ V5)) @ ((V2 @ ((V2 @ V3) @ V5)) @ V4))))))))))))))))
(TGroups.group_add_class.eq_neg_iff_add_eq_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero)))))))
(TGroups.group_add_class.neg_equal_iff_equal,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TGroups.linordered_ab_group_add.double_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V6) @ V6)) @ V1)) @ ((cHOL.eq @ V6) @ V1))))))))))))))))))
(TGroups.linordered_ab_group_add_class.intro,((c==> @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ ((c==> @ (cOrderings.linorder_class @ cTYPE)) @ (cGroups.linordered_ab_group_add_class @ cTYPE))))
(TGroups.linordered_ab_group_add_class.super_2,((c==> @ (cGroups.linordered_ab_group_add_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE)))
(TGroups.linordered_ab_group_add_class.super_1,((c==> @ (cGroups.linordered_ab_group_add_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_class @ cTYPE)))
(TGroups.monoid_mult_class.mult.left_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.one_class.one) @ V0)) @ V0))))
(TGroups.ordered_ab_group_add.less_minus_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V6) @ (V3 @ V7))) @ ((V5 @ V7) @ (V3 @ V6)))))))))))))))))))))
(TGroups.ordered_ab_group_add.minus_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ (V3 @ V6)) @ V7)) @ ((V5 @ (V3 @ V7)) @ V6))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((V5 @ (V0 @ V7)) @ V8)) @ ((cHOL.conj @ ((V5 @ V7) @ V8)) @ ((V5 @ (V4 @ V7)) @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_of_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V6 @ V7) @ V2)) @ ((cHOL.eq @ (V0 @ V7)) @ (V4 @ V7)))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_of_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V6 @ V2) @ V7)) @ ((cHOL.eq @ (V0 @ V7)) @ V7))))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_neg_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V4) @ V1)) @ ((c==> @ ((V3 @ V5) @ V1)) @ ((V3 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_pos_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V1) @ V4)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((V3 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TGroups.ordered_comm_monoid_add_class.intro,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ordered_comm_monoid_add_class @ cTYPE))))
(TGroups.ordered_comm_monoid_add_class.super_2,((c==> @ (cGroups.ordered_comm_monoid_add_class @ cTYPE)) @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)))
(TGroups.ordered_comm_monoid_add_class.super_1,((c==> @ (cGroups.ordered_comm_monoid_add_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TLattices.bounded_lattice_bot.inf_bot_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V5) @ V4)) @ V4)))))))))))))))
(TLattices.bounded_lattice_bot.sup_bot_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V3 @ V5) @ V4)) @ V5)))))))))))))))
(TLattices.bounded_lattice_top.inf_top_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V0 @ V5) @ V4)) @ V5)))))))))))))))
(TLattices.bounded_lattice_top.sup_top_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V3 @ V5) @ V4)) @ V4)))))))))))))))
(TLattices.semilattice_inf_class.inf.absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0)))))))
(TLattices.semilattice_inf_class.inf.absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ V0)) @ V0)))))))
(TLattices.semilattice_inf_class.inf.commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V1) @ V0)))))))
(TLattices.semilattice_inf_class.inf_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0)))))))
(TLattices.semilattice_inf_class.inf_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ V0)) @ V0)))))))
(TLattices.semilattice_inf_class.inf_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V1) @ V0)))))))
(TLattices.semilattice_order.strict_boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ ((V0 @ V4) @ V5))) @ ((c==> @ ((c==> @ ((V2 @ V3) @ V4)) @ ((c==> @ ((V2 @ V3) @ V5)) @ V6))) @ V6))))))))))))))))))
(TLattices.semilattice_sup_class.sup.absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ V0)) @ V1)))))))
(TLattices.semilattice_sup_class.sup.absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V1)))))))
(TLattices.semilattice_sup_class.sup.commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TLattices.semilattice_sup_class.sup_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ V0)) @ V1)))))))
(TLattices.semilattice_sup_class.sup_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V1)))))))
(TLattices.semilattice_sup_class.sup_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TLazy_Sequence.lazy_sequence.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V2) @ V0)) @ ((cLazy_Sequence.lazy_sequence.lazy_sequence_case @ V2) @ V1))))))))))
(TLazy_Sequence.list_of_lazy_sequence_append,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ ((cLazy_Sequence.append @ V0) @ V1))) @ ((cList.append @ (cLazy_Sequence.list_of_lazy_sequence @ V0)) @ (cLazy_Sequence.list_of_lazy_sequence @ V1))))))))
(TLazy_Sequence.list_of_lazy_sequence_single,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ (cLazy_Sequence.single @ V0))) @ ((cList.list.Cons @ V0) @ cList.list.Nil)))))
(TLazy_Sequence.small_lazy_list_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy_list_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((cLazy_Sequence.small_lazy_list_graph @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((V2 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((V2 @ V4) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (cLazy_Sequence.single @ ((cList.list.Cons @ V5) @ V6))))))) @ cLazy_Sequence.empty)))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.small_lazy_list_graph.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ ((cLazy_Sequence.small_lazy_list_graph @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V1 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cLazy_Sequence.small_lazy_list_graph @ V0) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V1 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (cLazy_Sequence.single @ ((cList.list.Cons @ V2) @ V3))))))) @ cLazy_Sequence.empty)))))))))
(TList.ab_group_add_class.uminus_listsum_map,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ V1)))) @ (cList.monoid_add_class.listsum @ ((cList.map @ ((cFun.comp @ cGroups.uminus_class.uminus) @ V0)) @ V1))))))))
(TList.linorder_class.distinct_insort_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.distinct @ V0)) @ (cList.distinct @ (((cList.linorder_class.insort_insert_key @ V1) @ V2) @ V0))))))))))
(TList.linorder_class.insort_insert_key_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ (V0 @ V1)) @ ((cSet.image @ V0) @ (cList.set @ V2)))) @ ((cHOL.eq @ (((cList.linorder_class.insort_insert_key @ V0) @ V1) @ V2)) @ V2)))))))))
(TList.linorder_class.sorted_equals_nth_mono,(call @ (^[V0]: ((cHOL.eq @ (cList.linorder_class.sorted @ V0)) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V1) @ (cNat.size_class.size @ V0))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cList.nth @ V0) @ V2)) @ ((cList.nth @ V0) @ V1))))))))))))
(TList.linorder_class.sorted_list_of_set_def,((cHOL.eq @ cList.linorder_class.sorted_list_of_set) @ ((cFinite_Set.folding.F @ (cList.linorder_class.insort_key @ (^[V0]: V0))) @ cList.list.Nil)))
(TList.monoid_add_class.length_product_lists,(call @ (^[V0]: ((cHOL.eq @ (cNat.size_class.size @ (cList.product_lists @ V0))) @ (((cList.foldr @ cNat.times_nat_inst.times_nat) @ ((cList.map @ cNat.size_class.size) @ V0)) @ cNat.one_nat_inst.one_nat)))))
(TMain.sumbool.full_exhaustive_sumbool.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cMain.full_exhaustive_sumbool_inst.full_exhaustive_sumbool @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cExtraction.sumbool.Left) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cExtraction.sumbool.Right) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))))))) @ cList.list.Nil))))))) @ cOption.option.None)))))))
(TNat.linordered_semidom_class.of_nat_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)))))))
(TNitpick.equal_pair_box_inst.equal_pair_box,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TNitpick.narrowing_word_inst.narrowing_word,((c== @ cNitpick.narrowing_word_inst.narrowing_word) @ cNitpick.narrowing_word_inst.narrowing_word))
(TNitpick.random_fun_box_inst.random_fun_box,((c== @ cNitpick.random_fun_box_inst.random_fun_box) @ cNitpick.random_fun_box_inst.random_fun_box))
(TNum.linordered_idom.less_neg_numeral_simps_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ V7) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_idom.less_neg_numeral_simps_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V7)))))))))))))))))))))))))
(TNum.linordered_idom.less_neg_numeral_simps_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_idom.less_neg_numeral_simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ V3)))))))))))))))))))))))))
(TNum.linordered_idom.less_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ (((cNum.numeral.numeral @ V7) @ V6) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11)))))))))))))))))))))))))))))
(TNum.linordered_idom.less_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ (((cNum.numeral.numeral @ V7) @ V6) @ V11))))))))))))))))))))))))))))
(TNum.linordered_idom.less_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11))) @ ((cNum.ord_num_inst.less_num @ V11) @ V10))))))))))))))))))))))))))))
(TNum.linordered_idom.neg_numeral_le_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V4 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ (((cNum.numeral.numeral @ V7) @ V6) @ V11))))))))))))))))))))))))))))
(TNum.linordered_idom.not_one_le_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V4 @ V7) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_idom_class.sub_non_negative,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cNum.neg_numeral_class.sub @ V0) @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V1) @ V0)))))))
(TNum.linordered_idom_class.sub_non_positive,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cNum.neg_numeral_class.sub @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.linordered_semidom.not_numeral_le_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V4 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V1))))))))))))))))))
(TNum.neg_numeral_class.diff_numeral_special_4,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ cNum.num.One))))))
(TNum.neg_numeral_class.diff_numeral_special_3,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.neg_numeral_class.sub @ V0) @ cNum.num.One)))))
(TNum.neg_numeral_class.diff_numeral_special_2,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ (cNum.numeral_class.numeral @ ((cNum.plus_num_inst.plus_num @ cNum.num.One) @ V0))))))
(TNum.neg_numeral_class.diff_numeral_special_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0)))))
(TNum.numeral_class.one_plus_numeral_commute,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.ring_char_0_class.eq_neg_numeral_simps_7,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.ring_char_0_class.eq_neg_numeral_simps_6,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.ring_char_0_class.eq_neg_numeral_simps_5,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.ring_char_0_class.eq_neg_numeral_simps_4,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.ring_char_0_class.eq_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TNum.ring_char_0_class.eq_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNum.ring_char_0_class.eq_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.ring_char_0_class.neg_numeral_neq_zero,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.ring_char_0_class.zero_neq_neg_numeral,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.semiring_char_0_class.eq_numeral_simps_5,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))))))
(TNum.semiring_char_0_class.eq_numeral_simps_4,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.semiring_char_0_class.eq_numeral_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cHOL.eq @ cNum.num.One) @ V0)))))
(TNum.semiring_char_0_class.eq_numeral_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ cNum.num.One)))))
(TNum.semiring_char_0_class.eq_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TNum.semiring_char_0_class.numeral_neq_zero,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.semiring_char_0_class.zero_neq_numeral,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))))))
(TNum.semiring_numeral.numeral_times_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cNum.class.semiring_numeral @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ (((cNum.numeral.numeral @ V0) @ V2) @ V3)) @ (((cNum.numeral.numeral @ V0) @ V2) @ V4))) @ (((cNum.numeral.numeral @ V0) @ V2) @ ((cNum.times_num_inst.times_num @ V3) @ V4)))))))))))))))
(TNumeral_Simprocs.nat_mult_less_cancel_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cNat.ord_nat_inst.less_nat @ ((cNat.times_nat_inst.times_nat @ V0) @ V1)) @ ((cNat.times_nat_inst.times_nat @ V0) @ V2))) @ ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TOption.option.size_option_inst.size_option,((c== @ cOption.option.size_option_inst.size_option) @ cOption.option.size_option_inst.size_option))
(TOrderings.linorder_class.less_max_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.linorder_class.max_less_iff_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ V2))))))))))
(TOrderings.linorder_class.min_less_iff_conj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TOrderings.linorder_class.min_less_iff_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ V2))))))))))
(TOrderings.order_bot_class.order_bot_axioms,(((cOrderings.class.order_bot @ cOrderings.bot_class.bot) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.order_top_class.order_top_axioms,(((cOrderings.class.order_top @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cOrderings.top_class.top))
(TOrderings.preorder_class.less_imp_not_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V1) @ V0))) @ cHOL.True)))))))
(TOrderings.wellorder_class.wellorder_axioms,((cOrderings.class.wellorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TPower.comm_semiring_1_class.dvd_power_same,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V1) @ V2))))))))))
(TPower.linordered_idom_class.zero_le_power2,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TPower.linordered_semidom.power_inject_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cHOL.eq @ ((((cPower.power.power @ V3) @ V2) @ V6) @ (cNat.Suc @ V7))) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ (cNat.Suc @ V7)))) @ ((c==> @ ((V4 @ V1) @ V6)) @ ((c==> @ ((V4 @ V1) @ V8)) @ ((cHOL.eq @ V6) @ V8))))))))))))))))))))))))
(TPower.linordered_semidom.power_strict_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V6) @ V7)) @ ((c==> @ ((V4 @ V1) @ V6)) @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V8)) @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V8)) @ ((((cPower.power.power @ V3) @ V2) @ V7) @ V8)))))))))))))))))))))))))
(TPower.monoid_mult_class.funpow_times_power,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cNat.compow @ (V0 @ V1)) @ (cGroups.times_class.times @ V1))) @ (cGroups.times_class.times @ ((cPower.power_class.power @ V1) @ (V0 @ V1)))))))))
(TPower.monoid_mult_class.power_numeral_even,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ V1)))) @ ((cHOL.Let @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ V1))) @ (^[V2]: ((cGroups.times_class.times @ V2) @ V2)))))))))
(TPower.semiring_numeral_class.power_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.pow @ V0) @ V1))))))))
(TProduct_Type.prod.prod_size_overloaded_def,((c== @ cNat.size_class.size) @ (cProduct_Type.prod.prod_rec @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat)))))
(TProduct_Type.prod.size_prod_inst.size_prod,((c== @ cProduct_Type.prod.size_prod_inst.size_prod) @ cProduct_Type.prod.size_prod_inst.size_prod))
(TProduct_Type.unit.size_unit_inst.size_unit,((c== @ cProduct_Type.unit.size_unit_inst.size_unit) @ cProduct_Type.unit.size_unit_inst.size_unit))
(TProduct_Type.unit.unit_size_overloaded_def,((c== @ cProduct_Type.unit.size_unit_inst.size_unit) @ (cProduct_Type.unit.unit_rec @ cNat.zero_nat_inst.zero_nat)))
(TQuickcheck_Exhaustive.arity_check_all_bool,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_char,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_prod,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_unit,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_exhaustive_fun,(cQuickcheck_Exhaustive.exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_exhaustive_int,(cQuickcheck_Exhaustive.exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_exhaustive_nat,(cQuickcheck_Exhaustive.exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_exhaustive_set,(cQuickcheck_Exhaustive.exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_random_unknown,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_nibble_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_nibble_inst.check_all_nibble @ V0)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble0) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble1) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble2) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble3) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble4) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble5) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble6) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble7) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble8) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble9) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleA) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleB) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleC) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleD) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleE) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleF) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))))))))))))))))))))
(TQuickcheck_Exhaustive.check_all_option_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_class.check_all @ V0)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cOption.option.None) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V1]: (^[V2]: (V0 @ ((cProduct_Type.Pair @ (cOption.option.Some @ V1)) @ (^[V3]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V2 @ cProduct_Type.Unity))))))))))))))
(TQuickcheck_Exhaustive.enum_term_of_fun_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_class.enum_term_of) @ (^[V0]: (^[V1]: ((cHOL.Let @ (cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE)) @ (^[V2]: ((cHOL.Let @ (((cQuickcheck_Exhaustive.mk_map_term @ (^[V3]: (cTyperep.typerep_class.typerep @ cTYPE))) @ (^[V3]: (cTyperep.typerep_class.typerep @ cTYPE))) @ V2)) @ (^[V3]: ((cList.map @ (^[V4]: ((V3 @ (^[V5]: V4)) @ cProduct_Type.Unity))) @ ((cList.n_lists @ (cNat.size_class.size @ (V2 @ cProduct_Type.Unity))) @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity)))))))))))
(TQuickcheck_Exhaustive.enum_term_of_set_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ V0) @ V1)) @ ((cList.map @ (cQuickcheck_Exhaustive.term_syntax.setify @ cTYPE)) @ (cList.sublists @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity)))))))))
(TQuickcheck_Exhaustive.enum_term_of_sum_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_class.enum_term_of) @ (^[V0]: (^[V1]: ((cHOL.Let @ (cTyperep.typerep_class.typerep @ cTYPE)) @ (^[V2]: ((cHOL.Let @ (cTyperep.typerep_class.typerep @ cTYPE)) @ (^[V3]: ((cList.append @ ((cList.map @ (cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ cList.list.Nil)))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity))) @ ((cList.map @ (cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ V2) @ ((cList.list.Cons @ V3) @ cList.list.Nil)))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity)))))))))))
(TQuickcheck_Exhaustive.exhaustive_class_def,((c== @ (cQuickcheck_Exhaustive.exhaustive_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TQuickcheck_Exhaustive.exhaustive_set.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_set.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cOrderings.bot_class.bot)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ V3)))))))) @ V3)))))))))))
(TQuickcheck_Exhaustive.exhaustive_set.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ cOrderings.bot_class.bot)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V2]: ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V3]: (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ cOption.option.None) @ (V0 @ ((cSet.insert @ V3) @ V2))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))))))))
(TQuickcheck_Exhaustive.neg_bound_cps_if_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.neg_bound_cps_if @ V0)) @ (((cHOL.If @ V0) @ (cQuickcheck_Exhaustive.neg_bound_cps_single @ cProduct_Type.Unity)) @ cQuickcheck_Exhaustive.neg_bound_cps_empty)))))
(TQuickcheck_Exhaustive.pos_bound_cps_if_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.pos_bound_cps_if @ V0)) @ (((cHOL.If @ V0) @ (cQuickcheck_Exhaustive.pos_bound_cps_single @ cProduct_Type.Unity)) @ cQuickcheck_Exhaustive.pos_bound_cps_empty)))))
(TQuickcheck_Exhaustive.term_of_unknown_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TQuickcheck_Exhaustive.three_valued.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Exhaustive.three_valued.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.three_valued.Value @ V2))) @ V1)))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V0) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ V1)) @ V1))))))))
(TQuickcheck_Exhaustive.three_valued.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((c==> @ (call @ (^[V2]: (V0 @ (cQuickcheck_Exhaustive.three_valued.Value @ V2))))) @ ((c==> @ (V0 @ cQuickcheck_Exhaustive.three_valued.No_value)) @ (V0 @ V1)))))))))
(TQuickcheck_Narrowing.arity_is_testable_fun,(cQuickcheck_Narrowing.is_testable_class @ cTYPE))
(TQuickcheck_Narrowing.arity_random_property,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero_graph_def,((c== @ cQuickcheck_Narrowing.around_zero_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V4)) @ cList.list.Nil))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int))) @ ((V0 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)))))))))))))))))
(TQuickcheck_Narrowing.around_zero_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.around_zero_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))) @ ((c==> @ ((cHOL.eq @ V1) @ V3)) @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int))) @ V2))))))) @ V2)))))))))
(TQuickcheck_Narrowing.around_zero_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.around_zero_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cInt.minus_int_inst.minus_int @ V2) @ cInt.one_int_inst.one_int))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.conj @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V2) @ cInt.zero_int_inst.zero_int))) @ (cHOL.Not @ ((cHOL.eq @ V2) @ cInt.zero_int_inst.zero_int)))))))))))))
(TQuickcheck_Narrowing.cfun.Abs_cfun_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.cfun.cfun_rep_set))) @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_cfun @ (cQuickcheck_Narrowing.Abs_cfun @ V0))) @ V0)))))
(TQuickcheck_Narrowing.cfun.Rep_cfun_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_cfun @ (cQuickcheck_Narrowing.Rep_cfun @ V0))) @ V0))))
(TQuickcheck_Narrowing.cfun.cfun_rec_set_def,((c== @ cQuickcheck_Narrowing.cfun.cfun_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.cfun.Constant @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4))))))))))))
(TQuickcheck_Narrowing.cfun.cfun_rep_set_def,((c== @ cQuickcheck_Narrowing.cfun.cfun_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.Leaf @ V2)))))))))
(TQuickcheck_Narrowing.cfun.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_cfun @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.cfun.Constant) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Narrowing.ffun.Abs_ffun_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.ffun.ffun_rep_set))) @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_ffun @ (cQuickcheck_Narrowing.Abs_ffun @ V0))) @ V0)))))
(TQuickcheck_Narrowing.ffun.Rep_ffun_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_ffun @ (cQuickcheck_Narrowing.Rep_ffun @ V0))) @ V0))))
(TQuickcheck_Narrowing.ffun.ffun_rec_set_def,((c== @ cQuickcheck_Narrowing.ffun.ffun_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Narrowing.ffun.Constant @ V5))) @ ((cHOL.eq @ V4) @ (V0 @ V5)))))) @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.ffun.Update @ V7) @ V8) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((((V1 @ V7) @ V8) @ V5) @ V6))) @ ((V2 @ V5) @ V6))))))))))))))))))))
(TQuickcheck_Narrowing.ffun.ffun_rep_set_def,((c== @ cQuickcheck_Narrowing.ffun.ffun_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.In0 @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V4))) @ V2))))) @ (V0 @ V2))))))))))))))
(TQuickcheck_Narrowing.ffun.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_ffun @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_ffun @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.ffun.Update) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)) @ V5)))))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.ffun.Constant) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Narrowing.is_testable_class_def,((c== @ (cQuickcheck_Narrowing.is_testable_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TQuickcheck_Narrowing.narrowing_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cQuickcheck_Narrowing.narrowing_class @ cTYPE)))
(TQuickcheck_Narrowing.narrowing_class.super,((c==> @ (cQuickcheck_Narrowing.narrowing_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TQuickcheck_Narrowing.narrowing_cons.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.narrowing_cons.inject,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_cons.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TQuickcheck_Narrowing.narrowing_cons.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cHOL.eq @ V2) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V3) @ V4))) @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))
(TQuickcheck_Narrowing.narrowing_integer_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_integer_inst.narrowing_integer @ V0)) @ ((cHOL.Let @ cQuickcheck_Narrowing.conv) @ (^[V1]: ((cHOL.Let @ (cCode_Numeral.int_of_integer @ V0)) @ (^[V2]: (cQuickcheck_Narrowing.drawn_from @ ((cList.map @ cCode_Numeral.integer_of_int) @ (cQuickcheck_Narrowing.around_zero @ V2)))))))))))
(TQuickcheck_Narrowing.narrowing_term.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (V0 @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V1 @ V5)) @ (V0 @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5)))))))) @ ((c==> @ (V1 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V0 @ V4)) @ ((c==> @ (V1 @ V5)) @ (V1 @ ((cList.list.Cons @ V4) @ V5))))))))) @ ((cHOL.conj @ (V0 @ V2)) @ (V1 @ V3)))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.inject_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.inject_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))) @ (cHOL.Not @ (V0 @ ((V1 @ V4) @ V5))))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5))) @ (cHOL.Not @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V1) @ V2) @ V3))) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))) @ (V0 @ ((V1 @ V4) @ V5)))))))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5))) @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: ((c==> @ (V0 @ V6)) @ (V1 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V6)))))) @ ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (V2 @ V6)) @ ((c==> @ (V0 @ V7)) @ (V0 @ ((cList.list.Cons @ V6) @ V7))))))))) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (V1 @ V6)) @ ((c==> @ (V2 @ V7)) @ (V2 @ ((cList.list.Cons @ V6) @ V7))))))))) @ ((cHOL.conj @ (V1 @ V3)) @ ((cHOL.conj @ (V0 @ V4)) @ (V2 @ V5)))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0)) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.splits_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.splits_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ (V0 @ (V1 @ V3)))))))))))))
(TQuickcheck_Narrowing.non_empty.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Narrowing.non_empty_rel) @ V1)))))))
(TQuickcheck_Narrowing.non_empty_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.non_empty_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4))) @ ((c==> @ ((cHOL.eq @ V1) @ (cHOL.Not @ (cList.null @ V4)))) @ V2))))))) @ V2)))))))))
(TQuickcheck_Narrowing.non_empty_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.non_empty_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ ((cHOL.eq @ V1) @ (cHOL.Not @ (cList.null @ V3))))))))))))))
(TQuickcheck_Narrowing.non_empty_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.non_empty_rel @ V0) @ V1)) @ ((V2 @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.property.Property_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Narrowing.property.Property @ V0)) @ (cQuickcheck_Narrowing.Abs_property @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.Leaf @ (cSum_Type.Inl @ V0)))))))))
(TQuickcheck_Narrowing.property.Rep_property,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Narrowing.Rep_property @ V0)) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set)))))
(TQuickcheck_Narrowing.term_of_property_triv,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.term_of_property_inst.term_of_property @ V0)) @ cHOL.undefined))))
(TQuickcheck_Random.random_lazy_sequence_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Random.random_aux_lazy_sequence @ V0) @ V0)))))
(TQuickcheck_Random.typerep.random_aux.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_typerep_list @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ ((cQuickcheck_Random.beyond @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_typerep @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_typerep_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Random.typerep.random_aux.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_typerep @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_literal_inst.random_literal @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Random.random_aux_typerep_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cTyperep.typerep.Typerep) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))))))))
(TRings.class.linordered_semiring_strict_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cHOL.conj @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V2) @ V3))) @ ((cHOL.conj @ ((cRings.class.semiring @ V0) @ V4)) @ (((cRings.class.linordered_semiring_strict_axioms @ V1) @ V3) @ V4)))))))))))))))
(TRings.class.ordered_cancel_semiring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cRings.class.ordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))
(TRings.class.ordered_cancel_semiring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)))))))))))))
(TRings.class.ring_1_no_zero_divisors.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cRings.class.ring_no_zero_divisors @ V1) @ V3) @ V2) @ V4) @ V5)))))))))))))))
(TRings.class.ring_1_no_zero_divisors.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cRings.class.ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))
(TRings.comm_ring_1_class.comm_ring_1_axioms,((((((cRings.class.comm_ring_1 @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TRings.comm_semiring_1_class.dvd_0_left_iff,(call @ (^[V0]: ((cHOL.eq @ ((cRings.dvd_class.dvd @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TRings.comm_semiring_1_class.dvd_mult_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cRings.dvd_class.dvd @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cRings.dvd_class.dvd @ V1) @ V2)))))))))
(TRings.comm_semiring_1_class.dvd_triv_right,(call @ (^[V0]: (call @ (^[V1]: ((cRings.dvd_class.dvd @ V0) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TRings.linordered_idom.mult_le_cancel_left1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ V10) @ ((V9 @ V10) @ V11))) @ ((cHOL.conj @ ((cHOL.implies @ ((V5 @ V3) @ V10)) @ ((V4 @ V7) @ V11))) @ ((cHOL.implies @ ((V5 @ V10) @ V3)) @ ((V4 @ V11) @ V7))))))))))))))))))))))))))))))
(TRings.linordered_idom.mult_le_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ ((V9 @ V10) @ V11)) @ V10)) @ ((cHOL.conj @ ((cHOL.implies @ ((V5 @ V3) @ V10)) @ ((V4 @ V11) @ V7))) @ ((cHOL.implies @ ((V5 @ V10) @ V3)) @ ((V4 @ V7) @ V11))))))))))))))))))))))))))))))
(TRings.linordered_idom.mult_right_le_one_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V4 @ V3) @ V10)) @ ((c==> @ ((V4 @ V3) @ V11)) @ ((c==> @ ((V4 @ V11) @ V7)) @ ((V4 @ ((V9 @ V10) @ V11)) @ V10))))))))))))))))))))))))))))))
(TRings.linordered_ring.not_square_less_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (cHOL.Not @ ((V5 @ ((V7 @ V8) @ V8)) @ V3))))))))))))))))))))))
(TRings.linordered_ring_class.zero_le_square,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V0)))))
(TRings.linordered_ring_strict.mult_le_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ ((V7 @ V8) @ V9)) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((V4 @ V3) @ V8)) @ ((V4 @ V9) @ V3))) @ ((cHOL.conj @ ((V4 @ V8) @ V3)) @ ((V4 @ V3) @ V9))))))))))))))))))))))))))
(TRings.linordered_semidom.not_one_less_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ V3) @ V1))))))))))))))))
(TRings.linordered_semidom_class.less_1_mult,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.linordered_semidom_class.zero_le_one,((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TRings.linordered_semiring_strict_class_def,((c== @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cGroups.comm_monoid_add_class @ cTYPE)) @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE))) @ ((cPure.conjunction @ (cRings.semiring_class @ cTYPE)) @ (((cRings.class.linordered_semiring_strict_axioms @ cGroups.zero_class.zero) @ cOrderings.ord_class.less) @ cGroups.times_class.times)))))
(TRings.no_zero_divisors_class.divisors_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))
(TRings.ordered_ring_class.split_mult_pos_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))))))))
(TRings.semiring_class.combine_common_factor,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V2) @ V1)) @ V3))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)) @ V3)))))))))))
(TSMT.pattern.size_pattern_inst.size_pattern,((c== @ cSMT.pattern.size_pattern_inst.size_pattern) @ cSMT.pattern.size_pattern_inst.size_pattern))
(TSet_Interval.dvd.atLeastLessThan_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((((cSet_Interval.ord.atLeastLessThan @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))))
(TSet_Interval.dvd.atLeastatMost_psubset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.disj @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V0)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V2)))) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V1)))))))) @ ((cRings.dvd_class.dvd @ V2) @ V3))))))))))))
(TSet_Interval.dvd.greaterThanLessThan_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ (((cSet_Interval.ord.greaterThanLessThan @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TSet_Interval.dvd.not_empty_eq_Ici_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord.atLeast @ cRings.dvd_class.dvd) @ V0))))))
(TSet_Interval.dvd.not_empty_eq_Iic_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord.atMost @ cRings.dvd_class.dvd) @ V0))))))
(TSet_Interval.finite_nat_set_iff_bounded_le,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V1)))))))))
(TSet_Interval.image_add_int_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ (^[V2]: ((cInt.plus_int_inst.plus_int @ V2) @ V0))) @ ((cSet_Interval.ord_class.atLeastLessThan @ cInt.zero_int_inst.zero_int) @ ((cInt.minus_int_inst.minus_int @ V1) @ V0)))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)))))))
(TSet_Interval.image_atLeastZeroLessThan_int,(call @ (^[V0]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ (cSet_Interval.ord_class.lessThan @ (cInt.nat @ V0))))))))
(TSet_Interval.ord_class.atLeastLessThan_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atLeast @ V0)) @ (cSet_Interval.ord_class.lessThan @ V1))))))))
(TSet_Interval.ord_class.atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet_Interval.order.atLeastAtMost_singleton,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V2)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))))))))))
(TSet_Interval.order.atLeastatMost_empty_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((V0 @ V2) @ V3)))))))))))))
(TSet_Interval.order.greaterThanAtMost_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V3) @ V2)) @ cOrderings.bot_class.bot))))))))))))
(TSet_Interval.order_bot.atLeast_eq_UNIV_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cOrderings.class.order_bot @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord.atLeast @ V1) @ V3)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ V3) @ V0))))))))))))
(TString.nibble.size_nibble_inst.size_nibble,((c== @ cString.nibble.size_nibble_inst.size_nibble) @ cString.nibble.size_nibble_inst.size_nibble))
(TTransitive_Closure.converse_rtrancl_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ (V3 @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V5)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ (V3 @ V5)) @ (V3 @ V4))))))))) @ (V3 @ V0)))))))))))))
(TTransitive_Closure.converse_tranclp_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((V0 @ V4) @ V2)) @ (V3 @ V4))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V5) @ V2)) @ ((c==> @ (V3 @ V5)) @ (V3 @ V4))))))))) @ (V3 @ V1)))))))))))))
(TTransitive_Closure.rtrancl_idemp_self_comp,(call @ (^[V0]: ((cHOL.eq @ ((cRelation.relcomp @ (cTransitive_Closure.rtrancl @ V0)) @ (cTransitive_Closure.rtrancl @ V0))) @ (cTransitive_Closure.rtrancl @ V0)))))
(TTransitive_Closure.rtranclp_is_Sup_relpowp,(call @ (^[V0]: ((cHOL.eq @ (cTransitive_Closure.rtranclp @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: ((cNat.compow @ V1) @ V0)))))))
(TTransitive_Closure.single_valued_confluent,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRelation.single_valued @ V0)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V2)) @ (cTransitive_Closure.rtrancl @ V0))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V0))) @ ((cHOL.disj @ ((cSet.member @ ((cProduct_Type.Pair @ V2) @ V3)) @ (cTransitive_Closure.rtrancl @ V0))) @ ((cSet.member @ ((cProduct_Type.Pair @ V3) @ V2)) @ (cTransitive_Closure.rtrancl @ V0)))))))))))))))
(TTransitive_Closure.trancl_finite_eq_relpow,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cTransitive_Closure.trancl @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ (cFinite_Set.card @ V0)))))) @ (^[V1]: ((cNat.compow @ V1) @ V0))))))))
(TTransitive_Closure.trancl_subset_Sigma_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ ((cProduct_Type.Sigma @ V3) @ (^[V4]: V3)))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V1)) @ ((cSet.member @ V0) @ V3)))))))))))))
(TTyperep.typerep_itself_inst.typerep_itself,((c== @ cTyperep.typerep_itself_inst.typerep_itself) @ cTyperep.typerep_itself_inst.typerep_itself))
(TTyperep.typerep_nibble_inst.typerep_nibble,((c== @ cTyperep.typerep_nibble_inst.typerep_nibble) @ cTyperep.typerep_nibble_inst.typerep_nibble))
(TTyperep.typerep_option_inst.typerep_option,((c== @ cTyperep.typerep_option_inst.typerep_option) @ cTyperep.typerep_option_inst.typerep_option))
(TBig_Operators.comm_monoid_set.insert_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V3) @ ((cSet.insert @ V4) @ V2))) @ ((V0 @ (V3 @ V4)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V3) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V4) @ cOrderings.bot_class.bot))))))))))))))))))
(TBig_Operators.comm_monoid_set.neutral_const,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V3]: V1)) @ V2)) @ V1)))))))))
(TBig_Operators.linorder_class.Max.coboundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.linorder_class.Max @ V0)))))))))
(TBig_Operators.linorder_class.Min.coboundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Min @ V0)) @ V1))))))))
(TBig_Operators.semilattice_neutr_set.eq_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((cHOL.eq @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2)) @ (((cFinite_Set.fold @ V0) @ V1) @ V2))))))))))
(TBig_Operators.semilattice_neutr_set.in_idem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2))) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2))))))))))))))
(TBig_Operators.semilattice_set.insert_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cSet.insert @ V2) @ V1))) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V2) @ ((V0 @ V2) @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))))))
(TCode_Evaluation.arity_term_of_lazy_sequence,(cCode_Evaluation.term_of_class @ cTYPE))
(TCode_Evaluation.arity_typerep_lazy_sequence,(cTyperep.typerep_class @ cTYPE))
(TCode_Numeral.arity_comm_monoid_diff_natural,(cGroups.comm_monoid_diff_class @ cTYPE))
(TCode_Numeral.integer.int_of_integer_inverse,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.integer_of_int @ (cCode_Numeral.int_of_integer @ V0))) @ V0))))
(TCode_Numeral.integer.integer_of_int_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_int @ V0))) @ V0)))))
(TCode_Numeral.natural.nat_of_natural_inverse,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.natural_of_nat @ (cCode_Numeral.nat_of_natural @ V0))) @ V0))))
(TCode_Numeral.natural.natural_of_nat_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (cCode_Numeral.nat_of_natural @ (cCode_Numeral.natural_of_nat @ V0))) @ V0)))))
(TCode_Numeral.natural.natural_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TCode_Numeral.natural.natural_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ (cCode_Numeral.Suc @ V2)) @ ((V1 @ V2) @ V3))))))))))))
(TCode_Numeral.natural.natural_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cCode_Numeral.natural.natural_rec_set @ V0) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural) @ V0))))))
(TCode_Numeral.plus_integer_inst.plus_integer,((c== @ cCode_Numeral.plus_integer_inst.plus_integer) @ cCode_Numeral.plus_integer_inst.plus_integer))
(TCode_Numeral.plus_natural_inst.plus_natural,((c== @ cCode_Numeral.plus_natural_inst.plus_natural) @ cCode_Numeral.plus_natural_inst.plus_natural))
(TCode_Numeral.zero_integer_inst.zero_integer,((c== @ cCode_Numeral.zero_integer_inst.zero_integer) @ cCode_Numeral.zero_integer_inst.zero_integer))
(TCode_Numeral.zero_natural_inst.zero_natural,((c== @ cCode_Numeral.zero_natural_inst.zero_natural) @ cCode_Numeral.zero_natural_inst.zero_natural))
(TComplete_Lattices.complete_lattice.INF_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ V8) @ V9)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V9)) @ ((cHOL.eq @ (V10 @ V12)) @ (V11 @ V12)))))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V12]: (V10 @ V12)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V12]: (V11 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((cSet.Bex @ V9) @ (^[V13]: ((V3 @ (V10 @ V13)) @ (V11 @ V12)))))))) @ ((V3 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V12]: (V10 @ V12)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V12]: (V11 @ V12)))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ cOrderings.top_class.top)) @ V6)))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((cSet.Bex @ V9) @ (^[V11]: ((V3 @ V11) @ V10))))))) @ ((V3 @ (V0 @ V9)) @ (V0 @ V8)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ V8) @ V9)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V9)) @ ((cHOL.eq @ (V10 @ V12)) @ (V11 @ V12)))))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: (V10 @ V12)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V12]: (V11 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((cSet.Bex @ V9) @ (^[V13]: ((V3 @ (V10 @ V12)) @ (V11 @ V13)))))))) @ ((V3 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: (V10 @ V12)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V12]: (V11 @ V12)))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_UNIV,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ cOrderings.top_class.top)) @ V7)))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((cSet.Bex @ V9) @ (^[V11]: ((V3 @ V10) @ V11))))))) @ ((V3 @ (V1 @ V8)) @ (V1 @ V9)))))))))))))))))))))))))
(TComplete_Partial_Order.ccpo.admissible_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V5]: (V3 @ V5)))) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V5]: (V4 @ V5)))) @ (((cComplete_Partial_Order.ccpo.admissible @ V0) @ V1) @ (^[V5]: ((cHOL.disj @ (V3 @ V5)) @ (V4 @ V5))))))))))))))))))
(TComplete_Partial_Order.ccpo.fixp_lowerbound,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ (((cComplete_Partial_Order.monotone @ V1) @ V1) @ V3)) @ ((c==> @ ((V1 @ (V3 @ V4)) @ V4)) @ ((V1 @ (((cComplete_Partial_Order.ccpo.fixp @ V0) @ V1) @ V3)) @ V4)))))))))))))))
(TComplete_Partial_Order.ccpo.iterates.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((c==> @ (V5 @ V6)) @ (V5 @ (V4 @ V6))))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V6)) @ ((c==> @ ((cSet.Ball @ V6) @ (^[V7]: ((cHOL.conj @ ((cSet.member @ V7) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ (V5 @ V7))))) @ (V5 @ (V0 @ V6))))))) @ (V5 @ V3))))))))))))))))))
(TComplete_Partial_Order.ccpo.iterates.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V5]: ((cSet.member @ V5) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))))) @ ((cSet.member @ (V0 @ V3)) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))))))))))))))))
(TComplete_Partial_Order.ccpo.iterates.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((cSet.member @ (V4 @ V3)) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4)))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V4)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V4) @ (V3 @ V6))) @ ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V6)) @ V5))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V4) @ (V0 @ V6))) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V6)) @ ((c==> @ ((cSet.Ball @ V6) @ (^[V7]: ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V7)))) @ V5)))))) @ V5)))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V4)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (V3 @ V5))) @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V5))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (V0 @ V5))) @ ((cHOL.conj @ ((cComplete_Partial_Order.chain @ V1) @ V5)) @ ((cSet.Ball @ V5) @ (^[V6]: ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V6)))))))))))))))))))))
(TDivides.semiring_div_class.div_mod_equality,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cDivides.div_class.div @ V0) @ V1)) @ V1)) @ ((cDivides.div_class.mod @ V0) @ V1))) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))
(TDivides.semiring_div_class.mod_add_right_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.plus_class.plus @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)))))))))
(TDivides.semiring_div_class.mod_div_equality,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ ((cDivides.div_class.div @ V0) @ V1)) @ V1)) @ ((cDivides.div_class.mod @ V0) @ V1))) @ V0))))))
(TDivides.semiring_div_class.mod_mult_left_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ ((cDivides.div_class.mod @ V0) @ V2)) @ V1)) @ V2)))))))))
(TDivides.semiring_numeral_div.divmod_digit_0_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V8 @ V4) @ V9)) @ ((c==> @ ((V8 @ ((V2 @ V10) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V9))) @ V9)) @ ((cHOL.eq @ ((V2 @ V10) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V9))) @ ((V2 @ V10) @ V9))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.divmod_digit_0_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V8 @ V4) @ V9)) @ ((c==> @ ((V8 @ ((V2 @ V10) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V9))) @ V9)) @ ((cHOL.eq @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ ((V1 @ V10) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V9)))) @ ((V1 @ V10) @ V9))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.divmod_digit_1_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V4) @ V9)) @ ((c==> @ ((V8 @ V4) @ V10)) @ ((c==> @ ((V7 @ V10) @ ((V2 @ V9) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V10)))) @ ((cHOL.eq @ ((V6 @ ((V2 @ V9) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V10))) @ V10)) @ ((V2 @ V9) @ V10)))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.divmod_digit_1_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V4) @ V9)) @ ((c==> @ ((V8 @ V4) @ V10)) @ ((c==> @ ((V7 @ V10) @ ((V2 @ V9) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V10)))) @ ((cHOL.eq @ ((V3 @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ ((V1 @ V9) @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V10)))) @ V5)) @ ((V1 @ V9) @ V10)))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.divmod_step_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ (((((((cDivides.semiring_numeral_div.divmod_step @ V0) @ V3) @ V5) @ V6) @ V7) @ V9) @ ((cProduct_Type.Pair @ V10) @ V11))) @ (((cHOL.If @ ((V7 @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)) @ V11)) @ ((cProduct_Type.Pair @ ((V3 @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V10)) @ V5)) @ ((V6 @ V11) @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)))) @ ((cProduct_Type.Pair @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V10)) @ V11)))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div_class.discrete,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.one_class.one)) @ V1)))))))
(TDivides.semiring_numeral_div_class.div_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_class.div @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TDivides.semiring_numeral_div_class.mod_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cDivides.div_class.mod @ V0) @ V1)) @ V0))))))))
(TExtraction.equal_sumbool_inst.equal_sumbool,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TFields.class.division_ring_inverse_zero_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cFields.class.division_ring_inverse_zero_axioms @ V0) @ V5))))))))))))))))))))
(TFields.division_ring_class.divide_zero_left,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TFields.division_ring_class.right_inverse_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ cGroups.one_class.one)) @ ((cHOL.eq @ V1) @ V0))))))))
(TFields.division_ring_inverse_zero_class_def,((c== @ (cFields.division_ring_inverse_zero_class @ cTYPE)) @ ((cPure.conjunction @ (cFields.division_ring_class @ cTYPE)) @ ((cFields.class.division_ring_inverse_zero_axioms @ cFields.inverse_class.inverse) @ cGroups.zero_class.zero))))
(TFields.field_inverse_zero.one_eq_divide_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ V3) @ ((V1 @ V8) @ V9))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ V8) @ V9)))))))))))))))))))))))))
(TFields.linordered_field.mult_imp_div_pos_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V9 @ V13) @ ((V2 @ V14) @ V12))) @ ((V9 @ ((V1 @ V13) @ V12)) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.mult_imp_le_div_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V9 @ ((V2 @ V13) @ V12)) @ V14)) @ ((V9 @ V13) @ ((V1 @ V14) @ V12))))))))))))))))))))))))))))))))))))
(TFields.linordered_field.nonzero_abs_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V12) @ V5))) @ ((cHOL.eq @ (V8 @ (V0 @ V12))) @ (V0 @ (V8 @ V12))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.less_half_sum,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ cGroups.one_class.one)))))))))
(TFinite_Set.comp_fun_commute.fold_graph_fold,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((((cFinite_Set.fold_graph @ V0) @ V2) @ V1) @ (((cFinite_Set.fold @ V0) @ V2) @ V1)))))))))))
(TFinite_Set.comp_fun_idem.comp_comp_fun_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.comp_fun_idem @ V0)) @ (cFinite_Set.comp_fun_idem @ ((cFun.comp @ V0) @ V1))))))))
(TGroups.ab_group_add_class.minus_add_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cGroups.plus_class.plus @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TGroups.ab_semigroup_mult_class.mult.commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TGroups.ab_semigroup_mult_class.mult_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TGroups.cancel_ab_semigroup_add_class.axioms,(cGroups.class.cancel_ab_semigroup_add_axioms @ cGroups.plus_class.plus))
(TGroups.cancel_semigroup_add.add_left_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.cancel_semigroup_add @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TGroups.cancel_semigroup_add.add_left_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.cancel_semigroup_add @ V0)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TGroups.class.ab_semigroup_mult_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (cGroups.class.ab_semigroup_mult_axioms @ V0)))))
(TGroups.class.cancel_ab_semigroup_add.axioms_2,(call @ (^[V0]: ((c==> @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ (cGroups.class.cancel_ab_semigroup_add_axioms @ V0)))))
(TGroups.class.cancel_ab_semigroup_add.axioms_1,(call @ (^[V0]: ((c==> @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ (cGroups.class.ab_semigroup_add @ V0)))))
(TGroups.class.linordered_ab_group_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cOrderings.class.linorder @ V4) @ V5)))))))))))))))
(TGroups.class.linordered_ab_group_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))
(TGroups.class.ordered_ab_group_add_abs.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (((((cGroups.class.ordered_ab_group_add_abs_axioms @ V6) @ V0) @ V1) @ V3) @ V4)) @ (((((((cGroups.class.ordered_ab_group_add_abs @ V6) @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))))
(TGroups.class.ordered_ab_semigroup_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cGroups.class.ab_semigroup_add @ V0)) @ ((c==> @ ((cOrderings.class.order @ V1) @ V2)) @ ((c==> @ ((cGroups.class.ordered_ab_semigroup_add_axioms @ V0) @ V1)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)))))))))))
(TGroups.class.ordered_comm_monoid_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V2) @ V3)))))))))))
(TGroups.class.ordered_comm_monoid_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))))))
(TGroups.comm_monoid_diff_class.diff_add_zero,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.plus_class.plus @ V0) @ V1))) @ cGroups.zero_class.zero))))))
(TGroups.comm_monoid_diff_class.diff_diff_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TGroups.monoid_mult_class.monoid_mult_axioms,((cGroups.class.monoid_mult @ cGroups.one_class.one) @ cGroups.times_class.times))
(TGroups.monoid_mult_class.mult.monoid_axioms,((cGroups.monoid @ cGroups.times_class.times) @ cGroups.one_class.one))
(TGroups.monoid_mult_class.mult.right_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.one_class.one)) @ V0))))
(TGroups.ordered_ab_group_add.neg_0_le_iff_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V1) @ (V3 @ V6))) @ ((V4 @ V6) @ V1))))))))))))))))))
(TGroups.ordered_ab_group_add.neg_le_0_iff_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (V3 @ V6)) @ V1)) @ ((V4 @ V1) @ V6))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_add_abs,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ (V0 @ ((V1 @ (V0 @ V7)) @ (V0 @ V8)))) @ ((V1 @ (V0 @ V7)) @ (V0 @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_ge_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ V7) @ (V0 @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_ge_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ V2) @ (V0 @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.intro,((c==> @ (cGroups.abs_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_ab_group_add_class @ cTYPE)) @ ((c==> @ (((((cGroups.class.ordered_ab_group_add_abs_axioms @ cGroups.abs_class.abs) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus) @ cOrderings.ord_class.less_eq)) @ (cGroups.ordered_ab_group_add_abs_class @ cTYPE)))))
(TGroups.ordered_ab_group_add_abs_class.super_2,((c==> @ (cGroups.ordered_ab_group_add_abs_class @ cTYPE)) @ (cGroups.ordered_ab_group_add_class @ cTYPE)))
(TGroups.ordered_ab_group_add_abs_class.super_1,((c==> @ (cGroups.ordered_ab_group_add_abs_class @ cTYPE)) @ (cGroups.abs_class @ cTYPE)))
(TGroups.ordered_ab_semigroup_add_class.intro,((c==> @ (cGroups.ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cOrderings.order_class @ cTYPE)) @ ((c==> @ ((cGroups.class.ordered_ab_semigroup_add_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)))))
(TGroups.ordered_ab_semigroup_add_class.super_2,((c==> @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ (cOrderings.order_class @ cTYPE)))
(TGroups.ordered_ab_semigroup_add_class.super_1,((c==> @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ab_semigroup_add_class @ cTYPE)))
(TInt.linordered_idom_class.of_int_0_less_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cInt.ring_1_class.of_int @ V0))) @ ((cInt.ord_int_inst.less_int @ cInt.zero_int_inst.zero_int) @ V0)))))
(TInt.linordered_idom_class.of_int_less_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cInt.ring_1_class.of_int @ V0)) @ cGroups.zero_class.zero)) @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)))))
(TLattices.boolean_algebra.compl_eq_compl_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V1 @ V8)) @ (V1 @ V9))) @ ((cHOL.eq @ V8) @ V9))))))))))))))))))))))))
(TLattices.boolean_algebra.compl_le_compl_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ (V1 @ V8)) @ (V1 @ V9))) @ ((V3 @ V9) @ V8))))))))))))))))))))))))
(TLattices.boolean_algebra_class.compl_bot_eq,((cHOL.eq @ (cGroups.uminus_class.uminus @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top))
(TLattices.boolean_algebra_class.compl_top_eq,((cHOL.eq @ (cGroups.uminus_class.uminus @ cOrderings.top_class.top)) @ cOrderings.bot_class.bot))
(TLattices.boolean_algebra_class.compl_unique,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((c==> @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ V1))))))))
(TLattices.boolean_algebra_class.double_compl,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cGroups.uminus_class.uminus @ V0))) @ V0))))
(TLattices.bounded_lattice_bot.bot_eq_sup_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ V4) @ ((V3 @ V5) @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ V4)) @ ((cHOL.eq @ V6) @ V4)))))))))))))))))))
(TLattices.bounded_lattice_bot.sup_eq_bot_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cLattices.class.bounded_lattice_bot @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ ((V3 @ V5) @ V6)) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ V4)) @ ((cHOL.eq @ V6) @ V4)))))))))))))))))))
(TLattices.bounded_lattice_top.inf_eq_top_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cLattices.class.bounded_lattice_top @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V5) @ V6)) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ V4)) @ ((cHOL.eq @ V6) @ V4)))))))))))))))))))
(TLattices.class.boolean_algebra_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: ((cHOL.eq @ ((V0 @ V6) @ (V1 @ V6))) @ V2)))) @ ((c==> @ (call @ (^[V6]: ((cHOL.eq @ ((V3 @ V6) @ (V1 @ V6))) @ V4)))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((cHOL.eq @ ((V5 @ V6) @ V7)) @ ((V0 @ V6) @ (V1 @ V7)))))))) @ ((((((cLattices.class.boolean_algebra_axioms @ V5) @ V1) @ V0) @ V3) @ V2) @ V4)))))))))))))))))
(TLattices.class.distrib_lattice_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ ((V0 @ V2) @ ((V1 @ V3) @ V4))) @ ((V1 @ ((V0 @ V2) @ V3)) @ ((V0 @ V2) @ V4)))))))))) @ ((cLattices.class.distrib_lattice_axioms @ V1) @ V0)))))))
(TLattices.class.semilattice_inf_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((V0 @ ((V1 @ V2) @ V3)) @ V2)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((V0 @ ((V1 @ V2) @ V3)) @ V3)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V2) @ V4)) @ ((V0 @ V2) @ ((V1 @ V3) @ V4))))))))))) @ ((cLattices.class.semilattice_inf_axioms @ V1) @ V0)))))))))
(TLattices.class.semilattice_sup_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((V0 @ V2) @ ((V1 @ V2) @ V3))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((V0 @ V2) @ ((V1 @ V3) @ V2))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V4) @ V3)) @ ((V0 @ ((V1 @ V2) @ V4)) @ V3)))))))))) @ ((cLattices.class.semilattice_sup_axioms @ V1) @ V0)))))))))
(TLattices.linorder_class.max.strict_boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.linorder_class.min.strict_boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.semilattice_inf_class.inf.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.semilattice_inf_class.inf.boundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2)))))))))))
(TLattices.semilattice_inf_class.inf_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2)))))))))))
(TLattices.semilattice_sup_class.sup.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.semilattice_sup_class.sup.boundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V2)) @ V1))))))))))
(TLazy_Sequence.list_of_lazy_sequence_hb_flat,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ (cLazy_Sequence.hb_flat @ V0))) @ (cList.concat @ ((cList.map @ ((cFun.comp @ (^[V1]: (((cOption.option.option_case @ ((cList.list.Cons @ cOption.option.None) @ cList.list.Nil)) @ (^[V2]: V2)) @ V1))) @ (cOption.map @ cLazy_Sequence.list_of_lazy_sequence))) @ (cLazy_Sequence.list_of_lazy_sequence @ V0)))))))
(TLazy_Sequence.small_lazy_list_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cLazy_Sequence.small_lazy_list_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((cLazy_Sequence.small_lazy_list_graph @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((V2 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((V2 @ V4) @ ((cLazy_Sequence.append @ (cLazy_Sequence.single @ cList.list.Nil)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V4)) @ ((cLazy_Sequence.bind @ ((cLazy_Sequence.product @ (cLazy_Sequence.small_lazy_class.small_lazy @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (cLazy_Sequence.single @ ((cList.list.Cons @ V5) @ V6))))))) @ cLazy_Sequence.empty)))))))))) @ ((V2 @ V0) @ V1))))))))))
(TLazy_Sequence.type_definition_lazy_sequence,(((cTypedef.type_definition @ cLazy_Sequence.Rep_lazy_sequence) @ cLazy_Sequence.Abs_lazy_sequence) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set)))
(TList.comp_fun_commute.fold_set_fold_remdups,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V1) @ (cList.set @ V2))) @ (((cList.fold @ V0) @ (cList.remdups @ V2)) @ V1))))))))))
(TList.linorder.finite_sorted_distinct_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ (cHOL.Ex1 @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ (cList.set @ V3)) @ V2)) @ ((cHOL.conj @ ((cList.linorder.sorted @ V0) @ V3)) @ (cList.distinct @ V3))))))))))))))
(TList.linorder.sorted_list_of_set_eq_Nil_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((cHOL.eq @ ((cList.linorder.sorted_list_of_set @ V0) @ V2)) @ cList.list.Nil)) @ ((cHOL.eq @ V2) @ cOrderings.bot_class.bot)))))))))))
(TList.linorder_class.comp_fun_commute_insort,(cFinite_Set.comp_fun_commute @ (cList.linorder_class.insort_key @ (^[V0]: V0))))
(TList.monoid_add_class.fold_plus_listsum_rev,(call @ (^[V0]: ((cHOL.eq @ ((cList.fold @ cGroups.plus_class.plus) @ V0)) @ (cGroups.plus_class.plus @ (cList.monoid_add_class.listsum @ (cList.rev @ V0)))))))
(TNat.linordered_semidom.less_imp_of_nat_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V6) @ V7)) @ ((V5 @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6)) @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V7)))))))))))))))))))))
(TNat.linordered_semidom.of_nat_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V6)) @ ((((cNat.semiring_1.of_nat @ V3) @ V0) @ V1) @ V7))) @ ((cNat.ord_nat_inst.less_nat @ V6) @ V7))))))))))))))))))))
(TNat_Transfer.transfer_int_nat_set_functions_5,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ V1))))) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ (cSet.Collect @ (^[V1]: (V0 @ (cNat.semiring_1_class.of_nat @ V1)))))))))
(TNat_Transfer.transfer_int_nat_set_functions_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ ((cLattices.inf_class.inf @ ((cSet.image @ cInt.nat) @ V0)) @ ((cSet.image @ cInt.nat) @ V1)))))))))))
(TNat_Transfer.transfer_int_nat_set_functions_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ ((cLattices.sup_class.sup @ ((cSet.image @ cInt.nat) @ V0)) @ ((cSet.image @ cInt.nat) @ V1)))))))))))
(TNat_Transfer.transfer_int_nat_set_functions_2,((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ cOrderings.bot_class.bot)))
(TNat_Transfer.transfer_int_nat_set_functions_1,(call @ (^[V0]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ ((cSet.image @ cInt.nat) @ V0)))))))
(TNat_Transfer.transfer_int_nat_set_relations_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ cInt.nat) @ V0)) @ ((cSet.image @ cInt.nat) @ V1))))))))))
(TNat_Transfer.transfer_int_nat_set_relations_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cSet.image @ cInt.nat) @ V0)) @ ((cSet.image @ cInt.nat) @ V1))))))))))
(TNat_Transfer.transfer_int_nat_set_relations_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.image @ cInt.nat) @ V0)) @ ((cSet.image @ cInt.nat) @ V1))))))))))
(TNat_Transfer.transfer_int_nat_set_relations_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((cHOL.eq @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ (cInt.nat @ V0)) @ ((cSet.image @ cInt.nat) @ V1))))))))))
(TNat_Transfer.transfer_int_nat_set_relations_1,(call @ (^[V0]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ ((cSet.image @ cInt.nat) @ V0)))))))
(TNat_Transfer.transfer_nat_int_set_functions_5,(call @ (^[V0]: ((cHOL.eq @ (cSet.Collect @ (^[V1]: (V0 @ V1)))) @ ((cSet.image @ cInt.nat) @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ (cInt.nat @ V1))))))))))
(TNat_Transfer.transfer_nat_int_set_functions_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cSet.image @ cInt.nat) @ ((cLattices.inf_class.inf @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_set_functions_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cSet.image @ cInt.nat) @ ((cLattices.sup_class.sup @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_set_functions_2,((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet.image @ cInt.nat) @ cOrderings.bot_class.bot)))
(TNat_Transfer.transfer_nat_int_set_functions_1,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.card @ V0)) @ (cFinite_Set.card @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0))))))
(TNat_Transfer.transfer_nat_int_set_relations_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1))))))))
(TNat_Transfer.transfer_nat_int_set_relations_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1))))))))
(TNat_Transfer.transfer_nat_int_set_relations_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1))))))))
(TNat_Transfer.transfer_nat_int_set_relations_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ V1)) @ ((cSet.member @ (cNat.semiring_1_class.of_nat @ V0)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V1))))))))
(TNat_Transfer.transfer_nat_int_set_relations_1,(call @ (^[V0]: ((cHOL.eq @ (cFinite_Set.finite @ V0)) @ (cFinite_Set.finite @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0))))))
(TNat_Transfer.transfer_nat_int_sum_prod_cong_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1))))))))))))))
(TNat_Transfer.transfer_nat_int_sum_prod_cong_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V4)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1))))))))))))))
(TNitpick.fun_box.fun_box_size_overloaded_def,((c== @ cNat.size_class.size) @ (cNitpick.fun_box.fun_box_rec @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TNum.linordered_idom.not_zero_le_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V4 @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_semidom.not_numeral_less_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V3))))))))))))))))))
(TNum.linordered_semidom.one_less_numeral_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V3) @ (((cNum.numeral.numeral @ V3) @ V0) @ V6))) @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ V6))))))))))))))))))
(TNum.linordered_semidom_class.numeral_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.linordered_semidom_class.one_le_numeral,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.neg_numeral_class.add_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ (cNum.neg_numeral_class.neg_numeral @ ((cNum.plus_num_inst.plus_num @ V0) @ V1))))))))
(TNum.neg_numeral_class.add_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V1) @ V0)))))))
(TNum.neg_numeral_class.add_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.neg_numeral_class.sub @ V0) @ V1)))))))
(TOrderings.order_class.order.ordering_axioms,((cOrderings.ordering @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.order_class.order_class.mono_dict,((c== @ cOrderings.order_class.mono) @ (cOrderings.order.mono @ cOrderings.ord_class.less_eq)))
(TOrderings.wellorder_class.LeastI2_wellorder,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (V0 @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((c==> @ (cHOL.All @ (^[V4]: ((cHOL.implies @ (V0 @ V4)) @ ((cOrderings.ord_class.less_eq @ V3) @ V4))))) @ (V2 @ V3)))))) @ (V2 @ (cOrderings.ord_class.Least @ V0)))))))))))
(TPower.linordered_idom_class.abs_power_minus,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cPower.power_class.power @ (cGroups.uminus_class.uminus @ V0)) @ V1))) @ (cGroups.abs_class.abs @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPower.linordered_semidom.power_Suc_less_one,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V1) @ V6)) @ ((c==> @ ((V5 @ V6) @ V3)) @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ (cNat.Suc @ V7))) @ V3)))))))))))))))))))))
(TPower.linordered_semidom_class.one_le_power,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPower.linordered_semidom_class.power_le_one,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V0) @ V1)) @ cGroups.one_class.one))))))))
(TProduct_Type.default_unit_inst.default_unit,((c== @ cProduct_Type.default_unit_inst.default_unit) @ cProduct_Type.default_unit_inst.default_unit))
(TQuickcheck_Exhaustive.arity_exhaustive_prod,(cQuickcheck_Exhaustive.exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_term_of_unknown,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_typerep_unknown,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_class.intro,((c==> @ (cCode_Evaluation.term_of_class @ cTYPE)) @ ((c==> @ (cEnum.enum_class @ cTYPE)) @ (cQuickcheck_Exhaustive.check_all_class @ cTYPE))))
(TQuickcheck_Exhaustive.check_all_class.super_2,((c==> @ (cQuickcheck_Exhaustive.check_all_class @ cTYPE)) @ (cEnum.enum_class @ cTYPE)))
(TQuickcheck_Exhaustive.check_all_class.super_1,((c==> @ (cQuickcheck_Exhaustive.check_all_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TQuickcheck_Exhaustive.check_all_n_lists_def,((c== @ cQuickcheck_Exhaustive.check_all_n_lists) @ (^[V0]: (^[V1]: (cQuickcheck_Exhaustive.check_all_n_lists_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TQuickcheck_Exhaustive.check_all_subsets_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets) @ (^[V0]: (^[V1]: (cQuickcheck_Exhaustive.term_syntax.check_all_subsets_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TQuickcheck_Exhaustive.class.check_all.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cEnum.class.enum @ V0) @ V1) @ V2)) @ (((cQuickcheck_Exhaustive.class.check_all @ V0) @ V1) @ V2)))))))))
(TQuickcheck_Exhaustive.enum_term_of_bool_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_bool_inst.enum_term_of_bool) @ (^[V0]: (^[V1]: ((cList.map @ cCode_Evaluation.term_of_bool_inst.term_of_bool) @ cEnum.enum_bool_inst.enum_bool)))))
(TQuickcheck_Exhaustive.enum_term_of_char_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_char_inst.enum_term_of_char) @ (^[V0]: (^[V1]: ((cList.map @ cCode_Evaluation.term_of_char_inst.term_of_char) @ cString.enum_char_inst.enum_char)))))
(TQuickcheck_Exhaustive.enum_term_of_prod_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_class.enum_term_of) @ (^[V0]: (^[V1]: ((cList.map @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((((cQuickcheck_Exhaustive.term_syntax.termify_pair @ cTYPE) @ cTYPE) @ V2) @ V3))))) @ ((cList.product @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity)) @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity)))))))
(TQuickcheck_Exhaustive.enum_term_of_unit_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_unit_inst.enum_term_of_unit) @ (^[V0]: (^[V1]: ((cList.list.Cons @ (cCode_Evaluation.term_of_unit_inst.term_of_unit @ cProduct_Type.Unity)) @ cList.list.Nil)))))
(TQuickcheck_Exhaustive.exhaustive_fun'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_fun'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V5 @ (^[V9]: V8)))) @ V7)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V6)) @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V10]: (V5 @ (((cFun.fun_upd @ V8) @ V9) @ V10)))) @ V7))) @ V7))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7)) @ cOption.option.None)))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ V0) @ V1) @ V2)) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V3]: (V0 @ (^[V4]: V3)))) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V1)) @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ (^[V3]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: (V0 @ (((cFun.fun_upd @ V3) @ V4) @ V5)))) @ V2))) @ V2))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)) @ cOption.option.None))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_int'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ V7)) @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V5) @ V6) @ ((cInt.plus_int_inst.plus_int @ V7) @ cInt.one_int_inst.one_int)))))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V0) @ V1) @ ((cInt.plus_int_inst.plus_int @ V2) @ cInt.one_int_inst.one_int))))))))))))
(TQuickcheck_Exhaustive.exhaustive_set.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_set.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_set_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cOrderings.bot_class.bot)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_set_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TQuickcheck_Exhaustive.exhaustive_set.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_set_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ cOrderings.bot_class.bot)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V2]: ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V3]: (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ cOption.option.None) @ (V0 @ ((cSet.insert @ V3) @ V2))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))
(TQuickcheck_Exhaustive.neg_bound_cps_not_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.neg_bound_cps_not @ V0)) @ (^[V1]: (^[V2]: (((cOption.option.option_case @ (V1 @ (cQuickcheck_Exhaustive.unknown.Known @ cProduct_Type.Unity))) @ (^[V3]: cQuickcheck_Exhaustive.three_valued.No_value)) @ ((V0 @ (^[V3]: (cOption.option.Some @ ((cProduct_Type.Pair @ cHOL.True) @ cList.list.Nil)))) @ V2))))))))
(TQuickcheck_Exhaustive.pos_bound_cps_not_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.pos_bound_cps_not @ V0)) @ (^[V1]: (^[V2]: ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ cOption.option.None) @ (^[V3]: cOption.option.None)) @ (V1 @ cProduct_Type.Unity)) @ ((V0 @ (^[V3]: (cQuickcheck_Exhaustive.three_valued.Value @ cList.list.Nil))) @ V2))))))))
(TQuickcheck_Exhaustive.three_valued.distinct_6,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.No_value) @ (cQuickcheck_Exhaustive.three_valued.Value @ V0))))))
(TQuickcheck_Exhaustive.three_valued.distinct_5,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ cQuickcheck_Exhaustive.three_valued.No_value)))))
(TQuickcheck_Exhaustive.three_valued.distinct_4,(cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.No_value) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)))
(TQuickcheck_Exhaustive.three_valued.distinct_3,(cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ cQuickcheck_Exhaustive.three_valued.No_value)))
(TQuickcheck_Exhaustive.three_valued.distinct_2,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)))))
(TQuickcheck_Exhaustive.three_valued.distinct_1,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (cQuickcheck_Exhaustive.three_valued.Value @ V0))))))
(TQuickcheck_Exhaustive.three_valued.eq.simps_9,((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ cHOL.True))
(TQuickcheck_Exhaustive.three_valued.eq.simps_8,((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.three_valued.No_value) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ cHOL.True))
(TQuickcheck_Exhaustive.three_valued.eq.simps_7,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ (cQuickcheck_Exhaustive.three_valued.Value @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.three_valued.eq.simps_6,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (cQuickcheck_Exhaustive.three_valued.Value @ V0))) @ cHOL.False))))
(TQuickcheck_Exhaustive.three_valued.eq.simps_5,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ cHOL.False))))
(TQuickcheck_Exhaustive.three_valued.eq.simps_4,((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ cHOL.False))
(TQuickcheck_Exhaustive.three_valued.eq.simps_3,((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.three_valued.No_value) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ cHOL.False))
(TQuickcheck_Exhaustive.three_valued.eq.simps_2,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ cHOL.False))))
(TQuickcheck_Exhaustive.three_valued.eq.simps_1,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ cQuickcheck_Exhaustive.three_valued.No_value) @ (cQuickcheck_Exhaustive.three_valued.Value @ V0))) @ cHOL.False))))
(TQuickcheck_Exhaustive.three_valued.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ ((cHOL.eq @ V0) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.three_valued.Value @ V1))))) @ ((cHOL.eq @ V0) @ cQuickcheck_Exhaustive.three_valued.No_value))))))
(TQuickcheck_Narrowing.arity_is_testable_bool,(cQuickcheck_Narrowing.is_testable_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_nibble,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_option,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_term_of_property,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_typerep_property,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.around_zero_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int))) @ ((V2 @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int)) @ V3)))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.around_zero_rel.intros,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((cQuickcheck_Narrowing.around_zero_rel @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int)) @ V0))))))
(TQuickcheck_Narrowing.narrowing_cons.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Narrowing.narrowing_cons.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ V3))) @ V1)))))) @ V1))))))
(TQuickcheck_Narrowing.narrowing_cons.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V0 @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ V3))))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.narrowing_term.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Narrowing.narrowing_term.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))) @ V1)))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))) @ V1)))))) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_term.inducts_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (V0 @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V1 @ V4)) @ (V0 @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V3) @ V4)))))))) @ ((c==> @ (V1 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V3)) @ ((c==> @ (V1 @ V4)) @ (V1 @ ((cList.list.Cons @ V3) @ V4))))))))) @ (V1 @ V2))))))))))))
(TQuickcheck_Narrowing.narrowing_term.inducts_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (V0 @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V1 @ V4)) @ (V0 @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V3) @ V4)))))))) @ ((c==> @ (V1 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (V0 @ V3)) @ ((c==> @ (V1 @ V4)) @ (V1 @ ((cList.list.Cons @ V3) @ V4))))))))) @ (V0 @ V2))))))))))))
(TQuickcheck_Narrowing.narrowing_type.eq.refl,(call @ (^[V0]: ((c== @ ((cHOL.equal_class.equal @ V0) @ V0)) @ cHOL.True))))
(TQuickcheck_Narrowing.narrowing_type.exhaust,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2))) @ V1)))) @ V1))))))
(TQuickcheck_Narrowing.narrowing_type.inducts_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V1 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4)))))) @ ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V2 @ V4)) @ ((c==> @ (V0 @ V5)) @ (V0 @ ((cList.list.Cons @ V4) @ V5))))))))) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V1 @ V4)) @ ((c==> @ (V2 @ V5)) @ (V2 @ ((cList.list.Cons @ V4) @ V5))))))))) @ (V2 @ V3)))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.inducts_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V1 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4)))))) @ ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V2 @ V4)) @ ((c==> @ (V0 @ V5)) @ (V0 @ ((cList.list.Cons @ V4) @ V5))))))))) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V1 @ V4)) @ ((c==> @ (V2 @ V5)) @ (V2 @ ((cList.list.Cons @ V4) @ V5))))))))) @ (V0 @ V3)))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.inducts_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V1 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4)))))) @ ((c==> @ (V0 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V2 @ V4)) @ ((c==> @ (V0 @ V5)) @ (V0 @ ((cList.list.Cons @ V4) @ V5))))))))) @ ((c==> @ (V2 @ cList.list.Nil)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (V1 @ V4)) @ ((c==> @ (V2 @ V5)) @ (V2 @ ((cList.list.Cons @ V4) @ V5))))))))) @ (V1 @ V3)))))))))))))))
(TQuickcheck_Narrowing.non_empty_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.non_empty_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4)) @ (cHOL.Not @ (cList.null @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.non_empty_graph.intros,(call @ (^[V0]: ((cQuickcheck_Narrowing.non_empty_graph @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0)) @ (cHOL.Not @ (cList.null @ V0))))))
(TQuickcheck_Narrowing.property.Universal_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cQuickcheck_Narrowing.property.Universal @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.Abs_property @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V0)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ (^[V3]: (cQuickcheck_Narrowing.Rep_property @ (V1 @ V3))))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V2)))))))))))))))
(TQuickcheck_Random.finite_1.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_finite_1 @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_1.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Random.finite_2.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_finite_2 @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Random.finite_3.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_finite_3 @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))) @ V2)))))))))
(TQuickcheck_Random.finite_4.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_finite_4 @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>4) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil)))))) @ V2)))))))))
(TQuickcheck_Random.finite_5.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_finite_5 @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>1) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>2) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>3) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>4) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>5) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cList.list.Nil))))))) @ V2)))))))))
(TRings.class.linordered_semidom_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cRings.class.linordered_semidom_axioms @ V1) @ V2) @ V0)))))))))
(TRings.classrel_idom_ring_1_no_zero_divisors,(cRings.ring_1_no_zero_divisors_class @ cTYPE))
(TRings.classrel_linordered_ring_ordered_ring,(cRings.ordered_ring_class @ cTYPE))
(TRings.classrel_semiring_0_cancel_semiring_0,(cRings.semiring_0_class @ cTYPE))
(TRings.classrel_semiring_1_cancel_semiring_1,(cRings.semiring_1_class @ cTYPE))
(TRings.comm_ring.square_diff_square_factored,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.comm_ring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V2 @ ((V4 @ V5) @ V5)) @ ((V4 @ V6) @ V6))) @ ((V4 @ ((V0 @ V5) @ V6)) @ ((V2 @ V5) @ V6)))))))))))))))))))
(TRings.linordered_idom.mult_le_cancel_right1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ V10) @ ((V9 @ V11) @ V10))) @ ((cHOL.conj @ ((cHOL.implies @ ((V5 @ V3) @ V10)) @ ((V4 @ V7) @ V11))) @ ((cHOL.implies @ ((V5 @ V10) @ V3)) @ ((V4 @ V11) @ V7))))))))))))))))))))))))))))))
(TRings.linordered_idom.mult_le_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ ((V9 @ V10) @ V11)) @ V11)) @ ((cHOL.conj @ ((cHOL.implies @ ((V5 @ V3) @ V11)) @ ((V4 @ V10) @ V7))) @ ((cHOL.implies @ ((V5 @ V11) @ V3)) @ ((V4 @ V7) @ V10))))))))))))))))))))))))))))))
(TRings.linordered_semidom_class.less_add_one,(call @ (^[V0]: ((cOrderings.ord_class.less @ V0) @ ((cGroups.plus_class.plus @ V0) @ cGroups.one_class.one)))))
(TRings.linordered_semiring_1.convex_bound_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((cRings.class.linordered_semiring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V1 @ V6) @ V7)) @ ((c==> @ ((V1 @ V8) @ V7)) @ ((c==> @ ((V1 @ V3) @ V9)) @ ((c==> @ ((V1 @ V3) @ V10)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V9) @ V10)) @ V5)) @ ((V1 @ ((V0 @ ((V4 @ V9) @ V6)) @ ((V4 @ V10) @ V8))) @ V7))))))))))))))))))))))))))))))
(TRings.ordered_ring_class.mult_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V2) @ V0)))))))))))
(TRings.ordered_ring_class.mult_nonpos_nonpos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.ordered_semiring_class.mult_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V2) @ V0)) @ ((cGroups.times_class.times @ V2) @ V1)))))))))))
(TRings.ring_1_class.square_diff_one_factored,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V0)) @ cGroups.one_class.one)) @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ cGroups.one_class.one)) @ ((cGroups.minus_class.minus @ V0) @ cGroups.one_class.one))))))
(TSet_Interval.dvd.atLeastLessThan_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((((cSet_Interval.ord.atLeastLessThan @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1))) @ (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))))
(TSet_Interval.finite_atLeastZeroLessThan_int,(call @ (^[V0]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.atLeastLessThan @ cInt.zero_int_inst.zero_int) @ V0)))))
(TSet_Interval.finite_greaterThanLessThan_int,(call @ (^[V0]: (call @ (^[V1]: (cFinite_Set.finite @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)))))))
(TSet_Interval.linorder.Int_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V2) @ V3)) @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V4) @ V5))) @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ (((cOrderings.ord.max @ V0) @ V2) @ V4)) @ (((cOrderings.ord.min @ V0) @ V3) @ V5)))))))))))))))))
(TSet_Interval.linorder.lessThan_Int_lessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.greaterThan @ V1) @ V2)) @ ((cSet_Interval.ord.greaterThan @ V1) @ V3))) @ ((cSet_Interval.ord.greaterThan @ V1) @ (((cOrderings.ord.max @ V0) @ V2) @ V3)))))))))))))
(TSet_Interval.order.atLeastAtMost_singleton',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ V3)) @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))))
(TSet_Interval.order.atLeastatMost_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3))) @ (cHOL.Not @ ((V0 @ V2) @ V3)))))))))))))
(TSet_Interval.order.atLeastatMost_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V4) @ V5))) @ ((cHOL.disj @ (cHOL.Not @ ((V0 @ V2) @ V3))) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V0 @ V3) @ V5))))))))))))))))))
(TSet_Interval.order_class.Icc_subset_Ici_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V2))) @ ((cHOL.disj @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V2) @ V0))))))))))
(TSet_Interval.order_class.Icc_subset_Iic_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.atMost @ V2))) @ ((cHOL.disj @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TSet_Interval.setsum_shift_bounds_cl_Suc_ivl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cNat.Suc @ V1)) @ (cNat.Suc @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (V0 @ (cNat.Suc @ V3)))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))))))))))
(TSet_Interval.setsum_shift_bounds_cl_nat_ivl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2)) @ ((cNat.plus_nat_inst.plus_nat @ V3) @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (V0 @ ((cNat.plus_nat_inst.plus_nat @ V4) @ V2)))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V3))))))))))))
(TSet_Interval.transfer_int_nat_set_functions,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ ((c==> @ (cNat_Transfer.is_nat @ V1)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cInt.nat @ V0)) @ (cInt.nat @ V1)))))))))))
(TSet_Interval.transfer_nat_int_set_functions_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet.image @ cInt.nat) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1)))))))))
(TSet_Interval.transfer_nat_int_set_functions_1,(call @ (^[V0]: ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet.image @ cInt.nat) @ ((cSet_Interval.ord_class.atLeastAtMost @ cInt.zero_int_inst.zero_int) @ (cNat.semiring_1_class.of_nat @ V0)))))))
(TTransitive_Closure.converse_rtrancl_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V0) @ V1)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cTransitive_Closure.rtrancl @ V4))) @ ((c==> @ ((V5 @ V2) @ V3)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V8) @ V9))) @ V4)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V8) @ V9)) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cTransitive_Closure.rtrancl @ V4))) @ ((c==> @ ((V5 @ V8) @ V9)) @ ((V5 @ V6) @ V7))))))))))))) @ ((V5 @ V0) @ V1)))))))))))))))))
(TTransitive_Closure.converse_rtranclp_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (V3 @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V5) @ V2)) @ ((c==> @ (V3 @ V5)) @ (V3 @ V4))))))))) @ (V3 @ V1)))))))))))))
(TTransitive_Closure.rtrancl_finite_eq_relpow,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cTransitive_Closure.rtrancl @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ (cSet.Collect @ (^[V1]: ((cNat.ord_nat_inst.less_eq_nat @ V1) @ (cFinite_Set.card @ V0))))) @ (^[V1]: ((cNat.compow @ V1) @ V0))))))))
(TTransitive_Closure.rtranclp_imp_Sup_relpowp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V3]: ((cNat.compow @ V3) @ V0))) @ V1) @ V2)))))))))
(TTransitive_Closure.rtranclp_tranclp_tranclp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.tranclp_rtranclp_tranclp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closure_trans_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.trancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTransitive_Closure.transitive_closure_trans_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTyperep.typerep.typerep_size_overloaded_def,((c== @ cTyperep.typerep.size_typerep_inst.size_typerep) @ (((cTyperep.typerep.typerep_rec_1 @ (^[V0]: (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TBig_Operators.comm_monoid_add.setsum_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V5]: ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V6]: ((V2 @ V5) @ V6))) @ V3))) @ V4)) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V5]: ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V6]: ((V2 @ V6) @ V5))) @ V4))) @ V3))))))))))))))
(TBig_Operators.comm_monoid_set.UNION_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V5]: (cFinite_Set.finite @ (V3 @ V5))))) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V5]: ((cSet.Ball @ V2) @ (^[V6]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ V6))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V3 @ V5)) @ (V3 @ V6))) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V2) @ V3))) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V5]: ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ (V3 @ V5)))) @ V2)))))))))))))))))
(TBig_Operators.comm_monoid_set.Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: (cFinite_Set.finite @ V4)))) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V4) @ V5)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V3) @ (cComplete_Lattices.Sup_class.Sup @ V2))) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V3)) @ V2))))))))))))))
(TBig_Operators.comm_monoid_set.union_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cLattices.sup_class.sup @ V2) @ V3))) @ ((V0 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V3))))))))))))))))))
(TBig_Operators.linorder_class.Max.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Max @ V0)) @ V1)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))))
(TBig_Operators.linorder_class.Max.hom_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ ((cOrderings.ord_class.max @ V2) @ V3))) @ ((cOrderings.ord_class.max @ (V0 @ V2)) @ (V0 @ V3)))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.linorder_class.Max @ V1))) @ (cBig_Operators.linorder_class.Max @ ((cSet.image @ V0) @ V1)))))))))))
(TBig_Operators.linorder_class.Min.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V1) @ V2)))))))))))
(TBig_Operators.linorder_class.Min.hom_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ ((cOrderings.ord_class.min @ V2) @ V3))) @ ((cOrderings.ord_class.min @ (V0 @ V2)) @ (V0 @ V3)))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.linorder_class.Min @ V1))) @ (cBig_Operators.linorder_class.Min @ ((cSet.image @ V0) @ V1)))))))))))
(TBig_Operators.linorder_class.hom_Max_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ ((cOrderings.ord_class.max @ V2) @ V3))) @ ((cOrderings.ord_class.max @ (V0 @ V2)) @ (V0 @ V3)))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.linorder_class.Max @ V1))) @ (cBig_Operators.linorder_class.Max @ ((cSet.image @ V0) @ V1)))))))))))
(TBig_Operators.linorder_class.hom_Min_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ ((cOrderings.ord_class.min @ V2) @ V3))) @ ((cOrderings.ord_class.min @ (V0 @ V2)) @ (V0 @ V3)))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.linorder_class.Min @ V1))) @ (cBig_Operators.linorder_class.Min @ ((cSet.image @ V0) @ V1)))))))))))
(TBig_Operators.linorder_class.min_max.distrib_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.distrib_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_aci_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.min @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.inf_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ V1) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_aci_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V1) @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_le1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V0))))))
(TBig_Operators.linorder_class.min_max.inf_le2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V1))))))
(TBig_Operators.linorder_class.min_max.le_infE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TBig_Operators.linorder_class.min_max.le_infI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2)))))))))))
(TBig_Operators.linorder_class.min_max.le_supE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ V3))) @ V3)))))))))))
(TBig_Operators.linorder_class.min_max.le_supI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V2)) @ V1))))))))))
(TBig_Operators.linorder_class.min_max.sup_aci_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.sup_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ V1) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_aci_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TBig_Operators.linorder_class.min_max.sup_ge1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.sup_ge2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TBig_Operators.semilattice_neutr_set.infinite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V2))) @ ((cHOL.eq @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V2)) @ V1))))))))))
(TBig_Operators.semilattice_order_set.antimono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V4)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((V1 @ ((cBig_Operators.semilattice_set.F @ V0) @ V4)) @ ((cBig_Operators.semilattice_set.F @ V0) @ V3)))))))))))))))))
(TBig_Operators.semilattice_order_set.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((c==> @ ((V1 @ V4) @ ((cBig_Operators.semilattice_set.F @ V0) @ V3))) @ ((c==> @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V3)) @ ((V1 @ V4) @ V6))))) @ V5)) @ V5))))))))))))))))))
(TBig_Operators.semilattice_order_set.boundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V3)) @ ((V1 @ V4) @ V5))))) @ ((V1 @ V4) @ ((cBig_Operators.semilattice_set.F @ V0) @ V3)))))))))))))))))
(TCode_Evaluation.term_of_fun_inst.term_of_fun,((c== @ cCode_Evaluation.term_of_fun_inst.term_of_fun) @ cCode_Evaluation.term_of_fun_inst.term_of_fun))
(TCode_Evaluation.term_of_int_inst.term_of_int,((c== @ cCode_Evaluation.term_of_int_inst.term_of_int) @ cCode_Evaluation.term_of_int_inst.term_of_int))
(TCode_Evaluation.term_of_nat_inst.term_of_nat,((c== @ cCode_Evaluation.term_of_nat_inst.term_of_nat) @ cCode_Evaluation.term_of_nat_inst.term_of_nat))
(TCode_Evaluation.term_of_num_inst.term_of_num,((c== @ cCode_Evaluation.term_of_num_inst.term_of_num) @ cCode_Evaluation.term_of_num_inst.term_of_num))
(TCode_Evaluation.term_of_seq_inst.term_of_seq,((c== @ cCode_Evaluation.term_of_seq_inst.term_of_seq) @ cCode_Evaluation.term_of_seq_inst.term_of_seq))
(TCode_Evaluation.term_of_set_inst.term_of_set,((c== @ cCode_Evaluation.term_of_set_inst.term_of_set) @ cCode_Evaluation.term_of_set_inst.term_of_set))
(TCode_Evaluation.term_of_sum_inst.term_of_sum,((c== @ cCode_Evaluation.term_of_sum_inst.term_of_sum) @ cCode_Evaluation.term_of_sum_inst.term_of_sum))
(TCode_Evaluation.typerep_seq_inst.typerep_seq,((c== @ cCode_Evaluation.typerep_seq_inst.typerep_seq) @ cCode_Evaluation.typerep_seq_inst.typerep_seq))
(TComplete_Lattices.arity_complete_lattice_fun,(cComplete_Lattices.complete_lattice_class @ cTYPE))
(TComplete_Lattices.arity_complete_lattice_set,(cComplete_Lattices.complete_lattice_class @ cTYPE))
(TComplete_Lattices.class.complete_lattice_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((cLattices.class.lattice @ V2) @ V3) @ V4) @ V5)) @ (((((cComplete_Lattices.class.complete_lattice_axioms @ V0) @ V1) @ V3) @ V6) @ V7))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_const,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V10]: V9))) @ V9))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ cOrderings.bot_class.bot) @ (^[V9]: (V8 @ V9)))) @ V7)))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ ((cSet.image @ V8) @ V9)) @ (^[V11]: (V10 @ V11)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (V10 @ (V8 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_lower,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((V3 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (V10 @ V11)))) @ (V10 @ V8)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_union,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ ((cLattices.sup_class.sup @ V8) @ V9)) @ (^[V11]: (V10 @ V11)))) @ ((V2 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (V10 @ V11)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ cOrderings.bot_class.bot)) @ V7)))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_lower,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((V3 @ (V0 @ V9)) @ V8))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_const,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V10]: V9))) @ V9))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ cOrderings.bot_class.bot) @ (^[V9]: (V8 @ V9)))) @ V6)))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ ((cSet.image @ V8) @ V9)) @ (^[V11]: (V10 @ V11)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (V10 @ (V8 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V11]: ((c==> @ ((cSet.member @ V11) @ V8)) @ ((V3 @ (V9 @ V11)) @ V10))))) @ ((V3 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (V9 @ V11)))) @ V10))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_lessD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: (V9 @ V12)))) @ V10)) @ ((c==> @ ((cSet.member @ V11) @ V8)) @ ((V4 @ (V9 @ V11)) @ V10)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_union,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ ((cLattices.sup_class.sup @ V8) @ V9)) @ (^[V11]: (V10 @ V11)))) @ ((V5 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (V10 @ V11)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_upper,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((V3 @ (V10 @ V8)) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ cOrderings.bot_class.bot)) @ V6)))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((V3 @ V10) @ V9))))) @ ((V3 @ (V1 @ V8)) @ V9))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_upper,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((V3 @ V8) @ (V1 @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice_class_def,((c== @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ ((cPure.conjunction @ ((cPure.conjunction @ (cComplete_Lattices.Inf_class @ cTYPE)) @ ((cPure.conjunction @ (cComplete_Lattices.Sup_class @ cTYPE)) @ (cLattices.lattice_class @ cTYPE)))) @ ((cPure.conjunction @ (cOrderings.bot_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.top_class @ cTYPE)) @ (((((cComplete_Lattices.class.complete_lattice_axioms @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))))))
(TComplete_Partial_Order.ccpo.iterates.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ ((c==> @ (V5 @ V6)) @ (V5 @ (V4 @ V6))))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V6)) @ ((c==> @ ((cSet.Ball @ V6) @ (^[V7]: ((cHOL.conj @ ((cSet.member @ V7) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V4))) @ (V5 @ V7))))) @ (V5 @ (V0 @ V6))))))) @ (V5 @ V3))))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V4)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V6)) @ ((c==> @ (V5 @ V6)) @ (V5 @ (V3 @ V6))))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V6)) @ ((c==> @ ((cSet.Ball @ V6) @ (^[V7]: ((cHOL.conj @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V7)) @ (V5 @ V7))))) @ (V5 @ (V0 @ V6))))))) @ (V5 @ V4))))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V5]: ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V4) @ V5)))) @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V4) @ (V0 @ V3))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V4)) @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ (V3 @ V4)))))))))))))))
(TComplete_Partial_Order.class.ccpo_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cComplete_Partial_Order.class.ccpo_axioms @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cComplete_Partial_Order.chain @ V1) @ V2)) @ ((cHOL.implies @ ((cSet.member @ V3) @ V2)) @ ((V1 @ V3) @ (V0 @ V2))))))))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cComplete_Partial_Order.chain @ V1) @ V2)) @ ((cHOL.implies @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.member @ V4) @ V2)) @ ((V1 @ V4) @ V3))))) @ ((V1 @ (V0 @ V2)) @ V3))))))))))))))
(TDivides.semiring_div_class.div_mod_equality2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.div @ V1) @ V0))) @ ((cDivides.div_class.mod @ V1) @ V0))) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V2)))))))))
(TDivides.semiring_div_class.div_mult_mult1_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero) @ ((cDivides.div_class.div @ V1) @ V2))))))))))
(TDivides.semiring_div_class.dvd_div_mult_self,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cDivides.div_class.div @ V1) @ V0)) @ V0)) @ V1)))))))
(TDivides.semiring_div_class.mod_div_equality',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cDivides.div_class.mod @ V0) @ V1)) @ ((cGroups.times_class.times @ ((cDivides.div_class.div @ V0) @ V1)) @ V1))) @ V0))))))
(TDivides.semiring_div_class.mod_div_equality2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.div @ V1) @ V0))) @ ((cDivides.div_class.mod @ V1) @ V0))) @ V1))))))
(TDivides.semiring_div_class.mod_mult_right_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.mod @ V1) @ V2))) @ V2)))))))))
(TDivides.semiring_numeral_div.divmod_step_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ (((((((cDivides.semiring_numeral_div.divmod_step @ V0) @ V3) @ V5) @ V6) @ V7) @ V9) @ V10)) @ ((cHOL.Let @ V10) @ (cProduct_Type.prod.prod_case @ (^[V11]: (^[V12]: (((cHOL.If @ ((V7 @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)) @ V12)) @ ((cProduct_Type.Pair @ ((V3 @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V11)) @ V5)) @ ((V6 @ V12) @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)))) @ ((cProduct_Type.Pair @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V11)) @ V12)))))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.mult_div_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ ((V0 @ V9) @ ((V1 @ V10) @ V9))) @ ((V6 @ V10) @ ((V2 @ V10) @ V9)))))))))))))))))))))))))))
(TDivides.semiring_numeral_div_class.diff_zero,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TEquiv_Relations.congruent2_implies_congruent,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ (((cEquiv_Relations.congruent2 @ V1) @ V2) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cEquiv_Relations.congruent @ V2) @ (V3 @ V4))))))))))))))))
(TEquiv_Relations.part_equivp_refl_symp_transp,(call @ (^[V0]: ((cHOL.eq @ (cEquiv_Relations.part_equivp @ V0)) @ ((cHOL.conj @ (cHOL.Ex @ (^[V1]: ((V0 @ V1) @ V1)))) @ ((cHOL.conj @ (cRelation.symp @ V0)) @ (cRelation.transp @ V0)))))))
(TFields.class.field_inverse_zero_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ V1)) @ ((cFields.class.field_inverse_zero_axioms @ V0) @ V1)))))))
(TFields.division_ring_class.divide_minus_left,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFields.inverse_class.divide @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ (cGroups.uminus_class.uminus @ ((cFields.inverse_class.divide @ V0) @ V1))))))))
(TFields.division_ring_class.inverse_eq_divide,(call @ (^[V0]: ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0)))))
(TFields.division_ring_class.minus_divide_left,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cFields.inverse_class.divide @ (cGroups.uminus_class.uminus @ V0)) @ V1)))))))
(TFields.field.nonzero_divide_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V1 @ V8) @ ((V2 @ V8) @ V9))) @ ((V1 @ V3) @ V9))))))))))))))))))))))))))
(TFields.field.nonzero_mult_divide_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V8) @ V9)) @ V8)) @ V9))))))))))))))))))))))))
(TFields.field_inverse_zero.divide_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ ((V1 @ V8) @ V10))) @ ((cHOL.disj @ ((cHOL.eq @ V8) @ V5)) @ ((cHOL.eq @ V9) @ V10)))))))))))))))))))))))))))
(TFields.field_inverse_zero.divide_minus_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ (V7 @ V9))) @ (V7 @ ((V1 @ V8) @ V9)))))))))))))))))))))))))
(TFields.field_inverse_zero.field_inverse_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ V5)) @ V5)))))))))))))))))))
(TFields.field_inverse_zero.minus_divide_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V7 @ ((V1 @ V8) @ V9))) @ ((V1 @ V8) @ (V7 @ V9)))))))))))))))))))))))))
(TFields.field_inverse_zero_class.add_frac_num,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.times_class.times @ V2) @ V0))) @ V0))))))))))
(TFields.field_inverse_zero_class.add_num_frac,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ V2) @ ((cGroups.times_class.times @ V1) @ V0))) @ V0))))))))))
(TFields.field_inverse_zero_class.divide_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ V2)) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))))))))))
(TFields.field_inverse_zero_class.eq_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ (cHOL.Not @ ((cHOL.eq @ V2) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))))))))))
(TFields.linordered_field_class.divide_neg_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1)))))))))
(TFields.linordered_field_class.divide_neg_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TFields.linordered_field_class.divide_pos_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TFields.linordered_field_class.divide_pos_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1)))))))))
(TFields.linordered_field_class.one_le_inverse,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cFields.inverse_class.inverse @ V0)))))))
(TFinite_Set.comp_fun_commute.comp_fun_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ (V0 @ V2))) @ ((cFun.comp @ (V0 @ V2)) @ (V0 @ V1)))))))))))
(TFinite_Set.complete_lattice.inf_INF_fold_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ ((V2 @ V9) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ V10))) @ (((cFinite_Set.fold @ ((cFun.comp @ V2) @ V10)) @ V9) @ V8)))))))))))))))))))))))))))
(TFinite_Set.complete_lattice.inf_Inf_fold_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ ((V2 @ (V0 @ V8)) @ V9)) @ (((cFinite_Set.fold @ V2) @ V9) @ V8)))))))))))))))))))))))))
(TFinite_Set.complete_lattice.sup_SUP_fold_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ ((V5 @ V9) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ V10))) @ (((cFinite_Set.fold @ ((cFun.comp @ V5) @ V10)) @ V9) @ V8)))))))))))))))))))))))))))
(TFinite_Set.complete_lattice.sup_Sup_fold_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cFinite_Set.finite @ V8)) @ ((cHOL.eq @ ((V5 @ (V1 @ V8)) @ V9)) @ (((cFinite_Set.fold @ V5) @ V9) @ V8)))))))))))))))))))))))))
(TFinite_Set.semilattice_inf.comp_fun_idem_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ (cFinite_Set.comp_fun_idem @ V0)))))))))
(TFinite_Set.semilattice_sup.comp_fun_idem_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ (cFinite_Set.comp_fun_idem @ V0)))))))))
(TGroups.cancel_semigroup_add.add_right_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.cancel_semigroup_add @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V3) @ V2))) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TGroups.cancel_semigroup_add.add_right_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cGroups.class.cancel_semigroup_add @ V0)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V3) @ V2))) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TGroups.class.cancel_semigroup_add_axioms_def,(call @ (^[V0]: ((c== @ (cGroups.class.cancel_semigroup_add_axioms @ V0)) @ ((cHOL.conj @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V3) @ V2))) @ ((cHOL.eq @ V1) @ V3)))))))))))))
(TGroups.class.linordered_ab_semigroup_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cGroups.class.linordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cOrderings.class.linorder @ V1) @ V2))))))))))
(TGroups.class.ordered_ab_group_add_abs.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (((((cGroups.class.ordered_ab_group_add_abs_axioms @ V0) @ V1) @ V2) @ V4) @ V5)))))))))))))))))
(TGroups.class.ordered_ab_group_add_abs.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((((((cGroups.class.ordered_ab_group_add @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)))))))))))))))))
(TGroups.class.ordered_ab_semigroup_add.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cGroups.class.ordered_ab_semigroup_add_axioms @ V0) @ V1)))))))))
(TGroups.class.ordered_ab_semigroup_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cOrderings.class.order @ V1) @ V2)))))))))
(TGroups.class.ordered_ab_semigroup_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ (cGroups.class.ab_semigroup_add @ V0)))))))))
(TGroups.classrel_comm_monoid_mult_monoid_mult,(cGroups.monoid_mult_class @ cTYPE))
(TGroups.comm_monoid_diff.add_diff_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5))) @ ((V2 @ V4) @ V5))))))))))))))))
(TGroups.group_add_class.neg_0_equal_iff_equal,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cGroups.uminus_class.uminus @ V0))) @ ((cHOL.eq @ cGroups.zero_class.zero) @ V0)))))
(TGroups.group_add_class.neg_equal_0_iff_equal,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_ab_semigroup_add_class_def,((c== @ (cGroups.linordered_ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE))))
(TGroups.ordered_ab_group_add.diff_le_0_iff_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ ((V2 @ V6) @ V7)) @ V1)) @ ((V4 @ V6) @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add.le_iff_diff_le_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V6) @ V7)) @ ((V4 @ ((V2 @ V6) @ V7)) @ V1))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.axioms,(((((cGroups.class.ordered_ab_group_add_abs_axioms @ cGroups.abs_class.abs) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.uminus_class.uminus) @ cOrderings.ord_class.less_eq))
(TGroups.ordered_ab_group_add_class.diff_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TGroups.ordered_ab_group_add_class.le_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TGroups.ordered_ab_semigroup_add_class.axioms,((cGroups.class.ordered_ab_semigroup_add_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq))
(THilbert_Choice.wf_iff_no_infinite_down_chain,(call @ (^[V0]: ((cHOL.eq @ (cWellfounded.wf @ V0)) @ (cHOL.Not @ (cHOL.Ex @ (^[V1]: (cHOL.All @ (^[V2]: ((cSet.member @ ((cProduct_Type.Pair @ (V1 @ (cNat.Suc @ V2))) @ (V1 @ V2))) @ V0))))))))))
(TLattices.boolean_algebra_class.compl_inf_bot,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ cOrderings.bot_class.bot))))
(TLattices.boolean_algebra_class.compl_sup_top,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ cOrderings.top_class.top))))
(TLattices.boolean_algebra_class.inf_compl_bot,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ cOrderings.bot_class.bot))))
(TLattices.boolean_algebra_class.sup_compl_top,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ cOrderings.top_class.top))))
(TLattices.linorder_class.max.semigroup_axioms,(cGroups.semigroup @ cOrderings.ord_class.max))
(TLattices.linorder_class.min.semigroup_axioms,(cGroups.semigroup @ cOrderings.ord_class.min))
(TLattices.semilattice_inf_class.inf.left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TLattices.semilattice_inf_class.inf.order_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))))))))
(TLattices.semilattice_inf_class.inf_left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TLattices.semilattice_sup_class.sup.left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TLattices.semilattice_sup_class.sup.order_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ ((cLattices.sup_class.sup @ V1) @ V0))))))))
(TLattices.semilattice_sup_class.sup_left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TList.linorder.map_sorted_distinct_set_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ ((cLattices.sup_class.sup @ (cList.set @ V3)) @ (cList.set @ V4)))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ V3))) @ ((c==> @ (cList.distinct @ ((cList.map @ V2) @ V3))) @ ((c==> @ ((cList.linorder.sorted @ V0) @ ((cList.map @ V2) @ V4))) @ ((c==> @ (cList.distinct @ ((cList.map @ V2) @ V4))) @ ((c==> @ ((cHOL.eq @ (cList.set @ V3)) @ (cList.set @ V4))) @ ((cHOL.eq @ V3) @ V4)))))))))))))))))))
(TList.linorder_class.insort_insert_insort_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cSet.member @ (V0 @ V1)) @ ((cSet.image @ V0) @ (cList.set @ V2))))) @ ((cHOL.eq @ (((cList.linorder_class.insort_insert_key @ V0) @ V1) @ V2)) @ (((cList.linorder_class.insort_key @ V0) @ V1) @ V2))))))))))
(TList.linorder_class.sorted_insort_insert_key,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ V1))) @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ (((cList.linorder_class.insort_insert_key @ V0) @ V2) @ V1)))))))))))
(TList.linorder_class.sorted_list_of_set.empty,((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ cOrderings.bot_class.bot)) @ cList.list.Nil))
(TList.linorder_class.sorted_list_of_set_empty,((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ cOrderings.bot_class.bot)) @ cList.list.Nil))
(TList.monoid_add_class.list_size_conv_listsum,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cList.list.list_size @ V0) @ V1)) @ ((cNat.plus_nat_inst.plus_nat @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ V1))) @ (cNat.size_class.size @ V1))))))))
(TNat.linordered_semidom_class.of_nat_0_le_iff,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TNat.linordered_semidom_class.of_nat_le_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNat.semiring_1_class.of_nat @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cNat.zero_nat_inst.zero_nat)))))
(TNat.linordered_semidom_class.of_nat_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNitpick.random_pair_box_inst.random_pair_box,((c== @ cNitpick.random_pair_box_inst.random_pair_box) @ cNitpick.random_pair_box_inst.random_pair_box))
(TNitpick.term_of_fun_box_inst.term_of_fun_box,((c== @ cNitpick.term_of_fun_box_inst.term_of_fun_box) @ cNitpick.term_of_fun_box_inst.term_of_fun_box))
(TNitpick.typerep_fun_box_inst.typerep_fun_box,((c== @ cNitpick.typerep_fun_box_inst.typerep_fun_box) @ cNitpick.typerep_fun_box_inst.typerep_fun_box))
(TNum.linordered_idom.neg_numeral_less_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((V5 @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)) @ (((cNum.numeral.numeral @ V7) @ V6) @ V11))))))))))))))))))))))))))))
(TNum.linordered_idom.not_one_less_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ V7) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_idom_class.neg_numeral_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V1) @ V0)))))))
(TNum.linordered_idom_class.neg_numeral_le_one,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNum.linordered_semidom.not_numeral_less_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cHOL.Not @ ((V5 @ (((cNum.numeral.numeral @ V3) @ V0) @ V6)) @ V1))))))))))))))))))
(TNum.linordered_semidom_class.zero_le_numeral,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.numeral_class.numeral_class.numeral_dict,((c== @ cNum.numeral_class.numeral) @ ((cNum.numeral.numeral @ cGroups.one_class.one) @ cGroups.plus_class.plus)))
(TNum.semiring_char_0_class.numeral_eq_one_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ cNum.num.One)))))
(TNum.semiring_char_0_class.one_eq_numeral_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cHOL.eq @ cNum.num.One) @ V0)))))
(TOrderings.class.unbounded_dense_linorder_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cOrderings.class.unbounded_dense_linorder @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.class.no_bot @ V0) @ V1)) @ ((cOrderings.class.no_top @ V0) @ V1)))))))))
(TOrderings.linorder_class.strict_mono_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.strict_mono @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ (V0 @ V2))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TOrderings.order_class.order.order_iff_strict,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_class.order.strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TOrderings.unbounded_dense_linorder_class_def,((c== @ (cOrderings.unbounded_dense_linorder_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.dense_linorder_class @ cTYPE)) @ ((cPure.conjunction @ (cOrderings.no_bot_class @ cTYPE)) @ (cOrderings.no_top_class @ cTYPE)))))
(TPower.comm_semiring_1_class.le_imp_power_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((cRings.dvd_class.dvd @ ((cPower.power_class.power @ V2) @ V0)) @ ((cPower.power_class.power @ V2) @ V1))))))))))
(TPower.linordered_idom.not_sum_power2_lt_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ ((V6 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V7) @ V9) @ V11) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ V3))))))))))))))))))))))))))))
(TPower.linordered_idom.sum_power2_eq_zero_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((cHOL.eq @ ((V6 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V7) @ V9) @ V11) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V10) @ V3)) @ ((cHOL.eq @ V11) @ V3)))))))))))))))))))))))))))))
(TPower.linordered_idom.sum_power2_gt_zero_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V3) @ ((V6 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V7) @ V9) @ V11) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))) @ ((cHOL.disj @ (cHOL.Not @ ((cHOL.eq @ V10) @ V3))) @ (cHOL.Not @ ((cHOL.eq @ V11) @ V3))))))))))))))))))))))))))))))
(TPower.linordered_idom.sum_power2_le_zero_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V4 @ ((V6 @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V7) @ V9) @ V11) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V10) @ V3)) @ ((cHOL.eq @ V11) @ V3)))))))))))))))))))))))))))))
(TPower.linordered_idom_class.zero_less_power2,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))))))
(TPower.linordered_semidom.power_le_imp_le_exp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((c==> @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V8))) @ ((cNat.ord_nat_inst.less_eq_nat @ V7) @ V8)))))))))))))))))))))))
(TPower.linordered_semidom_class.zero_le_power,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TPower.ring_1_no_zero_divisors.zero_eq_power2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ V3)) @ ((cHOL.eq @ V6) @ V3))))))))))))))))))
(TQuickcheck_Exhaustive.arity_check_all_nibble,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_option,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_finite_1_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_finite_1_inst.check_all_finite_1 @ V0)) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_1.a\<__caret__sub>1) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))))))
(TQuickcheck_Exhaustive.check_all_finite_2_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_finite_2_inst.check_all_finite_2 @ V0)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>1) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>2) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))))))
(TQuickcheck_Exhaustive.check_all_finite_3_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_finite_3_inst.check_all_finite_3 @ V0)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>1) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>2) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>3) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))))))))
(TQuickcheck_Exhaustive.check_all_finite_4_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.check_all_finite_4_inst.check_all_finite_4 @ V0)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>1) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>2) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>3) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>4) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))))))))
(TQuickcheck_Exhaustive.class.check_all.axioms,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cQuickcheck_Exhaustive.class.check_all @ V0) @ V1) @ V2)) @ (((cEnum.class.enum @ V0) @ V1) @ V2)))))))))
(TQuickcheck_Exhaustive.equal_three_valued_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.exhaustive_class.intro,((c==> @ (cCode_Evaluation.term_of_class @ cTYPE)) @ (cQuickcheck_Exhaustive.exhaustive_class @ cTYPE)))
(TQuickcheck_Exhaustive.exhaustive_class.super,((c==> @ (cQuickcheck_Exhaustive.exhaustive_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TQuickcheck_Exhaustive.exhaustive_fun'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (((V0 @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V5 @ (^[V9]: V8)))) @ V7)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V6)) @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V10]: (V5 @ (((cFun.fun_upd @ V8) @ V9) @ V10)))) @ V7))) @ V7))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7)) @ cOption.option.None)))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ V0) @ V1) @ V2)) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V3]: (V0 @ (^[V4]: V3)))) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V1)) @ (((cQuickcheck_Exhaustive.exhaustive_fun' @ (^[V3]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: (V0 @ (((cFun.fun_upd @ V3) @ V4) @ V5)))) @ V2))) @ V2))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)) @ cOption.option.None)))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ (((V0 @ V4) @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ V7)) @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V5) @ V6) @ ((cInt.plus_int_inst.plus_int @ V7) @ cInt.one_int_inst.one_int)))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ (((cQuickcheck_Exhaustive.exhaustive_int' @ V0) @ V1) @ ((cInt.plus_int_inst.plus_int @ V2) @ cInt.one_int_inst.one_int)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_integer_inst.exhaustive_integer @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V0) @ (cCode_Numeral.integer_of_natural @ V1)) @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ (cCode_Numeral.integer_of_natural @ V1)))))))))
(TQuickcheck_Exhaustive.exhaustive_natural_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_natural_inst.exhaustive_natural @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V0) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)))))))
(TQuickcheck_Exhaustive.exhaustive_set.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_set_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_set_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_set_rel_def,((c== @ cQuickcheck_Exhaustive.exhaustive_set_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))
(TQuickcheck_Exhaustive.neg_bound_cps_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.neg_bound_cps_bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V2 @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((V0 @ (^[V4]: (((cQuickcheck_Exhaustive.unknown.unknown_case @ (V2 @ cQuickcheck_Exhaustive.unknown.Unknown)) @ (^[V5]: (((V1 @ V5) @ V2) @ V3))) @ V4))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))
(TQuickcheck_Exhaustive.neg_bound_cps_plus_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.neg_bound_cps_plus @ V0) @ V1)) @ (^[V2]: (^[V3]: ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (^[V4]: (cQuickcheck_Exhaustive.three_valued.Value @ V4))) @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ ((V1 @ V2) @ V3))) @ (^[V4]: (cQuickcheck_Exhaustive.three_valued.Value @ V4))) @ ((V1 @ V2) @ V3)) @ ((V0 @ V2) @ V3))))))))))
(TQuickcheck_Exhaustive.pos_bound_cps_bind_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.pos_bound_cps_bind @ V0) @ V1)) @ (^[V2]: (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((V0 @ (^[V4]: (((V1 @ V4) @ V2) @ V3))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))
(TQuickcheck_Exhaustive.pos_bound_cps_plus_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.pos_bound_cps_plus @ V0) @ V1)) @ (^[V2]: (^[V3]: (((cOption.option.option_case @ ((V1 @ V2) @ V3)) @ (^[V4]: (cOption.option.Some @ V4))) @ ((V0 @ V2) @ V3))))))))))
(TQuickcheck_Exhaustive.random_aux_unknown_def,((c== @ cQuickcheck_Exhaustive.random_aux_unknown) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.unknown.Unknown) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.unknown.Known) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil)))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.unknown.Unknown) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.unknown.Known) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil)))) @ V4)))))) @ V0))))
(TQuickcheck_Exhaustive.term_syntax.setify_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.setify @ V0) @ V1)) @ (((cList.foldr @ (cQuickcheck_Exhaustive.term_syntax.termify_insert @ V0)) @ V1) @ (cQuickcheck_Exhaustive.term_syntax.term_emptyset @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.Value_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Exhaustive.three_valued.Value @ V0)) @ (cQuickcheck_Exhaustive.Abs_three_valued @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.Leaf @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Exhaustive.three_valued.Value @ V8))) @ ((cHOL.eq @ (V4 @ V8)) @ (V5 @ V8)))))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V1) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ ((cHOL.eq @ V6) @ V7))) @ ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V2) @ V4) @ V6) @ V0)) @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V3) @ V5) @ V7) @ V1)))))))))))))))))))))))
(TQuickcheck_Exhaustive.three_valued.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (V0 @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V1) @ V2) @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ (cHOL.Not @ (V0 @ V1)))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cQuickcheck_Exhaustive.three_valued.Value @ V5))) @ (cHOL.Not @ (V0 @ (V2 @ V5))))))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ (cHOL.Not @ (V0 @ V3))))))))))))))))))
(TQuickcheck_Exhaustive.unknown.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V2) @ V3) @ V0)) @ (((cQuickcheck_Exhaustive.unknown.unknown_case @ V2) @ V3) @ V1))))))))))))
(TQuickcheck_Exhaustive.valtermify_fun_upd_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V0) @ V1) @ V2)) @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cFun.fun_upd) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)) @ V1)) @ V2)))))))))
(TQuickcheck_Narrowing.arity_narrowing_integer,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_natural,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_unknown,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V1) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cInt.zero_int_inst.zero_int))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cInt.minus_int_inst.minus_int @ V1) @ cInt.one_int_inst.one_int)) @ V1)) @ V0)))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Narrowing.around_zero_rel) @ V1))))))))
(TQuickcheck_Narrowing.around_zero_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.around_zero_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V4)) @ cList.list.Nil))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int))) @ ((cQuickcheck_Narrowing.around_zero_graph @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)))))) @ V2)))))))) @ V2)))))))))
(TQuickcheck_Narrowing.around_zero_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.around_zero_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (V2 @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V3) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V3)) @ cList.list.Nil))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int))) @ ((cQuickcheck_Narrowing.around_zero_graph @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int)) @ (V2 @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int)))))))))))))))))
(TQuickcheck_Narrowing.around_zero_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.around_zero_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cInt.zero_int_inst.zero_int))) @ ((V2 @ ((cInt.minus_int_inst.minus_int @ V3) @ cInt.one_int_inst.one_int)) @ V3)))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.cfun.cfun_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuickcheck_Narrowing.cfun.cfun_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.cfun.Constant @ V4))) @ ((c==> @ ((cHOL.eq @ V2) @ (V0 @ V4))) @ V3))))) @ V3)))))))))))
(TQuickcheck_Narrowing.cfun.cfun_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.cfun.cfun_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.cfun.Constant @ V3))) @ ((cHOL.eq @ V2) @ (V0 @ V3)))))))))))))
(TQuickcheck_Narrowing.ffun.ffun_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.ffun.Constant @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ (V0 @ V5))) @ V4))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V2) @ (((cQuickcheck_Narrowing.ffun.Update @ V7) @ V8) @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ ((((V1 @ V7) @ V8) @ V5) @ V6))) @ ((c==> @ ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ V5) @ V6)) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Narrowing.ffun.ffun_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.ffun.Constant @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4)))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cQuickcheck_Narrowing.ffun.Update @ V6) @ V7) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ ((((V1 @ V6) @ V7) @ V4) @ V5))) @ ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ V4) @ V5))))))))))))))))))))))
(TQuickcheck_Narrowing.is_testable_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cQuickcheck_Narrowing.is_testable_class @ cTYPE)))
(TQuickcheck_Narrowing.is_testable_class.super,((c==> @ (cQuickcheck_Narrowing.is_testable_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TQuickcheck_Narrowing.narrowing_cons.eq.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_cons.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_term.distinct_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.distinct_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (cHOL.Not @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.eq.simps_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.eq.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_term.eq.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.narrowing_term.eq.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((cHOL.equal_class.equal @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1)) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V3))) @ cHOL.False))))))))))
(TQuickcheck_Narrowing.narrowing_term.nchotomy,(cHOL.All @ (^[V0]: ((cHOL.disj @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V1) @ V2))))))) @ (cHOL.Ex @ (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V0) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V1) @ V2))))))))))
(TQuickcheck_Narrowing.narrowing_type.eq.simps,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cHOL.equal_class.equal @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0)) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.nchotomy,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V1)))))))
(TQuickcheck_Narrowing.nat.narrowing_nat.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_nat_inst.narrowing_nat) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cNat.zero_nat_inst.zero_nat)) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cNat.Suc)) @ cQuickcheck_Narrowing.narrowing_nat_inst.narrowing_nat))))
(TQuickcheck_Narrowing.non_empty_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.non_empty_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4)) @ (cHOL.Not @ (cList.null @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.num.narrowing_num.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_num_inst.narrowing_num) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cNum.num.One)) @ ((cQuickcheck_Narrowing.sum @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cNum.num.Bit0)) @ cQuickcheck_Narrowing.narrowing_num_inst.narrowing_num)) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cNum.num.Bit1)) @ cQuickcheck_Narrowing.narrowing_num_inst.narrowing_num)))))
(TQuickcheck_Narrowing.property.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((((cQuickcheck_Narrowing.property.property_case @ V2) @ V3) @ V4) @ V0)) @ ((((cQuickcheck_Narrowing.property.property_case @ V2) @ V3) @ V4) @ V1))))))))))))))
(TQuickcheck_Narrowing.random_aux_property_def,((c== @ cQuickcheck_Narrowing.random_aux_property) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_bool_inst.random_bool @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.property.Property) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_fun_lift @ (V2 @ V3))) @ (^[V6]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V7]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.property.Universal) @ (^[V8]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)) @ V7)))))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_fun_lift @ (V2 @ V3))) @ (^[V6]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V7]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.property.Existential) @ (^[V8]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)) @ V7)))))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_bool_inst.random_bool @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.property.Property) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil))))) @ V4)))))) @ V0))))
(TQuickcheck_Narrowing.sum.narrowing_sum.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.sum @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cSum_Type.Inl)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cSum_Type.Inr)) @ cQuickcheck_Narrowing.narrowing_class.narrowing))))
(TQuickcheck_Random.arity_random_lazy_sequence,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Random.random_fun_inst.random_fun,((c== @ cQuickcheck_Random.random_fun_inst.random_fun) @ cQuickcheck_Random.random_fun_inst.random_fun))
(TQuickcheck_Random.random_int_inst.random_int,((c== @ cQuickcheck_Random.random_int_inst.random_int) @ cQuickcheck_Random.random_int_inst.random_int))
(TQuickcheck_Random.random_nat_inst.random_nat,((c== @ cQuickcheck_Random.random_nat_inst.random_nat) @ cQuickcheck_Random.random_nat_inst.random_nat))
(TQuickcheck_Random.random_num_inst.random_num,((c== @ cQuickcheck_Random.random_num_inst.random_num) @ cQuickcheck_Random.random_num_inst.random_num))
(TQuickcheck_Random.random_seq_inst.random_seq,((c== @ cQuickcheck_Random.random_seq_inst.random_seq) @ cQuickcheck_Random.random_seq_inst.random_seq))
(TQuickcheck_Random.random_set_inst.random_set,((c== @ cQuickcheck_Random.random_set_inst.random_set) @ cQuickcheck_Random.random_set_inst.random_set))
(TQuickcheck_Random.random_sum_inst.random_sum,((c== @ cQuickcheck_Random.random_sum_inst.random_sum) @ cQuickcheck_Random.random_sum_inst.random_sum))
(TRecord.iso_tuple_surjective_proof_assist_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRecord.iso_tuple_surjective_proof_assist @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (V2 @ V0)) @ V1)))))))))
(TRecord.iso_tuple_surjective_proof_assist_idE,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cRecord.iso_tuple_surjective_proof_assist @ V0) @ V1) @ cFun.id)) @ ((cHOL.eq @ V0) @ V1)))))))
(TRings.class.linordered_semiring_1_strict_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c== @ ((((((cRings.class.linordered_semiring_1_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((((cRings.class.semiring_1 @ V5) @ V4) @ V0) @ V1))))))))))))))))
(TRings.class.linordered_semiring_strict.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V2) @ V3)) @ ((c==> @ ((cRings.class.semiring @ V0) @ V4)) @ ((c==> @ (((cRings.class.linordered_semiring_strict_axioms @ V1) @ V3) @ V4)) @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))))
(TRings.class.ordered_cancel_comm_semiring_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.ordered_cancel_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ (((((cRings.class.ordered_comm_semiring @ V0) @ V2) @ V3) @ V1) @ V4))))))))))))))
(TRings.class.ordered_comm_semiring_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.ordered_comm_semiring_axioms @ V0) @ V1) @ V2)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((cHOL.implies @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))))))))))
(TRings.linordered_idom.mult_less_cancel_left1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V10) @ ((V9 @ V10) @ V11))) @ ((cHOL.conj @ ((cHOL.implies @ ((V4 @ V3) @ V10)) @ ((V5 @ V7) @ V11))) @ ((cHOL.implies @ ((V4 @ V10) @ V3)) @ ((V5 @ V11) @ V7))))))))))))))))))))))))))))))
(TRings.linordered_idom.mult_less_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ ((V9 @ V10) @ V11)) @ V10)) @ ((cHOL.conj @ ((cHOL.implies @ ((V4 @ V3) @ V10)) @ ((V5 @ V11) @ V7))) @ ((cHOL.implies @ ((V4 @ V10) @ V3)) @ ((V5 @ V7) @ V11))))))))))))))))))))))))))))))
(TRings.linordered_ring_strict.mult_less_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ ((V7 @ V8) @ V9)) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((V5 @ V3) @ V8)) @ ((V5 @ V9) @ V3))) @ ((cHOL.conj @ ((V5 @ V8) @ V3)) @ ((V5 @ V3) @ V9))))))))))))))))))))))))))
(TRings.linordered_semidom_class.zero_less_one,((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TRings.linordered_semidom_class.zero_less_two,((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ cGroups.one_class.one)))
(TRings.linordered_semiring_1_strict_class_def,((c== @ (cRings.linordered_semiring_1_strict_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ (cRings.semiring_1_class @ cTYPE))))
(TRings.linordered_semiring_strict_class.intro,((c==> @ (cGroups.comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cRings.semiring_class @ cTYPE)) @ ((c==> @ (((cRings.class.linordered_semiring_strict_axioms @ cGroups.zero_class.zero) @ cOrderings.ord_class.less) @ cGroups.times_class.times)) @ (cRings.linordered_semiring_strict_class @ cTYPE))))))
(TRings.linordered_semiring_strict_class.super_3,((c==> @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ (cRings.semiring_class @ cTYPE)))
(TRings.linordered_semiring_strict_class.super_2,((c==> @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)))
(TRings.linordered_semiring_strict_class.super_1,((c==> @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ (cGroups.comm_monoid_add_class @ cTYPE)))
(TRings.ordered_cancel_comm_semiring_class_def,((c== @ (cRings.ordered_cancel_comm_semiring_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ (cRings.ordered_comm_semiring_class @ cTYPE))))
(TRings.ordered_ring_class.mult_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V1) @ V2)) @ ((cGroups.times_class.times @ V0) @ V2)))))))))))
(TRings.ordered_ring_class.ordered_ring_axioms,(((((((cRings.class.ordered_ring @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.times_class.times) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TRings.ordered_semiring_class.mult_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2)))))))))))
(TRings.ring_no_zero_divisors.mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V5) @ V6)) @ ((V0 @ V5) @ V7))) @ ((cHOL.disj @ ((cHOL.eq @ V5) @ V1)) @ ((cHOL.eq @ V6) @ V7)))))))))))))))))))))
(TRings.zero_neq_one_class.zero_neq_one_axioms,((cRings.class.zero_neq_one @ cGroups.one_class.one) @ cGroups.zero_class.zero))
(TSMT.narrowing_pattern_inst.narrowing_pattern,((c== @ cSMT.narrowing_pattern_inst.narrowing_pattern) @ cSMT.narrowing_pattern_inst.narrowing_pattern))
(TSet_Interval.dvd.atLeastAtMost_singleton_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ cRings.dvd_class.dvd) @ V0) @ V1)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TSet_Interval.dvd.greaterThanAtMost_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((((cSet_Interval.ord.greaterThanAtMost @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))))
(TSet_Interval.no_bot_class.lessThan_non_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.lessThan @ V0)) @ cOrderings.bot_class.bot)))))
(TSet_Interval.ord_class.greaterThanAtMost_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.greaterThan @ V0)) @ (cSet_Interval.ord_class.atMost @ V1))))))))
(TSet_Interval.ord_class.greaterThanAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSet_Interval.ord_class.ord_class.atMost_dict,((c== @ cSet_Interval.ord_class.atMost) @ (cSet_Interval.ord.atMost @ cOrderings.ord_class.less_eq)))
(TSet_Interval.order.atLeastLessThan_empty_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V2) @ V3)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((V1 @ V2) @ V3)))))))))))))
(TSet_Interval.order.atLeastatMost_psubset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.disj @ (cHOL.Not @ ((V0 @ V2) @ V3))) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((cHOL.conj @ ((V0 @ V3) @ V5)) @ ((cHOL.disj @ ((V1 @ V4) @ V2)) @ ((V1 @ V3) @ V5)))))) @ ((V0 @ V4) @ V5)))))))))))))))))
(TSet_Interval.order.greaterThanLessThan_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((cHOL.eq @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V3) @ V2)) @ cOrderings.bot_class.bot))))))))))))
(TSet_Interval.order.not_empty_eq_Ici_eq_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord.atLeast @ V0) @ V2)))))))))))
(TSet_Interval.order.not_empty_eq_Iic_eq_empty,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord.atMost @ V0) @ V2)))))))))))
(TSet_Interval.order_class.atLeastatMost_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TTransitive_Closure.converse_rtranclp_induct2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((V5 @ V3) @ V4)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((V0 @ ((cProduct_Type.Pair @ V6) @ V7)) @ ((cProduct_Type.Pair @ V8) @ V9))) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ ((cProduct_Type.Pair @ V8) @ V9)) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((V5 @ V8) @ V9)) @ ((V5 @ V6) @ V7))))))))))))) @ ((V5 @ V1) @ V2)))))))))))))))))
(TTransitive_Closure.trancl.trancl_into_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.trancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.trancl @ V2)))))))))))))
(TTyperep.typerep_integer_inst.typerep_integer,((c== @ cTyperep.typerep_integer_inst.typerep_integer) @ cTyperep.typerep_integer_inst.typerep_integer))
(TTyperep.typerep_literal_inst.typerep_literal,((c== @ cTyperep.typerep_literal_inst.typerep_literal) @ cTyperep.typerep_literal_inst.typerep_literal))
(TTyperep.typerep_natural_inst.typerep_natural,((c== @ cTyperep.typerep_natural_inst.typerep_natural) @ cTyperep.typerep_natural_inst.typerep_natural))
(TTyperep.typerep_typerep_inst.typerep_typerep,((c== @ cTyperep.typerep_typerep_inst.typerep_typerep) @ cTyperep.typerep_typerep_inst.typerep_typerep))
(TBig_Operators.complete_linorder_class.Max_Sup,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))
(TBig_Operators.complete_linorder_class.Min_Inf,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_idem,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V0)) @ V0))))
(TBig_Operators.linorder_class.min_max.inf_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V3)))))))))))))
(TBig_Operators.linorder_class.min_max.le_infI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V2)) @ V1)))))))))
(TBig_Operators.linorder_class.min_max.le_infI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V2) @ V0)) @ V1)))))))))
(TBig_Operators.linorder_class.min_max.le_supI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.le_supI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V2) @ V1))))))))))
(TBig_Operators.linorder_class.min_max.mono_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ (V0 @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cLattices.inf_class.inf @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TBig_Operators.linorder_class.min_max.mono_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (V0 @ V1)) @ (V0 @ V2))) @ (V0 @ ((cOrderings.ord_class.max @ V1) @ V2)))))))))))
(TBig_Operators.linorder_class.min_max.sup_idem,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V0)) @ V0))))
(TBig_Operators.linorder_class.min_max.sup_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.max @ V1) @ V3)))))))))))))
(TBig_Operators.linorder_class.mono_Max_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.linorder_class.Max @ V1))) @ (cBig_Operators.linorder_class.Max @ ((cSet.image @ V0) @ V1)))))))))))
(TBig_Operators.linorder_class.mono_Min_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.linorder_class.Min @ V1))) @ (cBig_Operators.linorder_class.Min @ ((cSet.image @ V0) @ V1)))))))))))
(TBig_Operators.semilattice_order_neutr_set_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((((cLattices.semilattice_neutr_order @ V0) @ V1) @ V2) @ V3)) @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1))))))))))))
(TBig_Operators.semilattice_set.insert_not_elem,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cBig_Operators.semilattice_set @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V1))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cBig_Operators.semilattice_set.F @ V0) @ ((cSet.insert @ V2) @ V1))) @ ((V0 @ V2) @ ((cBig_Operators.semilattice_set.F @ V0) @ V1))))))))))))))
(TCode_Evaluation.term.size_term_inst.size_term,((c== @ cCode_Evaluation.term.size_term_inst.size_term) @ cCode_Evaluation.term.size_term_inst.size_term))
(TCode_Evaluation.term.term_size_overloaded_def,((c== @ cCode_Evaluation.term.size_term_inst.size_term) @ (cCode_Evaluation.term.term_rec @ cNat.zero_nat_inst.zero_nat)))
(TCode_Numeral.equal_integer_inst.equal_integer,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TCode_Numeral.equal_natural_inst.equal_natural,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TCode_Numeral.minus_integer_inst.minus_integer,((c== @ cCode_Numeral.minus_integer_inst.minus_integer) @ cCode_Numeral.minus_integer_inst.minus_integer))
(TCode_Numeral.minus_natural_inst.minus_natural,((c== @ cCode_Numeral.minus_natural_inst.minus_natural) @ cCode_Numeral.minus_natural_inst.minus_natural))
(TCode_Numeral.ord_integer_inst.less_eq_integer,((c== @ cCode_Numeral.ord_integer_inst.less_eq_integer) @ cCode_Numeral.ord_integer_inst.less_eq_integer))
(TCode_Numeral.ord_natural_inst.less_eq_natural,((c== @ cCode_Numeral.ord_natural_inst.less_eq_natural) @ cCode_Numeral.ord_natural_inst.less_eq_natural))
(TCode_Numeral.times_integer_inst.times_integer,((c== @ cCode_Numeral.times_integer_inst.times_integer) @ cCode_Numeral.times_integer_inst.times_integer))
(TCode_Numeral.times_natural_inst.times_natural,((c== @ cCode_Numeral.times_natural_inst.times_natural) @ cCode_Numeral.times_natural_inst.times_natural))
(TComplete_Lattices.arity_complete_lattice_bool,(cComplete_Lattices.complete_lattice_class @ cTYPE))
(TComplete_Lattices.class.complete_linorder_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cOrderings.class.linorder @ V3) @ V4))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((cHOL.eq @ ((V2 @ (V10 @ V8)) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (V10 @ V11))))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ ((cSet.insert @ V8) @ V9)) @ (^[V11]: (V10 @ V11)))) @ ((V2 @ (V10 @ V8)) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ V10)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_le_SUP,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((V3 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ V9)) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_lower2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((c==> @ ((V3 @ (V10 @ V8)) @ V11)) @ ((V3 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V12]: (V10 @ V12)))) @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ ((cSet.insert @ V8) @ V9))) @ ((V2 @ V8) @ (V0 @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_le_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((V3 @ (V0 @ V8)) @ (V1 @ V8)))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_lower2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((c==> @ ((V3 @ V8) @ V10)) @ ((V3 @ (V0 @ V9)) @ V10)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ (V10 @ V8)) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (V10 @ V11))))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ ((cSet.insert @ V8) @ V9)) @ (^[V11]: (V10 @ V11)))) @ ((V5 @ (V10 @ V8)) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ V10)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (V9 @ V11)))) @ V10)) @ ((cSet.Ball @ V8) @ (^[V11]: ((V3 @ (V9 @ V11)) @ V10))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_upper2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((c==> @ ((V3 @ V10) @ (V11 @ V8))) @ ((V3 @ V10) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V12]: (V11 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ ((cSet.insert @ V8) @ V9))) @ ((V5 @ V8) @ (V1 @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ (V1 @ V8)) @ V9)) @ ((cSet.Ball @ V8) @ (^[V10]: ((V3 @ V10) @ V9))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_upper2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cSet.member @ V8) @ V9)) @ ((c==> @ ((V3 @ V10) @ V8)) @ ((V3 @ V10) @ (V1 @ V9))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.le_INF_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ V8) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (V10 @ V11))))) @ ((cSet.Ball @ V9) @ (^[V11]: ((V3 @ V8) @ (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.le_Inf_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ V8) @ (V0 @ V9))) @ ((cSet.Ball @ V9) @ (^[V10]: ((V3 @ V8) @ V10))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.less_INF_D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ V8) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V12]: (V10 @ V12))))) @ ((c==> @ ((cSet.member @ V11) @ V9)) @ ((V4 @ V8) @ (V10 @ V11))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder_class_def,((c== @ (cComplete_Lattices.complete_linorder_class @ cTYPE)) @ ((cPure.conjunction @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE))))
(TComplete_Partial_Order.ccpo.iteratesp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V4)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V6)) @ ((c==> @ (V5 @ V6)) @ (V5 @ (V3 @ V6))))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V6)) @ ((c==> @ ((cSet.Ball @ V6) @ (^[V7]: ((cHOL.conj @ ((((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3) @ V7)) @ (V5 @ V7))))) @ (V5 @ (V0 @ V6))))))) @ (V5 @ V4))))))))))))))))))
(TComplete_Partial_Order.ccpo_class.ccpo_axioms,(((cComplete_Partial_Order.class.ccpo @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TComplete_Partial_Order.ccpo_class.fixp_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ (((cComplete_Partial_Order.monotone @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq) @ V1)) @ ((c==> @ (call @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (V1 @ V2)))))) @ (V0 @ (cComplete_Partial_Order.ccpo_class.fixp @ V1))))))))))
(TComplete_Partial_Order.ccpo_class.fixp_unfold,(call @ (^[V0]: ((c==> @ (((cComplete_Partial_Order.monotone @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq) @ V0)) @ ((cHOL.eq @ (cComplete_Partial_Order.ccpo_class.fixp @ V0)) @ (V0 @ (cComplete_Partial_Order.ccpo_class.fixp @ V0)))))))
(TDivides.class.semiring_numeral_div_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c== @ (((((((((cDivides.class.semiring_numeral_div_axioms @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.conj @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: (cHOL.All @ (^[V11]: ((cHOL.implies @ ((cHOL.eq @ ((V3 @ V9) @ V10)) @ V11)) @ ((cHOL.eq @ V9) @ ((V6 @ V11) @ V10)))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V7 @ V9) @ V10)) @ ((cHOL.eq @ ((V3 @ ((V6 @ V10) @ V9)) @ V9)) @ V10))))))) @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.eq @ ((V0 @ V9) @ ((V1 @ V10) @ V9))) @ ((V6 @ V10) @ ((V2 @ V10) @ V9)))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V7 @ V4) @ V9)) @ ((cHOL.implies @ ((V8 @ V9) @ V10)) @ ((cHOL.eq @ ((V1 @ V9) @ V10)) @ V4)))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V7 @ V4) @ V9)) @ ((cHOL.implies @ ((V8 @ V9) @ V10)) @ ((cHOL.eq @ ((V2 @ V9) @ V10)) @ V9)))))))) @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V8 @ V4) @ V9)) @ ((cHOL.implies @ ((V7 @ V9) @ V10)) @ ((V8 @ V4) @ ((V1 @ V10) @ V9)))))))))))) @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V7 @ V4) @ V9)) @ ((V7 @ ((V2 @ V9) @ V10)) @ V9))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V8 @ V4) @ V9)) @ ((V8 @ ((V2 @ V10) @ V9)) @ V9))))))) @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V8 @ V4) @ V9)) @ ((V7 @ V4) @ ((V2 @ V10) @ V9)))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: (cHOL.All @ (^[V11]: ((cHOL.implies @ ((V7 @ V4) @ V9)) @ ((cHOL.eq @ ((V2 @ V10) @ ((V0 @ V11) @ V9))) @ ((V3 @ ((V0 @ V11) @ ((V2 @ ((V1 @ V10) @ V11)) @ V9))) @ ((V2 @ V10) @ V11))))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: (cHOL.All @ (^[V11]: ((cHOL.implies @ ((V7 @ V4) @ V9)) @ ((cHOL.eq @ ((V1 @ V10) @ ((V0 @ V11) @ V9))) @ ((V1 @ ((V1 @ V10) @ V11)) @ V9)))))))))) @ (cHOL.All @ (^[V9]: (cHOL.All @ (^[V10]: ((cHOL.eq @ ((V8 @ V9) @ V10)) @ ((V7 @ ((V3 @ V9) @ V5)) @ V10))))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.diff_invert_add1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((cHOL.eq @ ((V3 @ V9) @ V10)) @ V11)) @ ((cHOL.eq @ V9) @ ((V6 @ V11) @ V10)))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div_class.divmod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)) @ ((cProduct_Type.Pair @ ((cDivides.div_class.div @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cDivides.div_class.mod @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))))
(TDivides.semiring_numeral_div_class.fst_divmod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.fst @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1))) @ ((cDivides.div_class.div @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TDivides.semiring_numeral_div_class.snd_divmod,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cProduct_Type.snd @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1))) @ ((cDivides.div_class.mod @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TFields.class.division_ring_inverse_zero.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cFields.class.division_ring_inverse_zero_axioms @ V0) @ V5)) @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7))))))))))))))))))))
(TFields.division_ring.nonzero_inverse_minus_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ (V0 @ (V7 @ V8))) @ (V7 @ (V0 @ V8))))))))))))))))))))))))
(TFields.division_ring_class.add_divide_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cFields.inverse_class.divide @ V0) @ V2)) @ ((cFields.inverse_class.divide @ V1) @ V2))))))))))
(TFields.division_ring_inverse_zero.divide_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ V5)) @ V5)))))))))))))))))))))
(TFields.division_ring_inverse_zero_class.intro,((c==> @ (cFields.division_ring_class @ cTYPE)) @ ((c==> @ ((cFields.class.division_ring_inverse_zero_axioms @ cFields.inverse_class.inverse) @ cGroups.zero_class.zero)) @ (cFields.division_ring_inverse_zero_class @ cTYPE))))
(TFields.division_ring_inverse_zero_class.super,((c==> @ (cFields.division_ring_inverse_zero_class @ cTYPE)) @ (cFields.division_ring_class @ cTYPE)))
(TFields.field.nonzero_divide_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V1 @ V9) @ ((V2 @ V8) @ V9))) @ ((V1 @ V3) @ V8))))))))))))))))))))))))))
(TFields.field.nonzero_mult_divide_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V9) @ V8)) @ V8)) @ V9))))))))))))))))))))))))
(TFields.field_inverse_zero.divide_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ ((V1 @ V10) @ V9))) @ ((cHOL.disj @ ((cHOL.eq @ V9) @ V5)) @ ((cHOL.eq @ V8) @ V10)))))))))))))))))))))))))))
(TFields.field_inverse_zero.minus_divide_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ (V7 @ V8)) @ (V7 @ V9))) @ ((V1 @ V8) @ V9))))))))))))))))))))))))
(TFields.linordered_field.inverse_le_iff_le_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((cHOL.eq @ ((V9 @ (V0 @ V12)) @ (V0 @ V13))) @ ((V9 @ V13) @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field.inverse_le_imp_le_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ (V0 @ V12)) @ (V0 @ V13))) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V9 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field.inverse_less_iff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V10 @ V5) @ V13)) @ ((cHOL.eq @ ((V10 @ (V0 @ V12)) @ (V0 @ V13))) @ ((V10 @ V13) @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field.inverse_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ (V0 @ V12)) @ (V0 @ V13))) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((V10 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field.le_imp_inverse_le_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V9 @ (V0 @ V13)) @ (V0 @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field.less_imp_inverse_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((V10 @ (V0 @ V13)) @ (V0 @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field.mult_imp_div_pos_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V10 @ V13) @ ((V2 @ V14) @ V12))) @ ((V10 @ ((V1 @ V13) @ V12)) @ V14)))))))))))))))))))))))))))))))))))
(TFields.linordered_field.mult_imp_less_div_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((c==> @ ((V10 @ ((V2 @ V13) @ V12)) @ V14)) @ ((V10 @ V13) @ ((V1 @ V14) @ V12))))))))))))))))))))))))))))))))))))
(TFinite_Set.comp_fun_commute.commute_left_comp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (V0 @ V1)) @ ((cFun.comp @ (V0 @ V2)) @ V3))) @ ((cFun.comp @ (V0 @ V2)) @ ((cFun.comp @ (V0 @ V1)) @ V3)))))))))))))
(TFinite_Set.comp_fun_commute.fold_graph_determ,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V4)) @ ((cHOL.eq @ V4) @ V3)))))))))))))))
(TFinite_Set.comp_fun_commute.fold_graph_finite,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ (cFinite_Set.finite @ V2))))))))))))
(TGroups.ab_group_add_class.ab_group_add_axioms,((((cGroups.class.ab_group_add @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TGroups.comm_monoid_add_class.add.comm_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TGroups.comm_monoid_add_class.add.left_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TGroups.comm_monoid_diff.add_diff_cancel_left',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V3) @ V4)) @ V3)) @ V4)))))))))))))
(TGroups.comm_monoid_diff.add_diff_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V3) @ V4)) @ ((V0 @ V5) @ V4))) @ ((V2 @ V3) @ V5))))))))))))))))
(TGroups.linordered_ab_group_add.equal_neg_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V6) @ (V3 @ V6))) @ ((cHOL.eq @ V6) @ V1))))))))))))))))))
(TGroups.linordered_ab_group_add.neg_equal_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (V3 @ V6)) @ V6)) @ ((cHOL.eq @ V6) @ V1))))))))))))))))))
(TGroups.ordered_ab_group_add.diff_eq_diff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cHOL.eq @ ((V2 @ V6) @ V7)) @ ((V2 @ V8) @ V9))) @ ((cHOL.eq @ ((V5 @ V6) @ V7)) @ ((V5 @ V8) @ V9)))))))))))))))))))))))))
(TGroups.ordered_ab_group_add.neg_less_iff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ (V3 @ V6)) @ (V3 @ V7))) @ ((V5 @ V7) @ V6))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_of_nonneg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V5 @ V2) @ V7)) @ ((cHOL.eq @ (V0 @ V7)) @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_of_nonpos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((V5 @ V7) @ V2)) @ ((cHOL.eq @ (V0 @ V7)) @ (V4 @ V7)))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_leI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ V0)) @ V1))))))))
(TGroups.ordered_ab_semigroup_add.add_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ ((V0 @ V5) @ V3)) @ ((V0 @ V5) @ V4)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((V2 @ V5) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_neg_nonpos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V4) @ V1)) @ ((c==> @ ((V2 @ V5) @ V1)) @ ((V3 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_nonneg_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((V3 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_nonpos_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V4) @ V1)) @ ((c==> @ ((V3 @ V5) @ V1)) @ ((V3 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_pos_nonneg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V1) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((V3 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TInductive.complete_lattice_class.lfp_greatest,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cInductive.complete_lattice_class.lfp @ V0))))))))
(TInt.arity_ordered_cancel_ab_semigroup_add_int,(cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE))
(TLattices.boolean_algebra.compl_less_compl_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ (V1 @ V8)) @ (V1 @ V9))) @ ((V4 @ V9) @ V8))))))))))))))))))))))))
(TLattices.boolean_algebra.dual_boolean_algebra,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cLattices.class.boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cLattices.class.boolean_algebra @ (^[V8]: (^[V9]: ((V5 @ V8) @ (V1 @ V9))))) @ V1) @ V5) @ (^[V8]: (^[V9]: ((V3 @ V9) @ V8)))) @ (^[V8]: (^[V9]: ((V4 @ V9) @ V8)))) @ V2) @ V7) @ V6)))))))))))))))))))
(TLattices.boolean_algebra_class.compl_le_swap1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cGroups.uminus_class.uminus @ V0))))))))
(TLattices.boolean_algebra_class.compl_le_swap2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V1)) @ V0)))))))
(TLattices.bounded_lattice.dual_bounded_lattice,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cLattices.class.bounded_lattice @ V3) @ (^[V6]: (^[V7]: ((V1 @ V7) @ V6)))) @ (^[V6]: (^[V7]: ((V2 @ V7) @ V6)))) @ V0) @ V5) @ V4)))))))))))))))
(TLattices.distrib_lattice.dual_distrib_lattice,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((((cLattices.class.distrib_lattice @ V3) @ (^[V4]: (^[V5]: ((V1 @ V5) @ V4)))) @ (^[V4]: (^[V5]: ((V2 @ V5) @ V4)))) @ V0)))))))))))
(TLattices.semilattice_inf_class.inf.cobounded1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V0))))))
(TLattices.semilattice_inf_class.inf.cobounded2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V1))))))
(TLattices.semilattice_inf_class.inf.right_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TLattices.semilattice_inf_class.inf_right_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V1)))))))
(TLattices.semilattice_sup_class.sup.cobounded1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TLattices.semilattice_sup_class.sup.cobounded2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V1) @ V0)))))))
(TLattices.semilattice_sup_class.sup.right_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V1)))))))
(TLazy_Sequence.lazy_sequence.Rep_lazy_sequence,(call @ (^[V0]: ((cSet.member @ (cLazy_Sequence.Rep_lazy_sequence @ V0)) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set)))))
(TLazy_Sequence.list_of_lazy_sequence_hit_bound,((cHOL.eq @ (cLazy_Sequence.list_of_lazy_sequence @ cLazy_Sequence.hit_bound)) @ ((cList.list.Cons @ cOption.option.None) @ cList.list.Nil)))
(TList.linorder.sorted_list_of_set_sort_remdups,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cList.linorder.sorted_list_of_set @ V0) @ (cList.set @ V2))) @ (((cList.linorder.sort_key @ V0) @ (^[V3]: V3)) @ (cList.remdups @ V2)))))))))))
(TList.linorder_class.sorted_list_of_set.insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ ((cSet.insert @ V1) @ V0))) @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V1) @ (cList.linorder_class.sorted_list_of_set @ V0))))))))))
(TList.linorder_class.sorted_list_of_set.remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ V0)) @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V1) @ (cList.linorder_class.sorted_list_of_set @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))
(TList.linorder_class.sorted_list_of_set_insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ ((cSet.insert @ V1) @ V0))) @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V1) @ (cList.linorder_class.sorted_list_of_set @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))
(TList.linorder_class.sorted_list_of_set_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))) @ ((cList.remove1 @ V1) @ (cList.linorder_class.sorted_list_of_set @ V0)))))))))
(TList.listrel1_rtrancl_subset_rtrancl_listrel1,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cList.listrel1 @ (cTransitive_Closure.rtrancl @ V0))) @ (cTransitive_Closure.rtrancl @ (cList.listrel1 @ V0))))))
(TMain.narrowing_sumbool_inst.narrowing_sumbool,((c== @ cMain.narrowing_sumbool_inst.narrowing_sumbool) @ cMain.narrowing_sumbool_inst.narrowing_sumbool))
(TNat.arity_ordered_cancel_comm_monoid_diff_nat,(cGroups.ordered_cancel_comm_monoid_diff_class @ cTYPE))
(TNitpick.fun_box.full_exhaustive_fun_box.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cNitpick.fun_box.FunBox @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TNitpick.pair_box.pair_box_size_overloaded_def,((c== @ cNat.size_class.size) @ (cNitpick.pair_box.pair_box_rec @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat)))))
(TNum.linordered_idom.not_zero_less_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ V3) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V10)))))))))))))))))))))))))))
(TNum.linordered_idom_class.neg_numeral_le_zero,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNum.linordered_semidom_class.le_numeral_extra_4,((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ cGroups.one_class.one))
(TNum.linordered_semidom_class.le_numeral_extra_3,((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ cGroups.zero_class.zero))
(TNum.linordered_semidom_class.le_numeral_extra_2,(cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNum.linordered_semidom_class.le_numeral_extra_1,((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TNum.linordered_semidom_class.le_numeral_simps_5,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.linordered_semidom_class.le_numeral_simps_4,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.linordered_semidom_class.le_numeral_simps_3,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ cNum.num.One)))))
(TNum.linordered_semidom_class.le_numeral_simps_2,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.linordered_semidom_class.le_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ V1)))))))
(TNum.linordered_semidom_class.numeral_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.neg_numeral_class.add_neg_numeral_special_2,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0)))))
(TNum.neg_numeral_class.add_neg_numeral_special_1,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))) @ ((cNum.neg_numeral_class.sub @ cNum.num.One) @ V0)))))
(TNum.neg_numeral_class.is_num_add_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cNum.neg_numeral_class.is_num @ V0)) @ ((c==> @ (cNum.neg_numeral_class.is_num @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))))
(TNum.ring_char_0_class.neg_numeral_neq_numeral,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))))))))
(TNum.ring_char_0_class.numeral_neq_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cHOL.eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TOrderings.order_bot_class.bot.extremum_strict,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ cOrderings.bot_class.bot)))))
(TOrderings.order_bot_class.bot.extremum_unique,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TOrderings.order_bot_class.bot.not_eq_extremum,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less @ cOrderings.bot_class.bot) @ V0)))))
(TOrderings.order_class.dual_order.strict_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.order_top_class.top.extremum_strict,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cOrderings.top_class.top) @ V0)))))
(TOrderings.order_top_class.top.extremum_unique,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ V0)) @ ((cHOL.eq @ V0) @ cOrderings.top_class.top)))))
(TOrderings.order_top_class.top.not_eq_extremum,(call @ (^[V0]: ((cHOL.eq @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.top_class.top))) @ ((cOrderings.ord_class.less @ V0) @ cOrderings.top_class.top)))))
(TPower.linordered_idom.odd_0_le_power_imp_0_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ ((V4 @ V3) @ ((((cPower.power.power @ V7) @ V9) @ V10) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V11))))) @ ((V4 @ V3) @ V10))))))))))))))))))))))))))))
(TPower.linordered_idom.zero_less_power_abs_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V3) @ ((((cPower.power.power @ V7) @ V9) @ (V0 @ V10)) @ V11))) @ ((cHOL.disj @ (cHOL.Not @ ((cHOL.eq @ V10) @ V3))) @ ((cHOL.eq @ V11) @ cNat.zero_nat_inst.zero_nat)))))))))))))))))))))))))))))
(TPower.linordered_idom_class.zero_le_power_abs,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ (cGroups.abs_class.abs @ V0)) @ V1)))))))
(TPower.linordered_ring.not_sum_squares_lt_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (cHOL.Not @ ((V5 @ ((V6 @ ((V7 @ V8) @ V8)) @ ((V7 @ V9) @ V9))) @ V3))))))))))))))))))))))))
(TPower.linordered_semidom.power2_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((((cPower.power.power @ V3) @ V2) @ V7) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((c==> @ ((V4 @ V1) @ V7)) @ ((V5 @ V6) @ V7)))))))))))))))))))))
(TPower.linordered_semidom.power_eq_imp_eq_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cHOL.eq @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V7))) @ ((c==> @ ((V4 @ V1) @ V6)) @ ((c==> @ ((V4 @ V1) @ V8)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V7)) @ ((cHOL.eq @ V6) @ V8)))))))))))))))))))))))))
(TPower.linordered_semidom.power_increasing_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((cHOL.eq @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V8))) @ ((cNat.ord_nat_inst.less_eq_nat @ V7) @ V8)))))))))))))))))))))))
(TPower.linordered_semidom.power_le_imp_le_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V4 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ (cNat.Suc @ V7))) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ (cNat.Suc @ V7)))) @ ((c==> @ ((V4 @ V1) @ V8)) @ ((V4 @ V6) @ V8)))))))))))))))))))))))
(TPower.linordered_semidom.power_less_power_Suc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((V2 @ V6) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7))))))))))))))))))))))
(TPower.linordered_semidom_class.one_less_power,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cPower.power_class.power @ V0) @ V1)))))))))
(TPower.linordered_semidom_class.power_Suc_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ V0) @ V1)))))))))
(TPower.ring_1_no_zero_divisors.power2_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V6) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V0)) @ ((cHOL.eq @ V6) @ (V5 @ V0))))))))))))))))))))
(TPredicate.arity_complete_boolean_algebra_pred,(cComplete_Lattices.complete_boolean_algebra_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_type_three_valued,(cHOL.type_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_n_lists.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TQuickcheck_Exhaustive.check_all_n_lists.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.check_all_n_lists @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V4 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V6]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: ((cQuickcheck_Exhaustive.check_all_n_lists @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))) @ V3)))))))) @ V3)))))))))))
(TQuickcheck_Exhaustive.check_all_n_lists.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.check_all_n_lists @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V0 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V2]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.check_all_n_lists @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V4)) @ (^[V6]: ((cList.list.Cons @ (V3 @ cProduct_Type.Unity)) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ cList.list.Nil))) @ V1)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ V1)))))))) @ V1)))))))
(TQuickcheck_Exhaustive.check_all_subsets.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ V3)))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6))) @ V3)))))))))) @ V3))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V3]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V3))) @ cOption.option.Some) @ (V0 @ V3)))) @ V2)))))))))
(TQuickcheck_Exhaustive.check_all_subsets.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ cList.list.Nil)) @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))
(TQuickcheck_Exhaustive.enum_term_of_nibble_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_nibble_inst.enum_term_of_nibble) @ (^[V0]: (^[V1]: ((cList.map @ cCode_Evaluation.term_of_nibble_inst.term_of_nibble) @ cString.enum_nibble_inst.enum_nibble)))))
(TQuickcheck_Exhaustive.enum_term_of_option_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_class.enum_term_of) @ (^[V0]: (^[V1]: ((cList.list.Cons @ (cCode_Evaluation.term_of_class.term_of @ cOption.option.None)) @ ((cList.map @ (cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.check_all_class.enum_term_of @ cTYPE) @ cProduct_Type.Unity)))))))
(TQuickcheck_Exhaustive.exhaustive_fun'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (((V3 @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_rel_def,((c== @ cQuickcheck_Exhaustive.exhaustive_fun'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V3 @ (((cFun.fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ (((V3 @ V4) @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_rel_def,((c== @ cQuickcheck_Exhaustive.exhaustive_int'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_def,((c== @ cQuickcheck_Exhaustive.exhaustive_integer') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.exhaustive_integer'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_def,((c== @ cQuickcheck_Exhaustive.exhaustive_natural') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.exhaustive_natural'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.exhaustive_set_sumC_def,((c== @ cQuickcheck_Exhaustive.exhaustive_set_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.exhaustive_set_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ V0) @ V1) @ V1)))))))
(TQuickcheck_Exhaustive.full_exhaustive_int_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_int_inst.full_exhaustive_int @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V0) @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_natural @ V1))) @ (cInt.uminus_int_inst.uminus_int @ (cCode_Numeral.int_of_integer @ (cCode_Numeral.integer_of_natural @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_nat_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_nat_inst.full_exhaustive_nat @ V0) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural_inst.full_exhaustive_natural @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cCode_Numeral.nat_of_natural @ V2)) @ (^[V4]: (cCode_Evaluation.term_of_nat_inst.term_of_nat @ (cCode_Numeral.nat_of_natural @ V2))))))))) @ V1)))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive) @ (^[V0]: (^[V1]: (cQuickcheck_Exhaustive.full_exhaustive_set_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TQuickcheck_Exhaustive.neg_bound_cps_empty_def,((cHOL.eq @ cQuickcheck_Exhaustive.neg_bound_cps_empty) @ (^[V0]: (^[V1]: cQuickcheck_Exhaustive.three_valued.No_value))))
(TQuickcheck_Exhaustive.pos_bound_cps_empty_def,((cHOL.eq @ cQuickcheck_Exhaustive.pos_bound_cps_empty) @ (^[V0]: (^[V1]: cOption.option.None))))
(TQuickcheck_Exhaustive.random_three_valued_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Exhaustive.random_aux_three_valued @ V0) @ V0)))))
(TQuickcheck_Exhaustive.type_definition_unknown,(((cTypedef.type_definition @ cQuickcheck_Exhaustive.Rep_unknown) @ cQuickcheck_Exhaustive.Abs_unknown) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set)))
(TQuickcheck_Exhaustive.unknown.unknown_rec_def,((c== @ cQuickcheck_Exhaustive.unknown.unknown_rec) @ (^[V0]: (^[V1]: (^[V2]: (cHOL.The @ (^[V3]: ((((cQuickcheck_Exhaustive.unknown.unknown_rec_set @ V0) @ V1) @ V2) @ V3))))))))
(TQuickcheck_Exhaustive.valtermify_absdummy_def,((cHOL.eq @ cQuickcheck_Exhaustive.valtermify_absdummy) @ (cProduct_Type.prod.prod_case @ (^[V0]: (^[V1]: ((cProduct_Type.Pair @ (^[V2]: V0)) @ (^[V2]: (((cCode_Evaluation.Abs @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil))) @ (cTyperep.typerep_class.typerep @ cTYPE)) @ (V1 @ cProduct_Type.Unity)))))))))
(TQuickcheck_Narrowing.arity_narrowing_finite_1,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_finite_2,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_finite_3,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_finite_4,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_narrowing_finite_5,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.around_zero_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int))) @ ((cQuickcheck_Narrowing.around_zero_graph @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int))) @ ((V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)))))) @ ((V2 @ V4) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V4)) @ cList.list.Nil))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.around_zero_graph.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int))) @ ((cQuickcheck_Narrowing.around_zero_graph @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int)) @ (V1 @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int)))))) @ ((cQuickcheck_Narrowing.around_zero_graph @ V0) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (V1 @ ((cInt.minus_int_inst.minus_int @ V0) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V0) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V0)) @ cList.list.Nil))))))))))))
(TQuickcheck_Narrowing.cfun.cfun_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Narrowing.cfun.cfun_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (((cQuickcheck_Narrowing.cfun.cfun_rec_set @ V0) @ (cQuickcheck_Narrowing.cfun.Constant @ V1)) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.cfun.cfun_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.cfun.cfun_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.cfun.cfun_rep_set.intros,(call @ (^[V0]: (cQuickcheck_Narrowing.cfun.cfun_rep_set @ (cDatatype.Leaf @ V0)))))
(TQuickcheck_Narrowing.equal_narrowing_cons_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.equal_narrowing_term_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.equal_narrowing_type_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.equal_class.equal @ V0) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.ffun.ffun_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Narrowing.ffun.ffun_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ (((cQuickcheck_Narrowing.ffun.Update @ V4) @ V5) @ V2)) @ ((((V1 @ V4) @ V5) @ V2) @ V3))))))))))))))))
(TQuickcheck_Narrowing.ffun.ffun_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cQuickcheck_Narrowing.ffun.ffun_rec_set @ V0) @ V1) @ (cQuickcheck_Narrowing.ffun.Constant @ V2)) @ (V0 @ V2)))))))))
(TQuickcheck_Narrowing.ffun.ffun_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.ffun.ffun_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In0 @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.ffun.ffun_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V4))) @ V2))))))))))))) @ (V1 @ V0)))))))))
(TQuickcheck_Narrowing.ffun.ffun_rep_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cQuickcheck_Narrowing.ffun.ffun_rep_set @ V0)) @ (cQuickcheck_Narrowing.ffun.ffun_rep_set @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1))) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ V0))))))))))))
(TQuickcheck_Narrowing.ffun.ffun_rep_set.intros_1,(call @ (^[V0]: (cQuickcheck_Narrowing.ffun.ffun_rep_set @ (cDatatype.In0 @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0)))))))
(TQuickcheck_Narrowing.narrowing_cons.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V4) @ V5))) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V3 @ V4) @ V5)))))))) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V2) @ V0)) @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V3) @ V1)))))))))))))
(TQuickcheck_Narrowing.narrowing_cons.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V3) @ V4))) @ (cHOL.Not @ (V0 @ ((V1 @ V3) @ V4)))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V6) @ V7))) @ ((cHOL.eq @ ((V2 @ V6) @ V7)) @ ((V3 @ V6) @ V7)))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V6) @ V7))) @ ((cHOL.eq @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))) @ ((cHOL.eq @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V2) @ V4) @ V0)) @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V3) @ V5) @ V1))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5))) @ (cHOL.Not @ (V0 @ ((V1 @ V4) @ V5))))))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V4) @ V5))) @ (cHOL.Not @ (V0 @ ((V2 @ V4) @ V5))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V4))) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V2) @ V0)) @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V3) @ V1)))))))))))))
(TQuickcheck_Narrowing.narrowing_type.split_asm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (V0 @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V1) @ V2))) @ (cHOL.Not @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V3))) @ (cHOL.Not @ (V0 @ (V1 @ V3)))))))))))))))
(TQuickcheck_Narrowing.partial_term_of_anything,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ V2))))))))
(TQuickcheck_Narrowing.partial_term_of_int_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_int_inst.partial_term_of_int @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_nat_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_nat_inst.partial_term_of_nat @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_num_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_num_inst.partial_term_of_num @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_seq_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_set_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_sum_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.property.Existential_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cQuickcheck_Narrowing.property.Existential @ V0) @ V1) @ V2)) @ (cQuickcheck_Narrowing.Abs_property @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V0)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ (^[V3]: (cQuickcheck_Narrowing.Rep_property @ (V1 @ V3))))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V2))))))))))))))))
(TQuickcheck_Narrowing.type_definition_property,(((cTypedef.type_definition @ cQuickcheck_Narrowing.Rep_property) @ cQuickcheck_Narrowing.Abs_property) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set)))
(TRecord.iso_tuple_update_accessor_cong_from_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)))))))))))))))
(TRecord.partial_term_of_tuple_isomorphism_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TRings.class.linordered_semiring_strict.axioms_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cRings.class.linordered_semiring_strict_axioms @ V1) @ V3) @ V4)))))))))))))
(TRings.class.linordered_semiring_strict.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cRings.class.semiring @ V0) @ V4)))))))))))))
(TRings.class.linordered_semiring_strict.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V2) @ V3)))))))))))))
(TRings.class.linordered_semiring_strict.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cGroups.class.comm_monoid_add @ V0) @ V1)))))))))))))
(TRings.classrel_ordered_comm_ring_ordered_ring,(cRings.ordered_ring_class @ cTYPE))
(TRings.linordered_idom.mult_less_cancel_right1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ V10) @ ((V9 @ V11) @ V10))) @ ((cHOL.conj @ ((cHOL.implies @ ((V4 @ V3) @ V10)) @ ((V5 @ V7) @ V11))) @ ((cHOL.implies @ ((V4 @ V10) @ V3)) @ ((V5 @ V11) @ V7))))))))))))))))))))))))))))))
(TRings.linordered_idom.mult_less_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ ((V5 @ ((V9 @ V10) @ V11)) @ V11)) @ ((cHOL.conj @ ((cHOL.implies @ ((V4 @ V3) @ V11)) @ ((V5 @ V10) @ V7))) @ ((cHOL.implies @ ((V4 @ V11) @ V3)) @ ((V5 @ V7) @ V10))))))))))))))))))))))))))))))
(TRings.linordered_idom_class.abs_diff_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V0) @ V1))) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V1) @ V2)) @ V0)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2)))))))))))
(TRings.linordered_ring_strict.zero_le_mult_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ V3) @ ((V7 @ V8) @ V9))) @ ((cHOL.disj @ ((cHOL.conj @ ((V4 @ V3) @ V8)) @ ((V4 @ V3) @ V9))) @ ((cHOL.conj @ ((V4 @ V8) @ V3)) @ ((V4 @ V9) @ V3))))))))))))))))))))))))))
(TRings.linordered_semidom_class.pos_add_strict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))))
(TRings.linordered_semiring_strict.mult_neg_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V1)) @ ((c==> @ ((V3 @ V1) @ V6)) @ ((V3 @ ((V4 @ V5) @ V6)) @ V1)))))))))))))))))))
(TRings.linordered_semiring_strict.mult_pos_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((c==> @ ((V3 @ V6) @ V1)) @ ((V3 @ ((V4 @ V5) @ V6)) @ V1)))))))))))))))))))
(TRings.linordered_semiring_strict.mult_pos_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((c==> @ ((V3 @ V1) @ V6)) @ ((V3 @ V1) @ ((V4 @ V5) @ V6))))))))))))))))))))
(TRings.linordered_semiring_strict_class.axioms,(((cRings.class.linordered_semiring_strict_axioms @ cGroups.zero_class.zero) @ cOrderings.ord_class.less) @ cGroups.times_class.times))
(TRings.no_zero_divisors_class.no_zero_divisors,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ (cHOL.Not @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)))))))))
(TRings.ring_1_no_zero_divisors.square_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V6) @ V6)) @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V0)) @ ((cHOL.eq @ V6) @ (V5 @ V0))))))))))))))))))))
(TRings.ring_no_zero_divisors.mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ring_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V5) @ V6)) @ ((V0 @ V7) @ V6))) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V1)) @ ((cHOL.eq @ V5) @ V7)))))))))))))))))))))
(TSet_Interval.atLeastLessThanSuc_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ (cNat.Suc @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)))))))
(TSet_Interval.dvd.greaterThanAtMost_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((((cSet_Interval.ord.greaterThanAtMost @ cRings.dvd_class.dvd) @ (^[V2]: (^[V3]: ((cHOL.conj @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V3) @ V2)))))) @ V0) @ V1))) @ (cHOL.Not @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V1) @ V0))))))))))
(TSet_Interval.linorder.Int_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V2) @ V3)) @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V4) @ V5))) @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ (((cOrderings.ord.max @ V0) @ V2) @ V4)) @ (((cOrderings.ord.min @ V0) @ V3) @ V5)))))))))))))))))
(TSet_Interval.linorder_class.Int_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ V3))) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V3))))))))))))
(TSet_Interval.ord_class.greaterThanLessThan_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.greaterThan @ V0)) @ (cSet_Interval.ord_class.lessThan @ V1))))))))
(TSet_Interval.ord_class.ord_class.atLeast_dict,((c== @ cSet_Interval.ord_class.atLeast) @ (cSet_Interval.ord.atLeast @ cOrderings.ord_class.less_eq)))
(TSet_Interval.order.atLeastLessThan_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((V1 @ V2) @ V3)))))))))))))
(TTransitive_Closure.tranclp.trancl_into_trancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V3))))))))))))
(TTransitive_Closure.transitive_closurep_trans'_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.tranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.tranclp @ V0) @ V1) @ V3))))))))))))
(TBig_Operators.card_cartesian_product_singleton,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFinite_Set.card @ ((cProduct_Type.Sigma @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)) @ (^[V2]: V1)))) @ (cFinite_Set.card @ V1)))))))
(TBig_Operators.comm_monoid_add_class.setsum_def,((cHOL.eq @ cBig_Operators.comm_monoid_add_class.setsum) @ ((cBig_Operators.comm_monoid_set.F @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))
(TBig_Operators.distrib_lattice.inf_Sup1_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ V5) @ ((cBig_Operators.semilattice_sup.Sup_fin @ V3) @ V4))) @ ((cBig_Operators.semilattice_sup.Sup_fin @ V3) @ (cSet.Collect @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V6) @ ((V0 @ V5) @ V7))) @ ((cSet.member @ V7) @ V4))))))))))))))))))))))))
(TBig_Operators.distrib_lattice.inf_Sup2_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ ((cBig_Operators.semilattice_sup.Sup_fin @ V3) @ V4)) @ ((cBig_Operators.semilattice_sup.Sup_fin @ V3) @ V5))) @ ((cBig_Operators.semilattice_sup.Sup_fin @ V3) @ (cSet.Collect @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V6) @ ((V0 @ V7) @ V8))) @ ((cHOL.conj @ ((cSet.member @ V7) @ V4)) @ ((cSet.member @ V8) @ V5)))))))))))))))))))))))))))))
(TBig_Operators.distrib_lattice.sup_Inf1_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V3 @ V5) @ ((cBig_Operators.semilattice_inf.Inf_fin @ V0) @ V4))) @ ((cBig_Operators.semilattice_inf.Inf_fin @ V0) @ (cSet.Collect @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V6) @ ((V3 @ V5) @ V7))) @ ((cSet.member @ V7) @ V4))))))))))))))))))))))))
(TBig_Operators.distrib_lattice.sup_Inf2_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cLattices.class.distrib_lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V3 @ ((cBig_Operators.semilattice_inf.Inf_fin @ V0) @ V4)) @ ((cBig_Operators.semilattice_inf.Inf_fin @ V0) @ V5))) @ ((cBig_Operators.semilattice_inf.Inf_fin @ V0) @ (cSet.Collect @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V6) @ ((V3 @ V7) @ V8))) @ ((cHOL.conj @ ((cSet.member @ V7) @ V4)) @ ((cSet.member @ V8) @ V5)))))))))))))))))))))))))))))
(TBig_Operators.linorder_class.Max.insert_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cSet.insert @ V1) @ V0))) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Max @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))
(TBig_Operators.linorder_class.Min.insert_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cSet.insert @ V1) @ V0))) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Min @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))
(TBig_Operators.linorder_class.min_max.inf_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V2)) @ V1))))))))))
(TBig_Operators.semilattice_order_set.coboundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ ((cSet.member @ V4) @ V3)) @ ((V1 @ ((cBig_Operators.semilattice_set.F @ V0) @ V3)) @ V4)))))))))))))))
(TCode_Evaluation.term_of_bool_inst.term_of_bool,((c== @ cCode_Evaluation.term_of_bool_inst.term_of_bool) @ cCode_Evaluation.term_of_bool_inst.term_of_bool))
(TCode_Evaluation.term_of_char_inst.term_of_char,((c== @ cCode_Evaluation.term_of_char_inst.term_of_char) @ cCode_Evaluation.term_of_char_inst.term_of_char))
(TCode_Evaluation.term_of_list_inst.term_of_list,((c== @ cCode_Evaluation.term_of_list_inst.term_of_list) @ cCode_Evaluation.term_of_list_inst.term_of_list))
(TCode_Evaluation.term_of_pred_inst.term_of_pred,((c== @ cCode_Evaluation.term_of_pred_inst.term_of_pred) @ cCode_Evaluation.term_of_pred_inst.term_of_pred))
(TCode_Evaluation.term_of_prod_inst.term_of_prod,((c== @ cCode_Evaluation.term_of_prod_inst.term_of_prod) @ cCode_Evaluation.term_of_prod_inst.term_of_prod))
(TCode_Evaluation.term_of_term_inst.term_of_term,((c== @ cCode_Evaluation.term_of_term_inst.term_of_term) @ cCode_Evaluation.term_of_term_inst.term_of_term))
(TCode_Evaluation.term_of_unit_inst.term_of_unit,((c== @ cCode_Evaluation.term_of_unit_inst.term_of_unit) @ cCode_Evaluation.term_of_unit_inst.term_of_unit))
(TCode_Evaluation.typerep_pred_inst.typerep_pred,((c== @ cCode_Evaluation.typerep_pred_inst.typerep_pred) @ cCode_Evaluation.typerep_pred_inst.typerep_pred))
(TCode_Evaluation.typerep_term_inst.typerep_term,((c== @ cCode_Evaluation.typerep_term_inst.typerep_term) @ cCode_Evaluation.typerep_term_inst.typerep_term))
(TCode_Numeral.arity_linordered_semiring_natural,(cRings.linordered_semiring_class @ cTYPE))
(TCode_Numeral.natural_of_nat_of_natural_inverse,(call @ (^[V0]: ((cHOL.eq @ (cCode_Numeral.natural_of_nat @ (cCode_Numeral.nat_of_natural @ V0))) @ V0))))
(TComplete_Lattices.class.complete_lattice.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cLattices.class.lattice @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (((((cComplete_Lattices.class.complete_lattice_axioms @ V4) @ V5) @ V1) @ V6) @ V7)) @ ((((((((cComplete_Lattices.class.complete_lattice @ V4) @ V5) @ V0) @ V1) @ V2) @ V3) @ V6) @ V7))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V12]: ((V10 @ V11) @ V12)))))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V12]: ((V10 @ V12) @ V11))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((V3 @ V10) @ V9))))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((V3 @ (V0 @ V8)) @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V12]: ((V10 @ V11) @ V12)))))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: ((V10 @ V12) @ V11))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.less_eq_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((V3 @ V9) @ V10))))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot))) @ ((V3 @ V9) @ (V1 @ V8))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.intro,((c==> @ (cComplete_Lattices.Inf_class @ cTYPE)) @ ((c==> @ (cComplete_Lattices.Sup_class @ cTYPE)) @ ((c==> @ (cLattices.lattice_class @ cTYPE)) @ ((c==> @ (cOrderings.bot_class @ cTYPE)) @ ((c==> @ (cOrderings.top_class @ cTYPE)) @ ((c==> @ (((((cComplete_Lattices.class.complete_lattice_axioms @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top)) @ (cComplete_Lattices.complete_lattice_class @ cTYPE))))))))
(TComplete_Lattices.complete_lattice_class.super_5,((c==> @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ (cOrderings.top_class @ cTYPE)))
(TComplete_Lattices.complete_lattice_class.super_4,((c==> @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ (cOrderings.bot_class @ cTYPE)))
(TComplete_Lattices.complete_lattice_class.super_3,((c==> @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ (cLattices.lattice_class @ cTYPE)))
(TComplete_Lattices.complete_lattice_class.super_2,((c==> @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ (cComplete_Lattices.Sup_class @ cTYPE)))
(TComplete_Lattices.complete_lattice_class.super_1,((c==> @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ (cComplete_Lattices.Inf_class @ cTYPE)))
(TComplete_Lattices.complete_linorder.INF_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ V9)) @ V10)) @ (cHOL.All @ (^[V11]: ((cHOL.implies @ ((V4 @ V10) @ V11)) @ ((cSet.Bex @ V8) @ (^[V12]: ((V4 @ (V9 @ V12)) @ V11)))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.Inf_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ (V0 @ V8)) @ V9)) @ (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V4 @ V9) @ V10)) @ ((cSet.Bex @ V8) @ (^[V11]: ((V4 @ V11) @ V10)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.le_SUP_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ V8) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ V10))) @ (cHOL.All @ (^[V11]: ((cHOL.implies @ ((V4 @ V11) @ V8)) @ ((cSet.Bex @ V9) @ (^[V12]: ((V4 @ V11) @ (V10 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.le_Sup_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V3 @ V8) @ (V1 @ V9))) @ (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V4 @ V10) @ V8)) @ ((cSet.Bex @ V9) @ (^[V11]: ((V4 @ V10) @ V11)))))))))))))))))))))))))))))
(TComplete_Partial_Order.ccpo_class.iterates.Sup,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.member @ V2) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))))) @ ((cSet.member @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1)))))))))
(TComplete_Partial_Order.ccpo_class.iterates_def,((c== @ cComplete_Partial_Order.ccpo_class.iterates) @ (^[V0]: (cSet.Collect @ (^[V1]: ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V1))))))
(TComplete_Partial_Order.class.ccpo_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((V0 @ V3) @ (V1 @ V2))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((V0 @ V4) @ V3))))) @ ((V0 @ (V1 @ V2)) @ V3)))))))) @ ((cComplete_Partial_Order.class.ccpo_axioms @ V1) @ V0))))))))
(TDivides.semiring_div_class.div_mult_div_if_dvd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((c==> @ ((cRings.dvd_class.dvd @ V2) @ V3)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cDivides.div_class.div @ V1) @ V0)) @ ((cDivides.div_class.div @ V3) @ V2))) @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V1) @ V3)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))))))
(TDivides.semiring_div_class.dvd_div_div_eq_mult,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V2)) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((cDivides.div_class.div @ V2) @ V0)) @ ((cDivides.div_class.div @ V3) @ V1))) @ ((cHOL.eq @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V0) @ V3))))))))))))))))
(TDivides.semiring_div_class.dvd_mult_div_cancel,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRings.dvd_class.dvd @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.div @ V1) @ V0))) @ V1)))))))
(TDivides.semiring_div_class.mod_mult_self1_is_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ cGroups.zero_class.zero))))))
(TDivides.semiring_div_class.mod_mult_self2_is_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.div_class.mod @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ cGroups.zero_class.zero))))))
(TDivides.semiring_div_class.semiring_div_axioms,((((((cDivides.class.semiring_div @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TDivides.semiring_numeral_div.divmod_step_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)) @ V10)) @ ((cHOL.eq @ (((((((cDivides.semiring_numeral_div.divmod_step @ V0) @ V3) @ V5) @ V6) @ V7) @ V9) @ ((cProduct_Type.Pair @ V11) @ V10))) @ ((cProduct_Type.Pair @ ((V3 @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V11)) @ V5)) @ ((V6 @ V10) @ (((cNum.numeral.numeral @ V5) @ V3) @ V9)))))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.divmod_step_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V8 @ V9) @ (((cNum.numeral.numeral @ V5) @ V3) @ V10))) @ ((cHOL.eq @ (((((((cDivides.semiring_numeral_div.divmod_step @ V0) @ V3) @ V5) @ V6) @ V7) @ V10) @ ((cProduct_Type.Pair @ V11) @ V9))) @ ((cProduct_Type.Pair @ ((V0 @ (((cNum.numeral.numeral @ V5) @ V3) @ (cNum.num.Bit0 @ cNum.num.One))) @ V11)) @ V9)))))))))))))))))))))))))))))
(TEnum.finite_1.size_finite_1_inst.size_finite_1,((c== @ cEnum.finite_1.size_finite_1_inst.size_finite_1) @ cEnum.finite_1.size_finite_1_inst.size_finite_1))
(TEnum.finite_2.size_finite_2_inst.size_finite_2,((c== @ cEnum.finite_2.size_finite_2_inst.size_finite_2) @ cEnum.finite_2.size_finite_2_inst.size_finite_2))
(TEnum.finite_3.size_finite_3_inst.size_finite_3,((c== @ cEnum.finite_3.size_finite_3_inst.size_finite_3) @ cEnum.finite_3.size_finite_3_inst.size_finite_3))
(TEnum.finite_4.size_finite_4_inst.size_finite_4,((c== @ cEnum.finite_4.size_finite_4_inst.size_finite_4) @ cEnum.finite_4.size_finite_4_inst.size_finite_4))
(TEnum.finite_5.size_finite_5_inst.size_finite_5,((c== @ cEnum.finite_5.size_finite_5_inst.size_finite_5) @ cEnum.finite_5.size_finite_5_inst.size_finite_5))
(TExtraction.sumbool.sumbool_size_overloaded_def,((c== @ cExtraction.sumbool.size_sumbool_inst.size_sumbool) @ ((cExtraction.sumbool.sumbool_rec @ cNat.zero_nat_inst.zero_nat) @ cNat.zero_nat_inst.zero_nat)))
(TFields.class.division_ring_inverse_zero.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cFields.class.division_ring_inverse_zero_axioms @ V0) @ V5)))))))))))))))))))
(TFields.class.division_ring_inverse_zero.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TFields.class.linordered_field_inverse_zero_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c== @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.conj @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11))))))))))))))))))))))))))))
(TFields.division_ring.division_ring_inverse_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V4 @ (V0 @ V8)) @ (V0 @ V9))) @ ((V3 @ ((V3 @ (V0 @ V8)) @ ((V4 @ V8) @ V9))) @ (V0 @ V9)))))))))))))))))))))))))))
(TFields.division_ring.nonzero_inverse_eq_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ (V0 @ V8)) @ ((V1 @ V2) @ V8)))))))))))))))))))))))
(TFields.division_ring.nonzero_inverse_eq_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ (V0 @ V8)) @ (V0 @ V9))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ V8) @ V9))))))))))))))))))))))))))
(TFields.division_ring_class.diff_divide_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cFields.inverse_class.divide @ V0) @ V2)) @ ((cFields.inverse_class.divide @ V1) @ V2))))))))))
(TFields.division_ring_inverse_zero.inverse_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ V5)) @ V5)))))))))))))))))))
(TFields.division_ring_inverse_zero_class.axioms,((cFields.class.division_ring_inverse_zero_axioms @ cFields.inverse_class.inverse) @ cGroups.zero_class.zero))
(TFields.field_inverse_zero.inverse_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ ((V2 @ V8) @ V9))) @ ((V2 @ (V0 @ V8)) @ (V0 @ V9)))))))))))))))))))))))))
(TFields.field_inverse_zero_class.inverse_divide,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFields.inverse_class.inverse @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cFields.inverse_class.divide @ V1) @ V0)))))))
(TFields.linordered_field.linordered_field_no_lb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ (cHOL.All @ (^[V12]: (cHOL.Ex @ (^[V13]: ((V10 @ V13) @ V12)))))))))))))))))))))))))))))))
(TFields.linordered_field.linordered_field_no_ub,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ (cHOL.All @ (^[V12]: (cHOL.Ex @ (^[V13]: ((V10 @ V12) @ V13)))))))))))))))))))))))))))))))
(TFields.linordered_field_class.divide_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V2) @ V1)) @ ((cFields.inverse_class.divide @ V2) @ V0))))))))))))
(TFields.linordered_field_class.field_le_epsilon,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2)))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TFields.linordered_field_class.neg_divide_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V2) @ V0)) @ V1))))))))))
(TFields.linordered_field_class.neg_le_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cOrderings.ord_class.less_eq @ V2) @ ((cGroups.times_class.times @ V1) @ V0)))))))))))
(TFields.linordered_field_class.one_less_inverse,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cFields.inverse_class.inverse @ V0)))))))
(TFields.linordered_field_class.pos_divide_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ V2) @ V0)))))))))))
(TFields.linordered_field_class.pos_le_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V1) @ V0)) @ V2))))))))))
(TFields.linordered_field_inverse_zero_class_def,((c== @ (cFields.linordered_field_inverse_zero_class @ cTYPE)) @ ((cPure.conjunction @ (cFields.field_inverse_zero_class @ cTYPE)) @ (cFields.linordered_field_class @ cTYPE))))
(TFinite_Set.comp_fun_commute.fold_fun_left_comm,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((V0 @ V2) @ (((cFinite_Set.fold @ V0) @ V3) @ V1))) @ (((cFinite_Set.fold @ V0) @ ((V0 @ V2) @ V3)) @ V1)))))))))))))
(TFinite_Set.comp_fun_commute.fold_graph_insertE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ ((cSet.insert @ V2) @ V3)) @ V4)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V2) @ V3))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V4) @ ((V0 @ V2) @ V6))) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V3) @ V6)) @ V5))))) @ V5)))))))))))))))))
(TFinite_Set.comp_fun_commute.fold_insert_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ (((cFinite_Set.fold @ V0) @ V2) @ ((cSet.insert @ V3) @ V1))) @ ((V0 @ V3) @ (((cFinite_Set.fold @ V0) @ V2) @ ((cGroups.minus_class.minus @ V1) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))))))))))))))))
(TFinite_Set.complete_lattice_class.INF_fold_inf,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1)) @ (((cFinite_Set.fold @ ((cFun.comp @ cLattices.inf_class.inf) @ V1)) @ cOrderings.top_class.top) @ V0))))))))
(TFinite_Set.complete_lattice_class.Inf_fold_inf,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (((cFinite_Set.fold @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ V0))))))
(TFinite_Set.complete_lattice_class.SUP_fold_sup,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (((cFinite_Set.fold @ ((cFun.comp @ cLattices.sup_class.sup) @ V1)) @ cOrderings.bot_class.bot) @ V0))))))))
(TFinite_Set.complete_lattice_class.Sup_fold_sup,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (((cFinite_Set.fold @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ V0))))))
(TGroups.ab_group_add_class.add_diff_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cGroups.minus_class.minus @ V1) @ V2)))))))))
(TGroups.ab_group_add_class.uminus_add_conv_diff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cGroups.minus_class.minus @ V1) @ V0)))))))
(TGroups.ab_semigroup_add_class.add.left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TGroups.ab_semigroup_add_class.add_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TGroups.class.cancel_semigroup_add_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V3) @ V2))) @ ((cHOL.eq @ V1) @ V3))))))))) @ (cGroups.class.cancel_semigroup_add_axioms @ V0))))))
(TGroups.class.linordered_ab_semigroup_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((cOrderings.class.linorder @ V1) @ V2)) @ (((cGroups.class.linordered_ab_semigroup_add @ V0) @ V1) @ V2))))))))))
(TGroups.classrel_group_add_cancel_semigroup_add,(cGroups.cancel_semigroup_add_class @ cTYPE))
(TGroups.comm_monoid_add_class.add.monoid_axioms,((cGroups.monoid @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.comm_monoid_add_class.add.right_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TGroups.comm_monoid_diff.add_diff_cancel_right',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V3) @ V4)) @ V4)) @ V3)))))))))))))
(TGroups.comm_monoid_diff_class.add_implies_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cGroups.minus_class.minus @ V2) @ V1))))))))))
(TGroups.linordered_ab_group_add.double_zero_sym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V1) @ ((V0 @ V6) @ V6))) @ ((cHOL.eq @ V6) @ V1))))))))))))))))))
(TGroups.linordered_ab_group_add.neg_less_nonneg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ (V3 @ V6)) @ V6)) @ ((V5 @ V1) @ V6))))))))))))))))))
(TGroups.linordered_ab_semigroup_add_class.intro,((c==> @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cOrderings.linorder_class @ cTYPE)) @ (cGroups.linordered_ab_semigroup_add_class @ cTYPE))))
(TGroups.linordered_ab_semigroup_add_class.super_2,((c==> @ (cGroups.linordered_ab_semigroup_add_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE)))
(TGroups.linordered_ab_semigroup_add_class.super_1,((c==> @ (cGroups.linordered_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)))
(TGroups.ordered_ab_group_add_abs.abs_idempotent,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ (V0 @ (V0 @ V7))) @ (V0 @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_0_eq,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ (cGroups.abs_class.abs @ V0))) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_group_add_abs_class.abs_eq_0,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_group_add_abs_class.abs_zero,((cHOL.eq @ (cGroups.abs_class.abs @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TGroups.ordered_ab_group_add_class.diff_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TGroups.ordered_ab_group_add_class.le_minus_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cGroups.uminus_class.uminus @ V0))))))))
(TGroups.ordered_ab_group_add_class.less_diff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.minus_class.minus @ V1) @ V2))) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TGroups.ordered_ab_group_add_class.minus_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V1)) @ V0)))))))
(TGroups.ordered_ab_semigroup_add.add_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V5)))))))))))))))))
(TGroups.ordered_ab_semigroup_add_class.add_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3)))))))))))))
(TGroups.ordered_comm_monoid_add.add_increasing2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((V2 @ V5) @ ((V0 @ V6) @ V4))))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V4) @ V1)) @ ((c==> @ ((V2 @ V5) @ V1)) @ ((V2 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V4) @ V1)) @ ((c==> @ ((V3 @ V5) @ V1)) @ ((V3 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V4) @ V1)) @ ((c==> @ ((V3 @ V5) @ V1)) @ ((V3 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V4) @ V1)) @ ((c==> @ ((V2 @ V5) @ V1)) @ ((V3 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((V2 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((V3 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V1) @ V4)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((V3 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_sign_intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V1) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((V3 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TLattices.bounded_semilattice_inf_top_class_def,((c== @ (cLattices.bounded_semilattice_inf_top_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.semilattice_inf_class @ cTYPE)) @ (cOrderings.order_top_class @ cTYPE))))
(TLattices.bounded_semilattice_sup_bot_class_def,((c== @ (cLattices.bounded_semilattice_sup_bot_class @ cTYPE)) @ ((cPure.conjunction @ (cLattices.semilattice_sup_class @ cTYPE)) @ (cOrderings.order_bot_class @ cTYPE))))
(TLattices.class.bounded_semilattice_inf_top_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cLattices.class.bounded_semilattice_inf_top @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ (((cOrderings.class.order_top @ V1) @ V2) @ V3))))))))))))
(TLattices.class.bounded_semilattice_sup_bot_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cLattices.class.bounded_semilattice_sup_bot @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ (((cOrderings.class.order_bot @ V3) @ V1) @ V2))))))))))))
(TLattices.distrib_lattice_class.inf_sup_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TLattices.distrib_lattice_class.inf_sup_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TLattices.distrib_lattice_class.sup_inf_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.distrib_lattice_class.sup_inf_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TLattices.linorder_class.max.semilattice_axioms,(cLattices.semilattice @ cOrderings.ord_class.max))
(TLattices.linorder_class.min.semilattice_axioms,(cLattices.semilattice @ cOrderings.ord_class.min))
(TLattices.semilattice_inf_class.inf.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TLattices.semilattice_inf_class.inf.coboundedI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V0) @ V2)) @ V1)))))))))
(TLattices.semilattice_inf_class.inf.coboundedI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cLattices.inf_class.inf @ V2) @ V0)) @ V1)))))))))
(TLattices.semilattice_sup_class.sup.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.sup.coboundedI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.semilattice_sup_class.sup.coboundedI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cLattices.sup_class.sup @ V2) @ V1))))))))))
(TList.comm_monoid_add_class.listsum_map_remove1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cList.set @ V1))) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V2) @ V1))) @ ((cGroups.plus_class.plus @ (V2 @ V0)) @ (cList.monoid_add_class.listsum @ ((cList.map @ V2) @ ((cList.remove1 @ V0) @ V1)))))))))))))
(TList.linorder_class.linorder_class.sorted_dict,((c== @ cList.linorder_class.sorted) @ (cList.linorder.sorted @ cOrderings.ord_class.less_eq)))
(TList.linorder_class.sorted_distinct_set_unique,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.linorder_class.sorted @ V0)) @ ((c==> @ (cList.distinct @ V0)) @ ((c==> @ (cList.linorder_class.sorted @ V1)) @ ((c==> @ (cList.distinct @ V1)) @ ((c==> @ ((cHOL.eq @ (cList.set @ V0)) @ (cList.set @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))))
(TList.linorder_class.sorted_list_of_set.eq_fold,(call @ (^[V0]: ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ V0)) @ (((cFinite_Set.fold @ (cList.linorder_class.insort_key @ (^[V1]: V1))) @ cList.list.Nil) @ V0)))))
(TList.semilattice_inf_class.Inf_fin.set_eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ (cList.set @ ((cList.list.Cons @ V0) @ V1)))) @ (((cList.fold @ cLattices.inf_class.inf) @ V1) @ V0)))))))
(TList.semilattice_sup_class.Sup_fin.set_eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ (cList.set @ ((cList.list.Cons @ V0) @ V1)))) @ (((cList.fold @ cLattices.sup_class.sup) @ V1) @ V0)))))))
(TNat.dvd.dual_order.not_eq_order_implies_strict,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ ((cHOL.conj @ ((cRings.dvd_class.dvd @ V1) @ V0)) @ (cHOL.Not @ ((cRings.dvd_class.dvd @ V0) @ V1))))))))))
(TNat.linordered_semidom_class.of_nat_0_less_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNat.semiring_1_class.of_nat @ V0))) @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V0)))))
(TNat.linordered_semidom_class.of_nat_less_0_iff,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNat.semiring_1_class.of_nat @ V0)) @ cGroups.zero_class.zero)))))
(TNat_Transfer.transfer_int_nat_set_return_embed,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cInt.nat) @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0))) @ V0))))
(TNat_Transfer.transfer_nat_int_set_return_embed,(call @ (^[V0]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((cHOL.eq @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ ((cSet.image @ cInt.nat) @ V0))) @ V0)))))
(TNat_Transfer.transfer_nat_int_sum_prod_closure_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (V1 @ V2)))))) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)))))))))
(TNat_Transfer.transfer_nat_int_sum_prod_closure_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V2)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (V1 @ V2)))))) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)))))))))
(TNitpick.fun_box.size_fun_box_inst.size_fun_box,((c== @ cNitpick.fun_box.size_fun_box_inst.size_fun_box) @ cNitpick.fun_box.size_fun_box_inst.size_fun_box))
(TNitpick.term_of_pair_box_inst.term_of_pair_box,((c== @ cNitpick.term_of_pair_box_inst.term_of_pair_box) @ cNitpick.term_of_pair_box_inst.term_of_pair_box))
(TNitpick.typerep_pair_box_inst.typerep_pair_box,((c== @ cNitpick.typerep_pair_box_inst.typerep_pair_box) @ cNitpick.typerep_pair_box_inst.typerep_pair_box))
(TNum.linordered_idom.not_numeral_le_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V4 @ (((cNum.numeral.numeral @ V7) @ V6) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11)))))))))))))))))))))))))))))
(TNum.linordered_idom_class.le_neg_numeral_simps_7,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.linordered_idom_class.le_neg_numeral_simps_6,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNum.linordered_idom_class.le_neg_numeral_simps_5,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.linordered_idom_class.le_neg_numeral_simps_4,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNum.linordered_idom_class.le_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNum.linordered_idom_class.le_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNum.linordered_idom_class.le_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_eq_num @ V1) @ V0)))))))
(TNum.linordered_idom_class.neg_numeral_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V1) @ V0)))))))
(TNum.linordered_idom_class.neg_numeral_less_one,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNum.linordered_semidom_class.zero_less_numeral,(call @ (^[V0]: ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TOrderings.class.unbounded_dense_linorder.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.class.no_bot @ V0) @ V1)) @ ((c==> @ ((cOrderings.class.no_top @ V0) @ V1)) @ ((cOrderings.class.unbounded_dense_linorder @ V0) @ V1)))))))))
(TOrderings.dense_order_class.dense_order_axioms,((cOrderings.class.dense_order @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TOrderings.linorder_class.not_less_iff_gr_or_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V1) @ V0)) @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_bot_class.bot.extremum_uniqueI,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TOrderings.order_class.dual_order.strict_trans1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.order_class.dual_order.strict_trans2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TOrderings.order_top_class.top.extremum_uniqueI,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less_eq @ cOrderings.top_class.top) @ V0)) @ ((cHOL.eq @ V0) @ cOrderings.top_class.top)))))
(TOrderings.ordering.not_eq_order_implies_strict,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ordering @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((V1 @ V2) @ V3)))))))))))))
(TOrderings.unbounded_dense_linorder_class.intro,((c==> @ (cOrderings.dense_linorder_class @ cTYPE)) @ ((c==> @ (cOrderings.no_bot_class @ cTYPE)) @ ((c==> @ (cOrderings.no_top_class @ cTYPE)) @ (cOrderings.unbounded_dense_linorder_class @ cTYPE)))))
(TOrderings.unbounded_dense_linorder_class.super_3,((c==> @ (cOrderings.unbounded_dense_linorder_class @ cTYPE)) @ (cOrderings.no_top_class @ cTYPE)))
(TOrderings.unbounded_dense_linorder_class.super_2,((c==> @ (cOrderings.unbounded_dense_linorder_class @ cTYPE)) @ (cOrderings.no_bot_class @ cTYPE)))
(TOrderings.unbounded_dense_linorder_class.super_1,((c==> @ (cOrderings.unbounded_dense_linorder_class @ cTYPE)) @ (cOrderings.dense_linorder_class @ cTYPE)))
(TPower.linordered_idom_class.sum_power2_ge_zero,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))
(TPower.linordered_semidom_class.power_gt1_lemma,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1)))))))))
(TPower.linordered_semidom_class.zero_less_power,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TQuickcheck_Exhaustive.arity_check_all_finite_1,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_finite_2,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_finite_3,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_check_all_finite_4,(cQuickcheck_Exhaustive.check_all_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_equal_three_valued,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_exhaustive_integer,(cQuickcheck_Exhaustive.exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_exhaustive_natural,(cQuickcheck_Exhaustive.exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.bounded_forall_class_def,((c== @ (cQuickcheck_Exhaustive.bounded_forall_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TQuickcheck_Exhaustive.check_all_n_lists.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Exhaustive.check_all_n_lists.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.check_all_n_lists @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.check_all_n_lists_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V4 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V6]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: ((cQuickcheck_Exhaustive.check_all_n_lists @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.check_all_n_lists_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TQuickcheck_Exhaustive.check_all_n_lists.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.check_all_n_lists_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.check_all_n_lists @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V0 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V2]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.check_all_n_lists @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V4)) @ (^[V6]: ((cList.list.Cons @ (V3 @ cProduct_Type.Unity)) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((V0 @ V3) @ cList.list.Nil)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((V0 @ V3) @ ((cList.list.Cons @ V4) @ V5)))))))))) @ ((V0 @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil))) @ V3))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ V3))))))))))) @ V3)))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.psimps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V3]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V3))) @ cOption.option.Some) @ (V0 @ V3)))) @ V2))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.psimps_1,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ cList.list.Nil)) @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_sumC_def,((c== @ cQuickcheck_Exhaustive.exhaustive_fun'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_int'_sumC_def,((c== @ cQuickcheck_Exhaustive.exhaustive_int'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_set_graph_def,((c== @ cQuickcheck_Exhaustive.exhaustive_set_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cOrderings.bot_class.bot)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_set_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_set_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ V2)))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_set_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_set_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.orelse @ (V2 @ V4)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: (((cHOL.If @ ((cSet.member @ V5) @ V4)) @ cOption.option.None) @ (V2 @ ((cSet.insert @ V5) @ V4))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_fun') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.full_exhaustive_fun'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_int') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.full_exhaustive_int'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.full_exhaustive_prod_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V2]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V3]: (V0 @ ((cQuickcheck_Exhaustive.term_syntax.valtermify_pair @ V2) @ V3)))) @ V1))) @ V1)))))))
(TQuickcheck_Exhaustive.neg_bound_cps_single_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.neg_bound_cps_single @ V0)) @ (^[V1]: (^[V2]: (V1 @ (cQuickcheck_Exhaustive.unknown.Known @ V0))))))))
(TQuickcheck_Exhaustive.pos_bound_cps_single_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.pos_bound_cps_single @ V0)) @ (^[V1]: (^[V2]: (V1 @ V0)))))))
(TQuickcheck_Exhaustive.typerep_three_valued_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TQuickcheck_Exhaustive.unknown.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.random_aux_unknown @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.unknown.Unknown) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.unknown.Known) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.unknown_case_def,((c== @ cQuickcheck_Exhaustive.unknown.unknown_case) @ (^[V0]: (^[V1]: ((cQuickcheck_Exhaustive.unknown.unknown_rec @ V0) @ (^[V2]: (V1 @ V2)))))))
(TQuickcheck_Exhaustive.unknown.unknown_size_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Exhaustive.unknown.unknown_size @ V0)) @ ((cQuickcheck_Exhaustive.unknown.unknown_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V1]: ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TQuickcheck_Narrowing.arity_partial_term_of_int,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_nat,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_num,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_seq,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_set,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_sum,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_type_narrowing_cons,(cHOL.type_class @ cTYPE))
(TQuickcheck_Narrowing.arity_type_narrowing_term,(cHOL.type_class @ cTYPE))
(TQuickcheck_Narrowing.arity_type_narrowing_type,(cHOL.type_class @ cTYPE))
(TQuickcheck_Narrowing.around_zero_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Narrowing.around_zero_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int))) @ ((cQuickcheck_Narrowing.around_zero_graph @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int))) @ ((V2 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)) @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int)))))) @ ((V2 @ V4) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ cInt.zero_int_inst.zero_int)) @ cList.list.Nil) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cInt.zero_int_inst.zero_int)) @ ((cList.list.Cons @ cInt.zero_int_inst.zero_int) @ cList.list.Nil)) @ ((cList.append @ (V3 @ ((cInt.minus_int_inst.minus_int @ V4) @ cInt.one_int_inst.one_int))) @ ((cList.list.Cons @ V4) @ ((cList.list.Cons @ (cInt.uminus_int_inst.uminus_int @ V4)) @ cList.list.Nil))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.bool.narrowing_bool.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_bool_inst.narrowing_bool) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cHOL.True)) @ (cQuickcheck_Narrowing.cons @ cHOL.False))))
(TQuickcheck_Narrowing.cfun.cfun_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.cfun.cfun_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.cfun.narrowing_cfun.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Narrowing.cfun.Constant)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)))
(TQuickcheck_Narrowing.char.narrowing_char.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_char_inst.narrowing_char) @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cString.char.Char)) @ cQuickcheck_Narrowing.narrowing_nibble_inst.narrowing_nibble)) @ cQuickcheck_Narrowing.narrowing_nibble_inst.narrowing_nibble)))
(TQuickcheck_Narrowing.ffun.ffun_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.ffun.ffun_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In0 @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.ffun.ffun_rep_set @ V2)) @ ((c==> @ (V1 @ V2)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V4))) @ V2))))))))))))) @ (V1 @ V0)))))))))
(TQuickcheck_Narrowing.ffun.narrowing_ffun.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.sum @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Narrowing.ffun.Constant)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Narrowing.ffun.Update)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ cQuickcheck_Narrowing.narrowing_class.narrowing))))
(TQuickcheck_Narrowing.list.narrowing_list.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cList.list.Nil)) @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cList.list.Cons)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ cQuickcheck_Narrowing.narrowing_class.narrowing))))
(TQuickcheck_Narrowing.partial_term_of_bool_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_bool_inst.partial_term_of_bool @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_cfun_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_char_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_char_inst.partial_term_of_char @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_class_def,((c== @ (cQuickcheck_Narrowing.partial_term_of_class @ cTYPE)) @ (cTyperep.typerep_class @ cTYPE)))
(TQuickcheck_Narrowing.partial_term_of_ffun_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_list_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_pred_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_prod_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_term_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_term_inst.partial_term_of_term @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_unit_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_unit_inst.partial_term_of_unit @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.prod.narrowing_prod.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cProduct_Type.Pair)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)))
(TQuickcheck_Narrowing.property.property_rec_def,((c== @ cQuickcheck_Narrowing.property.property_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cHOL.The @ (^[V4]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)))))))))
(TQuickcheck_Narrowing.property.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_property @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_fun_lift @ ((cQuickcheck_Narrowing.random_aux_property @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1))) @ (^[V4]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.property.Universal) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)) @ V5)))))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_fun_lift @ ((cQuickcheck_Narrowing.random_aux_property @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1))) @ (^[V4]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.property.Existential) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)) @ V5)))))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_bool_inst.random_bool @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.property.Property) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))))) @ V2)))))))))
(TQuickcheck_Narrowing.random_narrowing_cons_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Random.random_class.random @ V0)) @ ((cQuickcheck_Narrowing.random_aux_narrowing_cons @ V0) @ V0)))))
(TQuickcheck_Narrowing.random_narrowing_term_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.random_narrowing_term_inst.random_narrowing_term @ V0)) @ ((cQuickcheck_Narrowing.random_aux_narrowing_term @ V0) @ V0)))))
(TQuickcheck_Narrowing.random_narrowing_type_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V0)) @ ((cQuickcheck_Narrowing.random_aux_narrowing_type @ ((cOrderings.ord_class.max @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ V0)))))
(TQuickcheck_Narrowing.term.narrowing_term.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_term_inst.narrowing_term) @ (cQuickcheck_Narrowing.cons @ cCode_Evaluation.term.dummy_term)))
(TQuickcheck_Narrowing.unit.narrowing_unit.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_unit_inst.narrowing_unit) @ (cQuickcheck_Narrowing.cons @ cProduct_Type.Unity)))
(TQuickcheck_Random.mutual_random_auxtyperep_def,((c== @ cQuickcheck_Random.mutual_random_auxtyperep) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ ((cProduct_Type.Pair @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ cList.list.Nil)) @ V2)))) @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil))) @ V2))))) @ (^[V1]: (^[V2]: ((cProduct_Type.Pair @ (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_literal_inst.random_literal @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ ((cProduct_Type.snd @ V2) @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cTyperep.typerep.Typerep) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ cList.list.Nil))) @ V4)))) @ (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ ((cQuickcheck_Random.beyond @ cCode_Numeral.one_natural_inst.one_natural) @ (cCode_Numeral.Suc @ V1))) @ ((cProduct_Type.scomp @ ((cProduct_Type.fst @ V2) @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ ((cProduct_Type.snd @ V2) @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V4))))))) @ V0))))
(TQuickcheck_Random.random_aux_lazy_sequence_def,((c== @ cQuickcheck_Random.random_aux_lazy_sequence) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cLazy_Sequence.lazy_sequence.lazy_sequence_of_list) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cLazy_Sequence.lazy_sequence.lazy_sequence_of_list) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_bool_inst.random_bool,((c== @ cQuickcheck_Random.random_bool_inst.random_bool) @ cQuickcheck_Random.random_bool_inst.random_bool))
(TQuickcheck_Random.random_char_inst.random_char,((c== @ cQuickcheck_Random.random_char_inst.random_char) @ cQuickcheck_Random.random_char_inst.random_char))
(TQuickcheck_Random.random_list_inst.random_list,((c== @ cQuickcheck_Random.random_list_inst.random_list) @ cQuickcheck_Random.random_list_inst.random_list))
(TQuickcheck_Random.random_pred_inst.random_pred,((c== @ cQuickcheck_Random.random_pred_inst.random_pred) @ cQuickcheck_Random.random_pred_inst.random_pred))
(TQuickcheck_Random.random_prod_inst.random_prod,((c== @ cQuickcheck_Random.random_prod_inst.random_prod) @ cQuickcheck_Random.random_prod_inst.random_prod))
(TQuickcheck_Random.random_term_inst.random_term,((c== @ cQuickcheck_Random.random_term_inst.random_term) @ cQuickcheck_Random.random_term_inst.random_term))
(TQuickcheck_Random.random_unit_inst.random_unit,((c== @ cQuickcheck_Random.random_unit_inst.random_unit) @ cQuickcheck_Random.random_unit_inst.random_unit))
(TRecord.arity_full_exhaustive_tuple_isomorphism,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TRecord.arity_partial_term_of_tuple_isomorphism,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TRecord.iso_tuple_update_accessor_eq_assist_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ ((V0 @ V3) @ V2)) @ V4)) @ ((cHOL.conj @ ((cHOL.eq @ (V1 @ V2)) @ V5)) @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)))))))))))))))))
(TRecord.iso_tuple_update_accessor_eq_assist_idI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ cFun.id) @ cFun.id) @ V2) @ V1) @ V0) @ V2)))))))))
(TRecord.tuple_isomorphism.Rep_tuple_isomorphism,(call @ (^[V0]: ((cSet.member @ (cRecord.Rep_tuple_isomorphism @ V0)) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set)))))
(TRecord.tuple_isomorphism.Tuple_Isomorphism_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V0) @ V1)) @ (cRecord.Abs_tuple_isomorphism @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1))))))))))
(TRings.class.linordered_semiring_1_strict.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((((cRings.class.semiring_1 @ V5) @ V4) @ V0) @ V1)) @ ((((((cRings.class.linordered_semiring_1_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TRings.class.ordered_cancel_comm_semiring.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)) @ ((c==> @ (((((cRings.class.ordered_comm_semiring @ V0) @ V2) @ V3) @ V1) @ V4)) @ (((((cRings.class.ordered_cancel_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4))))))))))))))
(TRings.class.ordered_comm_semiring_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))) @ (((cRings.class.ordered_comm_semiring_axioms @ V0) @ V1) @ V2)))))))))
(TRings.comm_semiring_class.comm_semiring_axioms,((cRings.class.comm_semiring @ cGroups.plus_class.plus) @ cGroups.times_class.times))
(TRings.linordered_semidom_class.not_one_le_zero,(cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TRings.linordered_semiring_1_strict_class.intro,((c==> @ (cRings.linordered_semiring_strict_class @ cTYPE)) @ ((c==> @ (cRings.semiring_1_class @ cTYPE)) @ (cRings.linordered_semiring_1_strict_class @ cTYPE))))
(TRings.linordered_semiring_1_strict_class.super_2,((c==> @ (cRings.linordered_semiring_1_strict_class @ cTYPE)) @ (cRings.semiring_1_class @ cTYPE)))
(TRings.linordered_semiring_1_strict_class.super_1,((c==> @ (cRings.linordered_semiring_1_strict_class @ cTYPE)) @ (cRings.linordered_semiring_strict_class @ cTYPE)))
(TRings.linordered_semiring_strict.mult_pos_neg2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((c==> @ ((V3 @ V6) @ V1)) @ ((V3 @ ((V4 @ V6) @ V5)) @ V1)))))))))))))))))))
(TRings.ordered_cancel_comm_semiring_class.intro,((c==> @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)) @ ((c==> @ (cRings.ordered_comm_semiring_class @ cTYPE)) @ (cRings.ordered_cancel_comm_semiring_class @ cTYPE))))
(TRings.ordered_cancel_comm_semiring_class.super_2,((c==> @ (cRings.ordered_cancel_comm_semiring_class @ cTYPE)) @ (cRings.ordered_comm_semiring_class @ cTYPE)))
(TRings.ordered_cancel_comm_semiring_class.super_1,((c==> @ (cRings.ordered_cancel_comm_semiring_class @ cTYPE)) @ (cGroups.cancel_comm_monoid_add_class @ cTYPE)))
(TSet_Interval.complete_lattice_class.Inf_atMost,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ (cSet_Interval.ord_class.atMost @ V0))) @ cOrderings.bot_class.bot))))
(TSet_Interval.complete_lattice_class.Sup_atMost,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ (cSet_Interval.ord_class.atMost @ V0))) @ V0))))
(TSet_Interval.ord_class.greaterThanLessThan_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.greaterThan @ V0)) @ (cSet_Interval.ord_class.lessThan @ V1))))))))
(TSet_Interval.ord_class.greaterThanLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.member @ V0) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ V0)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSet_Interval.ord_class.ord_class.lessThan_dict,((c== @ cSet_Interval.ord_class.lessThan) @ (cSet_Interval.ord.lessThan @ cOrderings.ord_class.less)))
(TSet_Interval.order.atLeastAtMost_singleton_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((cSet.insert @ V4) @ cOrderings.bot_class.bot))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ V3)) @ ((cHOL.eq @ V3) @ V4)))))))))))))))
(TSet_Interval.order.greaterThanAtMost_empty_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V2) @ V3)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((V1 @ V2) @ V3)))))))))))))
(TSet_Interval.order_class.atLeastLessThan_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TTyperep.typerep.size_typerep_inst.size_typerep,((c== @ cTyperep.typerep.size_typerep_inst.size_typerep) @ cTyperep.typerep.size_typerep_inst.size_typerep))
(TTyperep.typerep_finite_1_inst.typerep_finite_1,((c== @ cTyperep.typerep_finite_1_inst.typerep_finite_1) @ cTyperep.typerep_finite_1_inst.typerep_finite_1))
(TTyperep.typerep_finite_2_inst.typerep_finite_2,((c== @ cTyperep.typerep_finite_2_inst.typerep_finite_2) @ cTyperep.typerep_finite_2_inst.typerep_finite_2))
(TTyperep.typerep_finite_3_inst.typerep_finite_3,((c== @ cTyperep.typerep_finite_3_inst.typerep_finite_3) @ cTyperep.typerep_finite_3_inst.typerep_finite_3))
(TTyperep.typerep_finite_4_inst.typerep_finite_4,((c== @ cTyperep.typerep_finite_4_inst.typerep_finite_4) @ cTyperep.typerep_finite_4_inst.typerep_finite_4))
(TTyperep.typerep_finite_5_inst.typerep_finite_5,((c== @ cTyperep.typerep_finite_5_inst.typerep_finite_5) @ cTyperep.typerep_finite_5_inst.typerep_finite_5))
(TBig_Operators.comm_monoid_add.setsum_UNION_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: (cFinite_Set.finite @ V4)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((c==> @ ((cSet.member @ V5) @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((c==> @ ((cSet.member @ V6) @ V4)) @ ((c==> @ ((cSet.member @ V6) @ V5)) @ ((cHOL.eq @ (V3 @ V6)) @ V1))))))))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V3) @ (cComplete_Lattices.Sup_class.Sup @ V2))) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V4]: ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V3) @ V4))) @ V2)))))))))))))))
(TBig_Operators.comm_monoid_add.setsum_reindex_id,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ V3)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V2) @ V3)) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ cFun.id) @ ((cSet.image @ V2) @ V3))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1)))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_Plus,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSum_Type.Plus @ V0) @ V1))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ ((cFun.comp @ V2) @ cSum_Type.Inl)) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ ((cFun.comp @ V2) @ cSum_Type.Inr)) @ V1))))))))))))
(TBig_Operators.comm_monoid_set.cartesian_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (^[V5]: ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (V2 @ V5)) @ V3))) @ V4)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ (cProduct_Type.prod.prod_case @ V2)) @ ((cProduct_Type.Sigma @ V4) @ (^[V5]: V3))))))))))))))))
(TBig_Operators.comm_monoid_set.mono_neutral_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V2) @ V3)) @ (^[V5]: ((cHOL.eq @ (V4 @ V5)) @ V1)))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V3)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)))))))))))))))))
(TBig_Operators.linorder_class.min_max.Inf_le_Sup,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.linorder_class.Min @ V0)) @ (cBig_Operators.linorder_class.Max @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ ((V0 @ V3) @ V4)) @ V3)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ ((V0 @ V3) @ V4)) @ V4)))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V4)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V5)) @ ((cOrderings.ord_class.less_eq @ V3) @ ((V0 @ V4) @ V5))))))))))) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))))
(TBig_Operators.linorder_class.min_max.le_iff_inf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V0)))))))
(TBig_Operators.linorder_class.min_max.le_iff_sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V1)))))))
(TBig_Operators.linorder_class.min_max.le_inf_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.le_sup_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.less_infI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cOrderings.ord_class.min @ V0) @ V2)) @ V1)))))))))
(TBig_Operators.linorder_class.min_max.less_infI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cOrderings.ord_class.min @ V2) @ V0)) @ V1)))))))))
(TBig_Operators.linorder_class.min_max.less_supI1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.less_supI2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cOrderings.ord_class.max @ V2) @ V1))))))))))
(TBig_Operators.linorder_class.min_max.sup_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ V3) @ ((V0 @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((cOrderings.ord_class.less_eq @ V4) @ ((V0 @ V3) @ V4))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V5) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((V0 @ V4) @ V5)) @ V3)))))))))) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin_def,((cHOL.eq @ cBig_Operators.semilattice_inf_class.Inf_fin) @ (cBig_Operators.semilattice_set.F @ cLattices.inf_class.inf)))
(TBig_Operators.semilattice_order_neutr_set.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.semilattice_neutr_order @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3))))))))))))
(TBig_Operators.semilattice_order_set.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cBig_Operators.semilattice_order_set @ V0) @ V1) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V1 @ V4) @ ((cBig_Operators.semilattice_set.F @ V0) @ V3))) @ ((cSet.Ball @ V3) @ (^[V5]: ((V1 @ V4) @ V5))))))))))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin_def,((cHOL.eq @ cBig_Operators.semilattice_sup_class.Sup_fin) @ (cBig_Operators.semilattice_set.F @ cLattices.sup_class.sup)))
(TCode_Numeral.arity_semiring_numeral_div_integer,(cDivides.semiring_numeral_div_class @ cTYPE))
(TCode_Numeral.uminus_integer_inst.uminus_integer,((c== @ cCode_Numeral.uminus_integer_inst.uminus_integer) @ cCode_Numeral.uminus_integer_inst.uminus_integer))
(TComplete_Lattices.class.complete_lattice.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (((((cComplete_Lattices.class.complete_lattice_axioms @ V0) @ V1) @ V3) @ V6) @ V7)))))))))))))))))))
(TComplete_Lattices.class.complete_lattice.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((cLattices.class.lattice @ V2) @ V3) @ V4) @ V5)))))))))))))))))))
(TComplete_Lattices.class.complete_linorder.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cOrderings.class.linorder @ V3) @ V4)) @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_constant,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V10]: V9))) @ (((cHOL.If @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot)) @ V7) @ V9))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V11]: ((c==> @ ((cSet.member @ V11) @ V8)) @ ((V3 @ V9) @ (V10 @ V11)))))) @ ((V3 @ V9) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_top_conv_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ V7) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V10]: (V9 @ V10))))) @ ((cSet.Ball @ V8) @ (^[V10]: ((cHOL.eq @ (V9 @ V10)) @ V7))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_top_conv_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V10]: (V9 @ V10)))) @ V7)) @ ((cSet.Ball @ V8) @ (^[V10]: ((cHOL.eq @ (V9 @ V10)) @ V7))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (call @ (^[V10]: ((c==> @ ((cSet.member @ V10) @ V8)) @ ((V3 @ V9) @ V10))))) @ ((V3 @ V9) @ (V0 @ V8)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_top_conv_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ V7) @ (V0 @ V8))) @ ((cSet.Ball @ V8) @ (^[V9]: ((cHOL.eq @ V9) @ V7))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_top_conv_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V8)) @ V7)) @ ((cSet.Ball @ V8) @ (^[V9]: ((cHOL.eq @ V9) @ V7))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_bot_conv_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ V6) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V10]: (V9 @ V10))))) @ ((cSet.Ball @ V8) @ (^[V10]: ((cHOL.eq @ (V9 @ V10)) @ V6))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_bot_conv_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V10]: (V9 @ V10)))) @ V6)) @ ((cSet.Ball @ V8) @ (^[V10]: ((cHOL.eq @ (V9 @ V10)) @ V6))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_constant,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V10]: V9))) @ (((cHOL.If @ ((cHOL.eq @ V8) @ cOrderings.bot_class.bot)) @ V6) @ V9))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_bot_conv_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ V6) @ (V1 @ V8))) @ ((cSet.Ball @ V8) @ (^[V9]: ((cHOL.eq @ V9) @ V6))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_bot_conv_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V1 @ V8)) @ V6)) @ ((cSet.Ball @ V8) @ (^[V9]: ((cHOL.eq @ V9) @ V6))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.axioms,(((((cComplete_Lattices.class.complete_lattice_axioms @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))
(TComplete_Lattices.complete_linorder_class.intro,((c==> @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ ((c==> @ (cOrderings.linorder_class @ cTYPE)) @ (cComplete_Lattices.complete_linorder_class @ cTYPE))))
(TComplete_Lattices.complete_linorder_class.super_2,((c==> @ (cComplete_Lattices.complete_linorder_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE)))
(TComplete_Lattices.complete_linorder_class.super_1,((c==> @ (cComplete_Lattices.complete_linorder_class @ cTYPE)) @ (cComplete_Lattices.complete_lattice_class @ cTYPE)))
(TComplete_Partial_Order.ccpo_class.iterates.step,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((cSet.member @ (V1 @ V0)) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))))))))
(TComplete_Partial_Order.ccpo_class.iterates_fixp,(call @ (^[V0]: ((c==> @ (((cComplete_Partial_Order.monotone @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq) @ V0)) @ ((cSet.member @ (cComplete_Partial_Order.ccpo_class.fixp @ V0)) @ (cComplete_Partial_Order.ccpo_class.iterates @ V0))))))
(TComplete_Partial_Order.ccpo_class.iterates_le_f,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((c==> @ (((cComplete_Partial_Order.monotone @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ (V1 @ V0)))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.Sup,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cComplete_Partial_Order.ccpo_class.iteratesp @ V1) @ V2)))) @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp_def,((c== @ cComplete_Partial_Order.ccpo_class.iteratesp) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (V0 @ V3))) @ (V1 @ V3))))) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cComplete_Lattices.Sup_class.Sup @ V3))) @ ((cHOL.conj @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V3)) @ ((cSet.Ball @ V3) @ (^[V4]: (V1 @ V4))))))))))))))
(TDivides.class.semiring_numeral_div_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((cHOL.eq @ ((V0 @ V9) @ V10)) @ V11)) @ ((cHOL.eq @ V9) @ ((V1 @ V11) @ V10)))))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((V2 @ V9) @ V10)) @ ((cHOL.eq @ ((V0 @ ((V1 @ V10) @ V9)) @ V9)) @ V10))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((cHOL.eq @ ((V3 @ V9) @ ((V4 @ V10) @ V9))) @ ((V1 @ V10) @ ((V5 @ V10) @ V9)))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((V2 @ V6) @ V9)) @ ((c==> @ ((V7 @ V9) @ V10)) @ ((cHOL.eq @ ((V4 @ V9) @ V10)) @ V6)))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((V2 @ V6) @ V9)) @ ((c==> @ ((V7 @ V9) @ V10)) @ ((cHOL.eq @ ((V5 @ V9) @ V10)) @ V9)))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((V7 @ V6) @ V9)) @ ((c==> @ ((V2 @ V9) @ V10)) @ ((V7 @ V6) @ ((V4 @ V10) @ V9))))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((V2 @ V6) @ V9)) @ ((V2 @ ((V5 @ V9) @ V10)) @ V9))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((V7 @ V6) @ V9)) @ ((V7 @ ((V5 @ V10) @ V9)) @ V9))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((V7 @ V6) @ V9)) @ ((V2 @ V6) @ ((V5 @ V10) @ V9)))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((V2 @ V6) @ V9)) @ ((cHOL.eq @ ((V5 @ V10) @ ((V3 @ V11) @ V9))) @ ((V0 @ ((V3 @ V11) @ ((V5 @ ((V4 @ V10) @ V11)) @ V9))) @ ((V5 @ V10) @ V11))))))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((V2 @ V6) @ V9)) @ ((cHOL.eq @ ((V4 @ V10) @ ((V3 @ V11) @ V9))) @ ((V4 @ ((V4 @ V10) @ V11)) @ V9)))))))))) @ ((c==> @ (call @ (^[V9]: (call @ (^[V10]: ((cHOL.eq @ ((V7 @ V9) @ V10)) @ ((V2 @ ((V0 @ V9) @ V8)) @ V10))))))) @ (((((((((cDivides.class.semiring_numeral_div_axioms @ V3) @ V4) @ V5) @ V0) @ V6) @ V8) @ V1) @ V2) @ V7))))))))))))))))))))))))))))))))
(TDivides.semiring_div_class.div_mult_self1_is_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ V1)))))))
(TDivides.semiring_div_class.div_mult_self2_is_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cDivides.div_class.div @ ((cGroups.times_class.times @ V1) @ V0)) @ V0)) @ V1)))))))
(TDivides.semiring_numeral_div.divmod_divmod_step,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((cHOL.eq @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ V9) @ V10)) @ (((cHOL.If @ ((cNum.ord_num_inst.less_num @ V9) @ V10)) @ ((cProduct_Type.Pair @ V4) @ (((cNum.numeral.numeral @ V5) @ V3) @ V9))) @ (((((((cDivides.semiring_numeral_div.divmod_step @ V0) @ V3) @ V5) @ V6) @ V7) @ V10) @ ((((((cDivides.semiring_numeral_div.divmod @ V1) @ V2) @ V3) @ V5) @ V9) @ (cNum.num.Bit0 @ V10)))))))))))))))))))))))))))))
(TDivides.semiring_numeral_div_class.div_mult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cDivides.div_class.div @ V1) @ ((cGroups.times_class.times @ V2) @ V0))) @ ((cDivides.div_class.div @ ((cDivides.div_class.div @ V1) @ V2)) @ V0))))))))))
(TDivides.semiring_numeral_div_class.div_positive,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cDivides.div_class.div @ V1) @ V0)))))))))
(TDivides.semiring_numeral_div_class.mod_mult2_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cDivides.div_class.mod @ V1) @ ((cGroups.times_class.times @ V2) @ V0))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V2) @ ((cDivides.div_class.mod @ ((cDivides.div_class.div @ V1) @ V2)) @ V0))) @ ((cDivides.div_class.mod @ V1) @ V2)))))))))))
(TDivides.semiring_numeral_div_class.pos_mod_sign,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cDivides.div_class.mod @ V1) @ V0))))))))
(TEquiv_Relations.congruent2_implies_congruent_UN,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cEquiv_Relations.equiv @ V0) @ V1)) @ ((c==> @ ((cEquiv_Relations.equiv @ V2) @ V3)) @ ((c==> @ (((cEquiv_Relations.congruent2 @ V1) @ V3) @ V4)) @ ((c==> @ ((cSet.member @ V5) @ V2)) @ ((cEquiv_Relations.congruent @ V1) @ (^[V6]: ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cRelation.Image @ V3) @ ((cSet.insert @ V5) @ cOrderings.bot_class.bot))) @ (^[V7]: ((V4 @ V6) @ V7))))))))))))))))))))))
(TFields.division_ring.division_ring_inverse_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V6 @ (V0 @ V8)) @ (V0 @ V9))) @ ((V3 @ ((V3 @ (V0 @ V8)) @ ((V6 @ V9) @ V8))) @ (V0 @ V9)))))))))))))))))))))))))))
(TFields.division_ring.nonzero_inverse_inverse_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ (V0 @ (V0 @ V8))) @ V8))))))))))))))))))))))
(TFields.division_ring.nonzero_minus_divide_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ (V7 @ ((V1 @ V9) @ V8))) @ ((V1 @ V9) @ (V7 @ V8))))))))))))))))))))))))))
(TFields.division_ring_class.division_ring_axioms,((((((((cFields.class.division_ring @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TFields.division_ring_class.nonzero_divide_eq_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cHOL.eq @ V1) @ ((cGroups.times_class.times @ V2) @ V0)))))))))))
(TFields.division_ring_class.nonzero_eq_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cHOL.eq @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cHOL.eq @ ((cGroups.times_class.times @ V1) @ V0)) @ V2))))))))))
(TFields.field_inverse_zero.divide_divide_eq_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ ((V1 @ V8) @ V9)) @ V10)) @ ((V1 @ V8) @ ((V2 @ V9) @ V10)))))))))))))))))))))))))))
(TFields.field_inverse_zero.times_divide_times_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ ((V1 @ V8) @ V9)) @ ((V1 @ V10) @ V11))) @ ((V1 @ ((V2 @ V8) @ V10)) @ ((V2 @ V9) @ V11)))))))))))))))))))))))))))))
(TFields.field_inverse_zero_class.divide_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))
(TFields.field_inverse_zero_class.divide_eq_1_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ V1))))))))
(TFields.linordered_field.divide_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((c==> @ ((V10 @ V5) @ V14)) @ ((c==> @ ((V10 @ V5) @ ((V2 @ V13) @ V12))) @ ((V10 @ ((V1 @ V14) @ V13)) @ ((V1 @ V14) @ V12)))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.divide_nonneg_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TFields.linordered_field_class.divide_nonneg_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1)))))))))
(TFields.linordered_field_class.divide_nonpos_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1)))))))))
(TFields.linordered_field_class.divide_nonpos_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TFields.linordered_field_class.inverse_le_iff_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))))
(TFields.linordered_field_class.inverse_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TFields.linordered_field_class.le_imp_inverse_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V1)) @ (cFields.inverse_class.inverse @ V0)))))))))
(TFields.linordered_field_inverse_zero.abs_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ (V8 @ ((V1 @ V12) @ V13))) @ ((V1 @ (V8 @ V12)) @ (V8 @ V13)))))))))))))))))))))))))))))))))
(TGroups.cancel_ab_semigroup_add_class.add_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2)))))))))
(TGroups.class.cancel_ab_semigroup_add_axioms_def,(call @ (^[V0]: ((c== @ (cGroups.class.cancel_ab_semigroup_add_axioms @ V0)) @ (cHOL.All @ (^[V1]: (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))))))
(TGroups.class.linordered_ab_semigroup_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.linordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cOrderings.class.linorder @ V1) @ V2)))))))))
(TGroups.class.linordered_ab_semigroup_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.linordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)))))))))
(TGroups.comm_monoid_mult_class.mult.comm_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.one_class.one)) @ V0))))
(TGroups.comm_monoid_mult_class.mult.left_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.one_class.one) @ V0)) @ V0))))
(TGroups.linordered_ab_group_add.minus_max_eq_min,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (V3 @ (((cOrderings.ord.max @ V4) @ V6) @ V7))) @ (((cOrderings.ord.min @ V4) @ (V3 @ V6)) @ (V3 @ V7)))))))))))))))))))))
(TGroups.linordered_ab_group_add.minus_min_eq_max,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (V3 @ (((cOrderings.ord.min @ V4) @ V6) @ V7))) @ (((cOrderings.ord.max @ V4) @ (V3 @ V6)) @ (V3 @ V7)))))))))))))))))))))
(TGroups.ordered_ab_group_add.neg_0_less_iff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V1) @ (V3 @ V6))) @ ((V5 @ V6) @ V1))))))))))))))))))
(TGroups.ordered_ab_group_add.neg_less_0_iff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ (V3 @ V6)) @ V1)) @ ((V5 @ V1) @ V6))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_le_zero_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((V5 @ (V0 @ V7)) @ V2)) @ ((cHOL.eq @ V7) @ V2))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_le_D1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ V0)) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TGroups.ordered_ab_group_add_abs_class.abs_le_D2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ V0)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ V1)))))))
(TGroups.ordered_ab_group_add_class.le_imp_neg_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TGroups.ordered_ab_group_add_class.neg_le_iff_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TGroups.ordered_cancel_comm_monoid_diff.diff_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V0 @ ((V2 @ V6) @ V5)) @ V5)) @ V6))))))))))))))))))
(TGroups.semigroup_add_class.add.semigroup_axioms,(cGroups.semigroup @ cGroups.plus_class.plus))
(TGroups.semigroup_add_class.semigroup_add_axioms,(cGroups.class.semigroup_add @ cGroups.plus_class.plus))
(TInductive.complete_lattice_class.lfp_lowerbound,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cInductive.complete_lattice_class.lfp @ V0)) @ V1)))))))
(TLattices.boolean_algebra_class.compl_less_swap1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less @ V1) @ (cGroups.uminus_class.uminus @ V0))))))))
(TLattices.boolean_algebra_class.compl_less_swap2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V1)) @ V0)))))))
(TLattices.bounded_lattice_bot_class.inf_bot_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ cOrderings.bot_class.bot) @ V0)) @ cOrderings.bot_class.bot))))
(TLattices.bounded_lattice_bot_class.sup_bot_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ cOrderings.bot_class.bot) @ V0)) @ V0))))
(TLattices.bounded_lattice_top_class.inf_top_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ cOrderings.top_class.top) @ V0)) @ V0))))
(TLattices.bounded_lattice_top_class.sup_top_left,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ cOrderings.top_class.top) @ V0)) @ cOrderings.top_class.top))))
(TLattices.distrib_lattice_class.inf_sup_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TLattices.distrib_lattice_class.inf_sup_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V2)) @ ((cLattices.inf_class.inf @ V1) @ V2))))))))))
(TLattices.distrib_lattice_class.sup_inf_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V1)) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TLattices.distrib_lattice_class.sup_inf_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cLattices.inf_class.inf @ V0) @ V1)) @ V2)) @ ((cLattices.inf_class.inf @ ((cLattices.sup_class.sup @ V0) @ V2)) @ ((cLattices.sup_class.sup @ V1) @ V2))))))))))
(TLattices.semilattice_inf_class.inf.left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TLattices.semilattice_inf_class.inf_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((cLattices.inf_class.inf @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))))))))))
(TLattices.semilattice_sup_class.dual_semilattice,(((cLattices.class.semilattice_inf @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TLattices.semilattice_sup_class.sup.left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ V1) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TLattices.semilattice_sup_class.sup_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cLattices.sup_class.sup @ V1) @ V2))) @ ((cLattices.sup_class.sup @ V1) @ ((cLattices.sup_class.sup @ V0) @ V2))))))))))
(TList.linorder_class.distinct_sorted_list_of_set,(call @ (^[V0]: (cList.distinct @ (cList.linorder_class.sorted_list_of_set @ V0)))))
(TList.linorder_class.sorted_list_of_set.infinite,(call @ (^[V0]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ V0)) @ cList.list.Nil)))))
(TList.ordered_ab_group_add_abs_class.listsum_abs,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ (cList.monoid_add_class.listsum @ V0))) @ (cList.monoid_add_class.listsum @ ((cList.map @ cGroups.abs_class.abs) @ V0))))))
(TNat.classrel_linordered_semidom_semiring_char_0,(cNat.semiring_char_0_class @ cTYPE))
(TNat.semiring_1_class.semiring_1_class.Nats_dict,((c== @ cNat.semiring_1_class.Nats) @ (((cNat.semiring_1.Nats @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))
(TNat_Transfer.transfer_int_nat_function_closures_9,(call @ (^[V0]: (cNat_Transfer.is_nat @ (cNat.semiring_1_class.of_nat @ V0)))))
(TNat_Transfer.transfer_int_nat_function_closures_8,(cNat_Transfer.is_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))))
(TNat_Transfer.transfer_int_nat_function_closures_7,(cNat_Transfer.is_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNat_Transfer.transfer_int_nat_function_closures_6,(cNat_Transfer.is_nat @ cInt.one_int_inst.one_int))
(TNat_Transfer.transfer_int_nat_function_closures_5,(cNat_Transfer.is_nat @ cInt.zero_int_inst.zero_int))
(TNat_Transfer.transfer_int_nat_function_closures_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ (cNat_Transfer.is_nat @ ((cPower.power_class.power @ V0) @ V1))))))))
(TNat_Transfer.transfer_int_nat_function_closures_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ ((c==> @ (cNat_Transfer.is_nat @ V1)) @ (cNat_Transfer.is_nat @ ((cNat_Transfer.tsub @ V0) @ V1)))))))))
(TNat_Transfer.transfer_int_nat_function_closures_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ ((c==> @ (cNat_Transfer.is_nat @ V1)) @ (cNat_Transfer.is_nat @ ((cInt.times_int_inst.times_int @ V0) @ V1)))))))))
(TNat_Transfer.transfer_int_nat_function_closures_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ ((c==> @ (cNat_Transfer.is_nat @ V1)) @ (cNat_Transfer.is_nat @ ((cInt.plus_int_inst.plus_int @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_function_closures_9,(call @ (^[V0]: ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cNat.semiring_1_class.of_nat @ V0)))))
(TNat_Transfer.transfer_nat_int_function_closures_8,((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cNum.numeral_class.numeral @ (cNum.num.Bit1 @ cNum.num.One))))
(TNat_Transfer.transfer_nat_int_function_closures_7,((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))
(TNat_Transfer.transfer_nat_int_function_closures_6,((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ cInt.one_int_inst.one_int))
(TNat_Transfer.transfer_nat_int_function_closures_5,((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ cInt.zero_int_inst.zero_int))
(TNat_Transfer.transfer_nat_int_function_closures_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TNat_Transfer.transfer_nat_int_function_closures_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cNat_Transfer.tsub @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_function_closures_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.times_int_inst.times_int @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_function_closures_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ ((cInt.plus_int_inst.plus_int @ V0) @ V1)))))))))
(TNitpick.pair_box.full_exhaustive_pair_box.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cNitpick.pair_box.PairBox @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ cList.list.Nil)))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TNum.linordered_idom_class.neg_numeral_less_zero,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNum.linordered_semidom_class.less_numeral_extra_4,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ cGroups.one_class.one)))
(TNum.linordered_semidom_class.less_numeral_extra_3,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ cGroups.zero_class.zero)))
(TNum.linordered_semidom_class.less_numeral_extra_2,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TNum.linordered_semidom_class.less_numeral_extra_1,((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ cGroups.one_class.one))
(TNum.linordered_semidom_class.less_numeral_simps_5,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.linordered_semidom_class.less_numeral_simps_4,(call @ (^[V0]: ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0)))))
(TNum.linordered_semidom_class.less_numeral_simps_3,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.linordered_semidom_class.less_numeral_simps_2,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ V0)))))
(TNum.linordered_semidom_class.less_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V0) @ V1)))))))
(TNum.linordered_semidom_class.numeral_le_one_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)) @ ((cNum.ord_num_inst.less_eq_num @ V0) @ cNum.num.One)))))
(TOrderings.class.unbounded_dense_linorder.axioms_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.unbounded_dense_linorder @ V0) @ V1)) @ ((cOrderings.class.no_top @ V0) @ V1)))))))
(TOrderings.class.unbounded_dense_linorder.axioms_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.unbounded_dense_linorder @ V0) @ V1)) @ ((cOrderings.class.no_bot @ V0) @ V1)))))))
(TOrderings.class.unbounded_dense_linorder.axioms_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.class.unbounded_dense_linorder @ V0) @ V1)) @ ((cOrderings.class.dense_linorder @ V0) @ V1)))))))
(TOrderings.dense_linorder_class.dense_ge_bounded,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V3)))))) @ ((cOrderings.ord_class.less_eq @ V2) @ V0))))))))))
(TOrderings.dense_linorder_class.dense_le_bounded,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less @ V3) @ V1)) @ ((cOrderings.ord_class.less_eq @ V3) @ V2)))))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TOrderings.wellorder_class.wellorder_Least_lemma_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((cOrderings.ord_class.less_eq @ (cOrderings.ord_class.Least @ (^[V2]: (V0 @ V2)))) @ V1)))))))
(TOrderings.wellorder_class.wellorder_Least_lemma_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (V0 @ V1)) @ (V0 @ (cOrderings.ord_class.Least @ (^[V2]: (V0 @ V2))))))))))
(TPower.comm_monoid_mult_class.power_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPower.power_class.power @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V1) @ V2))))))))))
(TPower.division_ring_class.nonzero_power_inverse,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cFields.inverse_class.inverse @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ (cFields.inverse_class.inverse @ V0)) @ V1))))))))
(TPower.linordered_idom_class.odd_power_less_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))) @ cGroups.zero_class.zero)))))))
(TPower.linordered_idom_class.zero_le_even_power',(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ V0) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))))))))
(TPower.linordered_ring_class.sum_squares_ge_zero,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cGroups.times_class.times @ V1) @ V1))))))))
(TPower.linordered_semidom_class.power2_eq_imp_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cHOL.eq @ V0) @ V1)))))))))
(TPower.linordered_semidom_class.power2_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1))))))))
(TPower.linordered_semidom_class.power_decreasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V2) @ V1)) @ ((cPower.power_class.power @ V2) @ V0))))))))))))
(TPower.linordered_semidom_class.power_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_eq_nat @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V2) @ V0)) @ ((cPower.power_class.power @ V2) @ V1)))))))))))
(TPower.linordered_semidom_class.power_inject_exp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.arity_full_exhaustive_fun,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_int,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_nat,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_num,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_seq,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_set,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_sum,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_random_three_valued,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_n_lists.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.check_all_n_lists_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.check_all_n_lists_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_rel_def,((c== @ cQuickcheck_Exhaustive.check_all_n_lists_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V3) @ cList.list.Nil))) @ ((V2 @ V3) @ cList.list.Nil))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ ((V2 @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((V2 @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_rel_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5))) @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))))))))
(TQuickcheck_Exhaustive.enum_term_of_finite_1_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_finite_1_inst.enum_term_of_finite_1) @ (^[V0]: (^[V1]: ((cList.list.Cons @ (cCode_Evaluation.term_of_finite_1_inst.term_of_finite_1 @ cEnum.finite_1.a\<__caret__sub>1)) @ cList.list.Nil)))))
(TQuickcheck_Exhaustive.enum_term_of_finite_2_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_finite_2_inst.enum_term_of_finite_2) @ (^[V0]: (^[V1]: ((cList.map @ cCode_Evaluation.term_of_finite_2_inst.term_of_finite_2) @ cEnum.enum_finite_2_inst.enum_finite_2)))))
(TQuickcheck_Exhaustive.enum_term_of_finite_3_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_finite_3_inst.enum_term_of_finite_3) @ (^[V0]: (^[V1]: ((cList.map @ cCode_Evaluation.term_of_finite_3_inst.term_of_finite_3) @ cEnum.enum_finite_3_inst.enum_finite_3)))))
(TQuickcheck_Exhaustive.enum_term_of_finite_4_def,((cHOL.eq @ cQuickcheck_Exhaustive.check_all_finite_4_inst.enum_term_of_finite_4) @ (^[V0]: (^[V1]: ((cList.map @ cCode_Evaluation.term_of_finite_4_inst.term_of_finite_4) @ cEnum.enum_finite_4_inst.enum_finite_4)))))
(TQuickcheck_Exhaustive.exhaustive_fun'_graph_def,((c== @ cQuickcheck_Exhaustive.exhaustive_fun'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (V4 @ (^[V8]: V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))) @ ((cHOL.induct_implies @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((V0 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_fun'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V3 @ (((cFun.fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_fun'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (V2 @ (((cFun.fun_upd @ V5) @ V6) @ V7)))) @ V4))) @ V4))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V3)))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_graph_def,((c== @ cQuickcheck_Exhaustive.exhaustive_int'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_int'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_int'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ V7)) @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V5) @ V6) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V7) @ cCode_Numeral.one_integer_inst.one_integer)))))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V0) @ V1) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V2) @ cCode_Numeral.one_integer_inst.one_integer))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ V7)) @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V5) @ V6) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V7) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V0) @ V1) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))
(TQuickcheck_Exhaustive.exhaustive_set_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_set_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_set_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.exhaustive_set_rel @ ((cProduct_Type.Pair @ (^[V2]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V2)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V3]: (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ cOption.option.None) @ (V1 @ ((cSet.insert @ V3) @ V2))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V0))))))))
(TQuickcheck_Exhaustive.fast_exhaustive_class_def,((c== @ (cQuickcheck_Exhaustive.fast_exhaustive_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TQuickcheck_Exhaustive.full_exhaustive_class_def,((c== @ (cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TQuickcheck_Exhaustive.full_exhaustive_set.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ V3))) @ V1)))))) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_set.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ V3)))))))) @ V3)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V2]: ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V3]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V3)) @ (cProduct_Type.fst @ V2))) @ cOption.option.None) @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V3) @ V2))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))))))))
(TQuickcheck_Exhaustive.term_of_three_valued_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TQuickcheck_Exhaustive.three_valued.No_value_def,((c== @ cQuickcheck_Exhaustive.three_valued.No_value) @ (cQuickcheck_Exhaustive.Abs_three_valued @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))))
(TQuickcheck_Exhaustive.unknown.Abs_unknown_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.Abs_unknown @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set))) @ V1))))) @ V1))))))
(TQuickcheck_Exhaustive.unknown.Rep_unknown_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.Rep_unknown @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Narrowing.arity_equal_narrowing_cons,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Narrowing.arity_equal_narrowing_term,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Narrowing.arity_equal_narrowing_type,(cHOL.equal_class @ cTYPE))
(TQuickcheck_Narrowing.arity_full_exhaustive_cfun,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Narrowing.arity_full_exhaustive_ffun,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_bool,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_cfun,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_char,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_ffun,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_list,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_pred,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_prod,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_term,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_unit,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.equal_cfun_inst.equal_cfun,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Narrowing.equal_ffun_inst.equal_ffun,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Narrowing.property.property_case_def,((c== @ cQuickcheck_Narrowing.property.property_case) @ (^[V0]: (^[V1]: (^[V2]: (((cQuickcheck_Narrowing.property.property_rec @ (^[V3]: (^[V4]: (^[V5]: (^[V6]: (((V0 @ V3) @ V4) @ V5)))))) @ (^[V3]: (^[V4]: (^[V5]: (^[V6]: (((V1 @ V3) @ V4) @ V5)))))) @ (^[V3]: (V2 @ V3))))))))
(TQuickcheck_Narrowing.typerep_narrowing_cons_def,(call @ (^[V0]: ((cHOL.eq @ (cTyperep.typerep_class.typerep @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))
(TQuickcheck_Narrowing.typerep_narrowing_term_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.typerep_narrowing_term_inst.typerep_narrowing_term @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)))))
(TQuickcheck_Narrowing.typerep_narrowing_type_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.typerep_narrowing_type_inst.typerep_narrowing_type @ V0)) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)))))
(TRecord.iso_tuple_update_accessor_cong_assist_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)) @ ((cHOL.eq @ (V0 @ cFun.id)) @ cFun.id)))))))
(TRecord.iso_tuple_update_accessor_eq_assist_triv,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_cons_conj_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V4)) @ V5))) @ V6)) @ ((cHOL.eq @ ((cHOL.conj @ ((cHOL.eq @ (((cRecord.iso_tuple_cons @ V0) @ V1) @ V3)) @ (((cRecord.iso_tuple_cons @ V0) @ V2) @ V4))) @ V5)) @ V6))))))))))))))))))
(TRings.class.linordered_comm_semiring_strict_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (((cRings.class.comm_semiring_0 @ V0) @ V3) @ V4)) @ (((cRings.class.linordered_comm_semiring_strict_axioms @ V2) @ V3) @ V4)))))))))))))))
(TRings.class.linordered_semiring_1_strict.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semiring_1_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((cRings.class.semiring_1 @ V5) @ V4) @ V0) @ V1)))))))))))))))
(TRings.class.linordered_semiring_1_strict.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.linordered_semiring_1_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))
(TRings.class.ordered_cancel_comm_semiring.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_cancel_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((((cRings.class.ordered_comm_semiring @ V0) @ V2) @ V3) @ V1) @ V4)))))))))))))
(TRings.class.ordered_cancel_comm_semiring.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.ordered_cancel_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cGroups.class.cancel_comm_monoid_add @ V0) @ V1)))))))))))))
(TRings.classrel_comm_ring_comm_semiring_0_cancel,(cRings.comm_semiring_0_cancel_class @ cTYPE))
(TRings.classrel_linordered_idom_ordered_ring_abs,(cRings.ordered_ring_abs_class @ cTYPE))
(TRings.linordered_comm_semiring_strict_class_def,((c== @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_semiring_0_class @ cTYPE)) @ (((cRings.class.linordered_comm_semiring_strict_axioms @ cOrderings.ord_class.less) @ cGroups.zero_class.zero) @ cGroups.times_class.times)))))
(TRings.linordered_idom_class.less_minus_self_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TRings.linordered_idom_class.mult_left_le_one_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V1) @ V0)) @ V0)))))))))
(TRings.linordered_ring_strict.zero_less_mult_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ V3) @ ((V7 @ V8) @ V9))) @ ((cHOL.disj @ ((cHOL.conj @ ((V5 @ V3) @ V8)) @ ((V5 @ V3) @ V9))) @ ((cHOL.conj @ ((V5 @ V8) @ V3)) @ ((V5 @ V9) @ V3))))))))))))))))))))))))))
(TRings.linordered_ring_strict_class.mult_neg_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.ordered_cancel_semiring.split_mult_neg_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((cHOL.disj @ ((cHOL.conj @ ((V2 @ V1) @ V5)) @ ((V2 @ V6) @ V1))) @ ((cHOL.conj @ ((V2 @ V5) @ V1)) @ ((V2 @ V1) @ V6)))) @ ((V2 @ ((V4 @ V5) @ V6)) @ V1))))))))))))))))))
(TRings.ordered_comm_semiring.comm_mult_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.ordered_comm_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V6)) @ ((c==> @ ((V1 @ V3) @ V7)) @ ((V1 @ ((V4 @ V7) @ V5)) @ ((V4 @ V7) @ V6))))))))))))))))))))))
(TRings.ring_1_no_zero_divisors.mult_cancel_left1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V6) @ ((V1 @ V6) @ V7))) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V3)) @ ((cHOL.eq @ V7) @ V0)))))))))))))))))))))
(TRings.ring_1_no_zero_divisors.mult_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V6) @ V7)) @ V6)) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V3)) @ ((cHOL.eq @ V7) @ V0)))))))))))))))))))))
(TRings.ring_no_zero_divisors_class.mult_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))
(TSet_Interval.atLeastSucAtMost_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ (cNat.Suc @ V0)) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)))))))
(TSet_Interval.complete_lattice.Inf_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V3 @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ (((cSet_Interval.ord.atLeastAtMost @ V3) @ V8) @ V9))) @ V8))))))))))))))))))))))))
(TSet_Interval.complete_lattice.Sup_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V3 @ V8) @ V9)) @ ((cHOL.eq @ (V1 @ (((cSet_Interval.ord.atLeastAtMost @ V3) @ V8) @ V9))) @ V9))))))))))))))))))))))))
(TSet_Interval.complete_lattice_class.Inf_atLeast,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ (cSet_Interval.ord_class.atLeast @ V0))) @ V0))))
(TSet_Interval.complete_lattice_class.Sup_atLeast,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ (cSet_Interval.ord_class.atLeast @ V0))) @ cOrderings.top_class.top))))
(TSet_Interval.linorder_class.Int_atLeastAtMostL1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.atMost @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TSet_Interval.linorder_class.Int_atLeastAtMostL2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ (cSet_Interval.ord_class.atLeast @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cOrderings.ord_class.max @ V0) @ V2)) @ V1)))))))))
(TSet_Interval.linorder_class.Int_atLeastAtMostR1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atMost @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TSet_Interval.linorder_class.Int_atLeastAtMostR2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.atLeast @ V0)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V1) @ V2))) @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)))))))))
(TSet_Interval.linorder_class.Int_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((cSet_Interval.ord_class.atLeastLessThan @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V3))))))))))))
(TSet_Interval.no_top_class.greaterThan_non_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ (cSet_Interval.ord_class.greaterThan @ V0)) @ cOrderings.bot_class.bot)))))
(TSet_Interval.order.greaterThanAtMost_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.order @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V2) @ V3))) @ (cHOL.Not @ ((V1 @ V2) @ V3)))))))))))))
(TSet_Interval.order_top_class.atMost_eq_UNIV_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cSet_Interval.ord_class.atMost @ V0)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ V0) @ cOrderings.top_class.top)))))
(TTransitive_Closure.acyclic_impl_antisym_rtrancl,(call @ (^[V0]: ((c==> @ (cTransitive_Closure.acyclic @ V0)) @ (cRelation.antisym @ (cTransitive_Closure.rtrancl @ V0))))))
(TTransitive_Closure.rtrancl.rtrancl_into_rtrancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ (V2 @ V3)) @ (V1 @ V3)))) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (cProduct_Type.prod.prod_case @ V2)) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.delta,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ V1)) @ (V2 @ V3)) @ cGroups.zero_class.zero))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.zero_class.zero))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.empty,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ cOrderings.bot_class.bot)) @ cGroups.zero_class.zero))))
(TBig_Operators.comm_monoid_add_class.setsum_cong2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cHOL.eq @ (V1 @ V3)) @ (V2 @ V3)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod_Un2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0)))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod_def,((cHOL.eq @ cBig_Operators.comm_monoid_mult_class.setprod) @ ((cBig_Operators.comm_monoid_set.F @ cGroups.times_class.times) @ cGroups.one_class.one)))
(TBig_Operators.comm_monoid_set.mono_neutral_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V2) @ V3)) @ (^[V5]: ((cHOL.eq @ (V4 @ V5)) @ V1)))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V3)))))))))))))))))
(TBig_Operators.complete_lattice_class.Inf_fin_Inf,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ V0)))))))
(TBig_Operators.complete_lattice_class.Sup_fin_Sup,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))
(TBig_Operators.linorder_class.Max.insert_not_elem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Max @ ((cSet.insert @ V1) @ V0))) @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Max @ V0)))))))))))
(TBig_Operators.linorder_class.Min.insert_not_elem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.linorder_class.Min @ ((cSet.insert @ V1) @ V0))) @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Min @ V0)))))))))))
(TBig_Operators.linorder_class.min_max.Inf_fin_def,((cHOL.eq @ cBig_Operators.linorder_class.Min) @ (cBig_Operators.semilattice_set.F @ cOrderings.ord_class.min)))
(TBig_Operators.linorder_class.min_max.Sup_fin_def,((cHOL.eq @ cBig_Operators.linorder_class.Max) @ (cBig_Operators.semilattice_set.F @ cOrderings.ord_class.max)))
(TBig_Operators.linorder_class.min_max.inf_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V1) @ V0)) @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V1) @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_8,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ V1) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_5,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_4,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.min @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ V1) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_sup_aci_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V1) @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_ord_4,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_ord_3,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_ord_2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V1))))))
(TBig_Operators.linorder_class.min_max.inf_sup_ord_1,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V0))))))
(TBig_Operators.linorder_class.min_max.sup_absorb1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V1) @ V0)) @ V1)))))))
(TBig_Operators.linorder_class.min_max.sup_absorb2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V1)))))))
(TBig_Operators.linorder_class.min_max.sup_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V1) @ V0)))))))
(TBig_Operators.semilattice_order_neutr_set.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)))))))))))
(TBig_Operators.semilattice_order_neutr_set.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((((cLattices.semilattice_neutr_order @ V0) @ V1) @ V2) @ V3)))))))))))
(TCode_Numeral.natural.natural_size_overloaded_def,((c== @ cCode_Numeral.natural.size_natural_inst.size_natural) @ ((cCode_Numeral.natural.natural_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))
(TComplete_Lattices.class.complete_linorder.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cOrderings.class.linorder @ V3) @ V4)))))))))))))))))))
(TComplete_Lattices.class.complete_linorder.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.INFI_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cSet.Bex @ V1) @ (^[V5]: ((cOrderings.ord_class.less_eq @ (V2 @ V5)) @ (V3 @ V4)))))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cSet.Bex @ V0) @ (^[V5]: ((cOrderings.ord_class.less_eq @ (V3 @ V5)) @ (V2 @ V4)))))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V3 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V2 @ V4)))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1)) @ (cComplete_Lattices.Inf_class.Inf @ ((cSet.image @ V1) @ V0))))))))
(TComplete_Lattices.complete_lattice_class.INF_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ (V2 @ V3)))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ V3) @ (V2 @ V4)))))) @ ((cOrderings.ord_class.less_eq @ V3) @ V1))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3)))) @ V1))))))))))
(TComplete_Lattices.complete_lattice_class.INF_top,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V1]: cOrderings.top_class.top))) @ cOrderings.top_class.top))))
(TComplete_Lattices.complete_lattice_class.Inf_Sup,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ (cSet.Collect @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TComplete_Lattices.complete_lattice_class.Inf_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))))) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1))))))))
(TComplete_Lattices.complete_lattice_class.SUPR_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cSet.Bex @ V1) @ (^[V5]: ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V3 @ V5)))))))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cSet.Bex @ V0) @ (^[V5]: ((cOrderings.ord_class.less_eq @ (V3 @ V4)) @ (V2 @ V5)))))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_bot,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V1]: cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot))))
(TComplete_Lattices.complete_lattice_class.SUP_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1)) @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ V1) @ V0))))))))
(TComplete_Lattices.complete_lattice_class.SUP_eqI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V2))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V4)) @ V3))))) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2))))))))))
(TComplete_Lattices.complete_lattice_class.Sup_Inf,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ (cSet.Collect @ (^[V1]: ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V2) @ V1))))))))))
(TComplete_Lattices.complete_lattice_class.Sup_eqI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((c==> @ (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V3) @ V2))))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1))))))))
(TComplete_Lattices.complete_linorder.INF_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (V9 @ V11)))) @ V10)) @ ((cSet.Bex @ V8) @ (^[V11]: ((V4 @ (V9 @ V11)) @ V10))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.Inf_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ (V0 @ V8)) @ V9)) @ ((cSet.Bex @ V8) @ (^[V10]: ((V4 @ V10) @ V9))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.less_SUP_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ V8) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (V10 @ V11))))) @ ((cSet.Bex @ V9) @ (^[V11]: ((V4 @ V8) @ (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.less_Sup_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ V8) @ (V1 @ V9))) @ ((cSet.Bex @ V9) @ (^[V10]: ((V4 @ V8) @ V10))))))))))))))))))))))))))
(TComplete_Partial_Order.ccpo_class.ccpo_Sup_least,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1))))))))
(TComplete_Partial_Order.ccpo_class.ccpo_Sup_upper,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))))
(TComplete_Partial_Order.ccpo_class.chain_iterates,(call @ (^[V0]: ((c==> @ (((cComplete_Partial_Order.monotone @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq) @ V0)) @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ (cComplete_Partial_Order.ccpo_class.iterates @ V0))))))
(TComplete_Partial_Order.ccpo_class.iterates.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (V1 @ V3))) @ ((c==> @ ((cSet.member @ V3) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ V2))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V3))) @ ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cSet.member @ V4) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))))) @ V2)))))) @ V2))))))))))
(TComplete_Partial_Order.ccpo_class.iterates.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.member @ V0) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ (V1 @ V2))) @ ((cSet.member @ V2) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1)))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V2))) @ ((cHOL.conj @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V2)) @ ((cSet.Ball @ V2) @ (^[V3]: ((cSet.member @ V3) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1)))))))))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.step,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V1)) @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ (V0 @ V1))))))))
(TDivides.semiring_numeral_div_class.divmod_cancel_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod @ (cNum.num.Bit1 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ V2) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3)) @ cGroups.one_class.one))))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1))))))))
(TDivides.semiring_numeral_div_class.divmod_cancel_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod @ (cNum.num.Bit0 @ V0)) @ (cNum.num.Bit0 @ V1))) @ ((cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cProduct_Type.Pair @ V2) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V3))))) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1))))))))
(TDivides.semiring_numeral_div_class.pos_mod_bound,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ ((cDivides.div_class.mod @ V1) @ V0)) @ V0)))))))
(TFields.class.linordered_field_inverse_zero.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11))))))))))))))))))))))))))))
(TFields.division_ring.nonzero_imp_inverse_nonzero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ (cHOL.Not @ ((cHOL.eq @ (V0 @ V8)) @ V5)))))))))))))))))))))))
(TFields.division_ring.nonzero_minus_divide_divide,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V1 @ (V7 @ V9)) @ (V7 @ V8))) @ ((V1 @ V9) @ V8)))))))))))))))))))))))))
(TFields.division_ring_class.inverse_zero_imp_zero,(call @ (^[V0]: ((c==> @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TFields.division_ring_class.times_divide_eq_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)))))))))
(TFields.division_ring_inverse_zero.divide_self_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ V8)) @ (((cHOL.If @ ((cHOL.eq @ V8) @ V5)) @ V5) @ V2))))))))))))))))))))))
(TFields.field_inverse_zero.divide_divide_eq_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ ((V1 @ V9) @ V10))) @ ((V1 @ ((V2 @ V8) @ V10)) @ V9))))))))))))))))))))))))))
(TFields.field_inverse_zero_class.inverse_eq_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ cGroups.one_class.one)))))
(TFields.linordered_field.divide_strict_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((c==> @ ((V10 @ V5) @ V14)) @ ((V10 @ ((V1 @ V12) @ V14)) @ ((V1 @ V13) @ V14))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.neg_divide_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V2) @ V0)) @ V1))))))))))
(TFields.linordered_field_class.neg_less_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cOrderings.ord_class.less @ V2) @ ((cGroups.times_class.times @ V1) @ V0)))))))))))
(TFields.linordered_field_class.nonzero_abs_divide,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cGroups.abs_class.abs @ ((cFields.inverse_class.divide @ V1) @ V0))) @ ((cFields.inverse_class.divide @ (cGroups.abs_class.abs @ V1)) @ (cGroups.abs_class.abs @ V0)))))))))
(TFields.linordered_field_class.pos_divide_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ V2) @ V0)))))))))))
(TFields.linordered_field_class.pos_less_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0))) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V1) @ V0)) @ V2))))))))))
(TFields.linordered_field_inverse_zero.abs_div_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V1 @ (V8 @ V13)) @ V12)) @ (V8 @ ((V1 @ V13) @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.abs_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ (V8 @ (V0 @ V12))) @ (V0 @ (V8 @ V12)))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.intro,((c==> @ (cFields.field_inverse_zero_class @ cTYPE)) @ ((c==> @ (cFields.linordered_field_class @ cTYPE)) @ (cFields.linordered_field_inverse_zero_class @ cTYPE))))
(TFields.linordered_field_inverse_zero_class.super_2,((c==> @ (cFields.linordered_field_inverse_zero_class @ cTYPE)) @ (cFields.linordered_field_class @ cTYPE)))
(TFields.linordered_field_inverse_zero_class.super_1,((c==> @ (cFields.linordered_field_inverse_zero_class @ cTYPE)) @ (cFields.field_inverse_zero_class @ cTYPE)))
(TGroups.ab_semigroup_mult_class.mult.left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TGroups.ab_semigroup_mult_class.mult_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TGroups.class.ordered_ab_group_add_abs_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cGroups.class.ordered_ab_group_add_abs_axioms @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((V4 @ V2) @ (V0 @ V5))))) @ (cHOL.All @ (^[V5]: ((V4 @ V5) @ (V0 @ V5)))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((V4 @ V5) @ V6)) @ ((cHOL.implies @ ((V4 @ (V3 @ V5)) @ V6)) @ ((V4 @ (V0 @ V5)) @ V6)))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: ((cHOL.eq @ (V0 @ (V3 @ V5))) @ (V0 @ V5))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((V4 @ (V0 @ ((V1 @ V5) @ V6))) @ ((V1 @ (V0 @ V5)) @ (V0 @ V6))))))))))))))))))))))
(TGroups.class.ordered_ab_semigroup_add_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.ordered_ab_semigroup_add_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((V1 @ ((V0 @ V4) @ V2)) @ ((V0 @ V4) @ V3)))))))))))))))
(TGroups.class.ordered_ab_semigroup_add_imp_le_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ V0) @ V1))))))))))
(TGroups.class.ordered_cancel_ab_semigroup_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2))))))))))
(TGroups.class.ordered_cancel_comm_monoid_diff_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V3) @ V4)) @ ((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ V0) @ V3)))))))))))))))
(TGroups.comm_monoid_diff_class.diff_right_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V1)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.minus_class.minus @ V0) @ V2)) @ V1)))))))))
(TGroups.comm_monoid_mult_class.mult.monoid_axioms,((cGroups.monoid @ cGroups.times_class.times) @ cGroups.one_class.one))
(TGroups.comm_monoid_mult_class.mult.right_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.one_class.one)) @ V0))))
(TGroups.linordered_ab_group_add.le_minus_self_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V6) @ (V3 @ V6))) @ ((V4 @ V6) @ V1))))))))))))))))))
(TGroups.linordered_ab_group_add.minus_le_self_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (V3 @ V6)) @ V6)) @ ((V4 @ V1) @ V6))))))))))))))))))
(TGroups.linordered_ab_group_add_class.double_zero,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_group_add.diff_eq_diff_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cHOL.eq @ ((V2 @ V6) @ V7)) @ ((V2 @ V8) @ V9))) @ ((cHOL.eq @ ((V4 @ V6) @ V7)) @ ((V4 @ V8) @ V9)))))))))))))))))))))))))
(TGroups.ordered_ab_group_add.diff_less_0_iff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ ((V2 @ V6) @ V7)) @ V1)) @ ((V5 @ V6) @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add.less_iff_diff_less_0,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V6) @ V7)) @ ((V5 @ ((V2 @ V6) @ V7)) @ V1))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_minus_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ (V0 @ (V4 @ V7))) @ (V0 @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ V0)) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ V1))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_of_neg,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ (cGroups.uminus_class.uminus @ V0))))))
(TGroups.ordered_ab_group_add_abs_class.abs_of_pos,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ V0)))))
(TGroups.ordered_ab_group_add_class.less_minus_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less @ V1) @ (cGroups.uminus_class.uminus @ V0))))))))
(TGroups.ordered_ab_group_add_class.minus_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ V1)) @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V1)) @ V0)))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class_def,((c== @ (cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq))))
(TGroups.ordered_cancel_ab_semigroup_add_class_def,((c== @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE))))
(TGroups.ordered_cancel_comm_monoid_diff_class_def,((c== @ (cGroups.ordered_cancel_comm_monoid_diff_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.comm_monoid_diff_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE)) @ ((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq)))))
(TGroups.ordered_comm_monoid_add.add_nonneg_nonneg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((V2 @ V1) @ ((V0 @ V4) @ V5))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_nonpos_nonpos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V4) @ V1)) @ ((c==> @ ((V2 @ V5) @ V1)) @ ((V2 @ ((V0 @ V4) @ V5)) @ V1)))))))))))))))))
(TGroups.ordered_comm_monoid_add_class.add_neg_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TGroups.ordered_comm_monoid_add_class.add_pos_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TLattices.bounded_lattice_bot_class.inf_bot_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))
(TLattices.bounded_lattice_bot_class.sup_bot_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ cOrderings.bot_class.bot)) @ V0))))
(TLattices.bounded_lattice_top_class.inf_top_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ cOrderings.top_class.top)) @ V0))))
(TLattices.bounded_lattice_top_class.sup_top_right,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ cOrderings.top_class.top)) @ cOrderings.top_class.top))))
(TLattices.bounded_semilattice_inf_top_class.intro,((c==> @ (cLattices.semilattice_inf_class @ cTYPE)) @ ((c==> @ (cOrderings.order_top_class @ cTYPE)) @ (cLattices.bounded_semilattice_inf_top_class @ cTYPE))))
(TLattices.bounded_semilattice_inf_top_class.super_2,((c==> @ (cLattices.bounded_semilattice_inf_top_class @ cTYPE)) @ (cOrderings.order_top_class @ cTYPE)))
(TLattices.bounded_semilattice_inf_top_class.super_1,((c==> @ (cLattices.bounded_semilattice_inf_top_class @ cTYPE)) @ (cLattices.semilattice_inf_class @ cTYPE)))
(TLattices.bounded_semilattice_sup_bot_class.intro,((c==> @ (cLattices.semilattice_sup_class @ cTYPE)) @ ((c==> @ (cOrderings.order_bot_class @ cTYPE)) @ (cLattices.bounded_semilattice_sup_bot_class @ cTYPE))))
(TLattices.bounded_semilattice_sup_bot_class.super_2,((c==> @ (cLattices.bounded_semilattice_sup_bot_class @ cTYPE)) @ (cOrderings.order_bot_class @ cTYPE)))
(TLattices.bounded_semilattice_sup_bot_class.super_1,((c==> @ (cLattices.bounded_semilattice_sup_bot_class @ cTYPE)) @ (cLattices.semilattice_sup_class @ cTYPE)))
(TLattices.class.bounded_semilattice_inf_top.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)) @ ((c==> @ (((cOrderings.class.order_top @ V1) @ V2) @ V3)) @ ((((cLattices.class.bounded_semilattice_inf_top @ V0) @ V1) @ V2) @ V3))))))))))))
(TLattices.class.bounded_semilattice_sup_bot.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)) @ ((c==> @ (((cOrderings.class.order_bot @ V3) @ V1) @ V2)) @ ((((cLattices.class.bounded_semilattice_sup_bot @ V0) @ V1) @ V2) @ V3))))))))))))
(TLazy_Sequence.small_lazy_int_inst.small_lazy_int,((c== @ cLazy_Sequence.small_lazy_int_inst.small_lazy_int) @ cLazy_Sequence.small_lazy_int_inst.small_lazy_int))
(TList.linorder.filter_equals_takeWhile_sorted_rev,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cList.linorder.sorted @ V0) @ (cList.rev @ ((cList.map @ V2) @ V3)))) @ ((cHOL.eq @ ((cList.filter @ (^[V5]: ((V1 @ V4) @ (V2 @ V5)))) @ V3)) @ ((cList.takeWhile @ (^[V5]: ((V1 @ V4) @ (V2 @ V5)))) @ V3)))))))))))))))
(TList.linorder_class.linorder_class.sort_key_dict,((c== @ cList.linorder_class.sort_key) @ (cList.linorder.sort_key @ cOrderings.ord_class.less_eq)))
(TList.monoid_add.listsum_distinct_conv_setsum_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((c==> @ (cList.distinct @ V2)) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V3) @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ (cList.set @ V2))))))))))))))
(TNat.semiring_char_0_class.semiring_char_0_axioms,((((cNat.class.semiring_char_0 @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TNum.linordered_idom.not_numeral_less_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ (cHOL.Not @ ((V5 @ (((cNum.numeral.numeral @ V7) @ V6) @ V10)) @ ((((cNum.neg_numeral.neg_numeral @ V6) @ V2) @ V7) @ V11)))))))))))))))))))))))))))))
(TNum.linordered_idom_class.less_neg_numeral_simps_7,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.linordered_idom_class.less_neg_numeral_simps_6,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.one_class.one))))
(TNum.linordered_idom_class.less_neg_numeral_simps_5,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.linordered_idom_class.less_neg_numeral_simps_4,(call @ (^[V0]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ cGroups.zero_class.zero))))
(TNum.linordered_idom_class.less_neg_numeral_simps_3,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNum.linordered_idom_class.less_neg_numeral_simps_2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNum.linordered_idom_class.less_neg_numeral_simps_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))) @ ((cNum.ord_num_inst.less_num @ V1) @ V0)))))))
(TNum.linordered_idom_class.neg_numeral_le_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNum.linordered_idom_class.not_one_le_neg_numeral,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.linordered_semidom_class.not_numeral_le_zero,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.neg_numeral_class.neg_numeral_class.dbl_dict,((c== @ cNum.neg_numeral_class.dbl) @ (cNum.neg_numeral.dbl @ cGroups.plus_class.plus)))
(TNum.neg_numeral_class.neg_numeral_class.sub_dict,((c== @ cNum.neg_numeral_class.sub) @ (((cNum.neg_numeral.sub @ cGroups.minus_class.minus) @ cGroups.plus_class.plus) @ cGroups.one_class.one)))
(TNum.semiring_numeral_class.numeral_times_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ V0)) @ (cNum.numeral_class.numeral @ V1))) @ (cNum.numeral_class.numeral @ ((cNum.times_num_inst.times_num @ V0) @ V1))))))))
(TOrderings.order_class.dual_order.ordering_axioms,((cOrderings.ordering @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TOrderings.order_class.order.strict_implies_order,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TPower.linordered_semidom.power_less_imp_less_exp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((c==> @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V8))) @ ((cNat.ord_nat_inst.less_nat @ V7) @ V8)))))))))))))))))))))))
(TPower.linordered_semidom.power_strict_decreasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V6) @ V7)) @ ((c==> @ ((V5 @ V1) @ V8)) @ ((cHOL.implies @ ((V5 @ V8) @ V3)) @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V6)))))))))))))))))))))))))
(TPower.linordered_semidom.power_strict_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ V6) @ V7)) @ ((cHOL.implies @ ((V5 @ V3) @ V8)) @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V6)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V7))))))))))))))))))))))))
(TPower.linordered_semidom_class.power_inject_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))) @ ((cPower.power_class.power @ V2) @ (cNat.Suc @ V1)))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cHOL.eq @ V0) @ V2)))))))))))
(TPower.linordered_semidom_class.power_strict_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V2)) @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.arity_full_exhaustive_bool,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_char,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_list,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_pred,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_prod,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_term,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_unit,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_term_of_three_valued,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_typerep_three_valued,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Exhaustive.bounded_forall_class.intro,((c==> @ (cHOL.type_class @ cTYPE)) @ (cQuickcheck_Exhaustive.bounded_forall_class @ cTYPE)))
(TQuickcheck_Exhaustive.bounded_forall_class.super,((c==> @ (cQuickcheck_Exhaustive.bounded_forall_class @ cTYPE)) @ (cHOL.type_class @ cTYPE)))
(TQuickcheck_Exhaustive.check_all_n_lists_sumC_def,((c== @ cQuickcheck_Exhaustive.check_all_n_lists_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.check_all_subsets_sumC_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_fun'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V3 @ (((cFun.fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ ((cQuickcheck_Exhaustive.exhaustive_fun'_rel @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: (V1 @ (((cFun.fun_upd @ V3) @ V4) @ V5)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V0) @ V2)))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_int'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.exhaustive_int'_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ (((V0 @ V4) @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ V7)) @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V5) @ V6) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V7) @ cCode_Numeral.one_integer_inst.one_integer)))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ (((cQuickcheck_Exhaustive.exhaustive_integer' @ V0) @ V1) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V2) @ cCode_Numeral.one_integer_inst.one_integer)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ (((V0 @ V4) @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ V7)) @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V5) @ V6) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V7) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ (((cQuickcheck_Exhaustive.exhaustive_natural' @ V0) @ V1) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_set.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ V4) @ V3)) @ cOption.option.None) @ (V1 @ ((cSet.insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_set_rel) @ V1))))))))
(TQuickcheck_Exhaustive.exhaustive_set_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cOrderings.bot_class.bot)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_set_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V3 @ cOrderings.bot_class.bot)) @ (V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_set_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_set_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ V6) @ V5)) @ cOption.option.None) @ (V3 @ ((cSet.insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V5 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V8)))) @ V7)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V6)) @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V10]: (V5 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V8) @ V9) @ V10)))) @ V7))) @ V7))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7)) @ cOption.option.None)))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ V0) @ V1) @ V2)) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V3]: (V0 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V3)))) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V1)) @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: (V0 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V3) @ V4) @ V5)))) @ V2))) @ V2))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)) @ cOption.option.None))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V6) @ V7)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V5) @ V6) @ ((cInt.plus_int_inst.plus_int @ V7) @ cInt.one_int_inst.one_int))) @ cOption.option.Some) @ (V5 @ ((cProduct_Type.Pair @ V7) @ (^[V8]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V7)))))))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V0) @ V1) @ ((cInt.plus_int_inst.plus_int @ V2) @ cInt.one_int_inst.one_int))) @ cOption.option.Some) @ (V0 @ ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V2))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((V0 @ V3) @ V4))))))) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_set_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ V5)) @ ((c==> @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_set_rel) @ ((cProduct_Type.Pair @ V4) @ V5))) @ V3))))))))) @ V3))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set.psimps,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_set_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cHOL.eq @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V2]: ((cQuickcheck_Exhaustive.orelse @ (V0 @ V2)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V3]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V3)) @ (cProduct_Type.fst @ V2))) @ cOption.option.None) @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V3) @ V2))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))
(TQuickcheck_Exhaustive.unknown.Abs_unknown_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set))) @ (V0 @ (cQuickcheck_Exhaustive.Abs_unknown @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Exhaustive.unknown.Abs_unknown_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.Abs_unknown @ V0)) @ (cQuickcheck_Exhaustive.Abs_unknown @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Exhaustive.unknown.Rep_unknown_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Exhaustive.Rep_unknown @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Exhaustive.unknown.Rep_unknown_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.Rep_unknown @ V0)) @ (cQuickcheck_Exhaustive.Rep_unknown @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.unknown.arity_size_unknown,(cNat.size_class @ cTYPE))
(TQuickcheck_Narrowing.arity_random_narrowing_cons,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Narrowing.arity_random_narrowing_term,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Narrowing.arity_random_narrowing_type,(cQuickcheck_Random.random_class @ cTYPE))
(TQuickcheck_Narrowing.partial_term_of_class.intro,((c==> @ (cTyperep.typerep_class @ cTYPE)) @ (cQuickcheck_Narrowing.partial_term_of_class @ cTYPE)))
(TQuickcheck_Narrowing.partial_term_of_class.super,((c==> @ (cQuickcheck_Narrowing.partial_term_of_class @ cTYPE)) @ (cTyperep.typerep_class @ cTYPE)))
(TQuickcheck_Narrowing.partial_term_of_itself_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_nibble_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_nibble_inst.partial_term_of_nibble @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_option_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.property.Abs_property_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Abs_property @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set))) @ V1))))) @ V1))))))
(TQuickcheck_Narrowing.property.Rep_property_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Rep_property @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Narrowing.term_of_narrowing_cons_triv,(call @ (^[V0]: ((cHOL.eq @ (cCode_Evaluation.term_of_class.term_of @ V0)) @ cHOL.undefined))))
(TQuickcheck_Narrowing.term_of_narrowing_term_triv,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.term_of_narrowing_term_inst.term_of_narrowing_term @ V0)) @ cHOL.undefined))))
(TQuickcheck_Narrowing.term_of_narrowing_type_triv,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.term_of_narrowing_type_inst.term_of_narrowing_type @ V0)) @ cHOL.undefined))))
(TQuickcheck_Random.lazy_sequence.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Random.random_aux_lazy_sequence @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cLazy_Sequence.lazy_sequence.lazy_sequence_of_list) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))))))))
(TRecord.iso_tuple_update_accessor_cong_assist_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V0) @ V1)) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V0 @ (^[V4]: (V2 @ (V1 @ V3)))) @ V3)) @ ((V0 @ V2) @ V3))))))) @ (cHOL.All @ (^[V2]: ((cHOL.eq @ ((V0 @ cFun.id) @ V2)) @ V2))))))))))
(TRings.classrel_linordered_idom_ordered_comm_ring,(cRings.ordered_comm_ring_class @ cTYPE))
(TRings.classrel_ordered_ring_ordered_ab_group_add,(cGroups.ordered_ab_group_add_class @ cTYPE))
(TRings.linordered_idom_class.mult_le_cancel_left1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one)))))))))
(TRings.linordered_idom_class.mult_le_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V1)))))))))
(TRings.linordered_idom_class.mult_right_le_one_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)))))))))
(TRings.linordered_ring_class.not_square_less_zero,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V0)) @ cGroups.zero_class.zero)))))
(TRings.linordered_ring_strict.mult_le_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ ((V7 @ V8) @ V9)) @ ((V7 @ V8) @ V10))) @ ((cHOL.conj @ ((cHOL.implies @ ((V5 @ V3) @ V8)) @ ((V4 @ V9) @ V10))) @ ((cHOL.implies @ ((V5 @ V8) @ V3)) @ ((V4 @ V10) @ V9))))))))))))))))))))))))))))
(TRings.linordered_ring_strict_class.mult_le_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)))))))))
(TRings.linordered_semidom_class.not_one_less_zero,(cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ cGroups.zero_class.zero)))
(TRings.ordered_cancel_semiring.mult_nonneg_nonneg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((c==> @ ((V2 @ V1) @ V6)) @ ((V2 @ V1) @ ((V4 @ V5) @ V6))))))))))))))))))))
(TRings.ordered_cancel_semiring.mult_nonneg_nonpos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((c==> @ ((V2 @ V6) @ V1)) @ ((V2 @ ((V4 @ V5) @ V6)) @ V1)))))))))))))))))))
(TRings.ordered_cancel_semiring.mult_nonpos_nonneg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V1)) @ ((c==> @ ((V2 @ V1) @ V6)) @ ((V2 @ ((V4 @ V5) @ V6)) @ V1)))))))))))))))))))
(TRings.ring_1_no_zero_divisors.mult_cancel_right1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ V6) @ ((V1 @ V7) @ V6))) @ ((cHOL.disj @ ((cHOL.eq @ V6) @ V3)) @ ((cHOL.eq @ V7) @ V0)))))))))))))))))))))
(TRings.ring_1_no_zero_divisors.mult_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V6) @ V7)) @ V7)) @ ((cHOL.disj @ ((cHOL.eq @ V7) @ V3)) @ ((cHOL.eq @ V6) @ V0)))))))))))))))))))))
(TSet_Interval.complete_lattice.Inf_atMostLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ V7) @ V8)) @ ((cHOL.eq @ (V0 @ ((cSet_Interval.ord.lessThan @ V4) @ V8))) @ V6))))))))))))))))))))))
(TSet_Interval.linorder.atLeastLessThan_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V2) @ V3)) @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V4) @ V5))) @ ((cHOL.disj @ ((V0 @ V3) @ V2)) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V0 @ V3) @ V5))))))))))))))))))
(TSet_Interval.order_bot_class.atLeast_eq_UNIV_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cSet_Interval.ord_class.atLeast @ V0)) @ cOrderings.top_class.top)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)))))
(TSet_Interval.order_class.atLeastAtMost_singleton,(call @ (^[V0]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V0)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot)))))
(TSet_Interval.order_class.atLeastatMost_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))))))))
(TSet_Interval.order_class.greaterThanAtMost_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanAtMost @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TTransitive_Closure.converse_rtrancl_into_rtrancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V1) @ V3)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V3)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TTransitive_Closure.rtranclp.rtrancl_into_rtrancl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V2)) @ ((c==> @ ((V0 @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V3))))))))))))
(TBig_Operators.comm_monoid_add.setsum_reindex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ V4) @ ((cSet.image @ V2) @ V3))) @ ((c==> @ (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ V3)) @ ((cHOL.eq @ (V5 @ V7)) @ (V6 @ (V2 @ V7))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V6) @ V4)) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V5) @ V3)))))))))))))))))))))
(TBig_Operators.comm_monoid_add.setsum_restrict_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V3) @ ((cLattices.inf_class.inf @ V2) @ V4))) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V5]: (((cHOL.If @ ((cSet.member @ V5) @ V4)) @ (V3 @ V5)) @ V1))) @ V2)))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.delta',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V1) @ V3)) @ (V2 @ V3)) @ cGroups.zero_class.zero))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.zero_class.zero))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet.insert @ V1) @ V0))) @ ((cGroups.plus_class.plus @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cGroups.plus_class.plus @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))))
(TBig_Operators.comm_monoid_mult.setprod_reindex_id,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ V3)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V2) @ V3)) @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ cFun.id) @ ((cSet.image @ V2) @ V3))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)))))))))))))
(TBig_Operators.comm_monoid_set.eq_general_reverses,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (call @ (^[V8]: ((c==> @ ((cSet.member @ V8) @ V2)) @ ((cHOL.conj @ ((cSet.member @ (V3 @ V8)) @ V4)) @ ((cHOL.eq @ (V5 @ (V3 @ V8))) @ V8)))))) @ ((c==> @ (call @ (^[V8]: ((c==> @ ((cSet.member @ V8) @ V4)) @ ((cHOL.conj @ ((cSet.member @ (V5 @ V8)) @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ (V3 @ (V5 @ V8))) @ V8)) @ ((cHOL.eq @ (V6 @ (V5 @ V8))) @ (V7 @ V8)))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V7) @ V4)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V6) @ V2))))))))))))))))))))))
(TBig_Operators.comm_monoid_set.union_inter_neutral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ ((cSet.Ball @ ((cLattices.inf_class.inf @ V2) @ V3)) @ (^[V5]: ((cHOL.eq @ (V4 @ V5)) @ V1)))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ ((cLattices.sup_class.sup @ V2) @ V3))) @ ((V0 @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V3))))))))))))))))))
(TBig_Operators.linorder.finite_linorder_max_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (V3 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ ((cSet.Ball @ V5) @ (^[V6]: ((V1 @ V6) @ V4)))) @ ((c==> @ (V3 @ V5)) @ (V3 @ ((cSet.insert @ V4) @ V5)))))))))) @ (V3 @ V2))))))))))))))
(TBig_Operators.linorder.finite_linorder_min_induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (V3 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cFinite_Set.finite @ V5)) @ ((c==> @ ((cSet.Ball @ V5) @ (^[V6]: ((V1 @ V4) @ V6)))) @ ((c==> @ (V3 @ V5)) @ (V3 @ ((cSet.insert @ V4) @ V5)))))))))) @ (V3 @ V2))))))))))))))
(TBig_Operators.linorder_class.min_max.distrib_imp1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V3) @ ((cOrderings.ord_class.max @ V4) @ V5))) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V3) @ V4)) @ ((cOrderings.ord_class.min @ V3) @ V5)))))))))) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V0) @ V2)))))))))))
(TBig_Operators.linorder_class.min_max.distrib_imp2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V3) @ ((cOrderings.ord_class.min @ V4) @ V5))) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V3) @ V4)) @ ((cOrderings.ord_class.max @ V3) @ V5)))))))))) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V0) @ V2)))))))))))
(TBig_Operators.linorder_class.min_max.dual_lattice,((((cLattices.class.lattice @ cOrderings.ord_class.max) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cOrderings.ord_class.min))
(TBig_Operators.linorder_class.min_max.inf_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2)))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.union,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V1))))))))))))
(TBig_Operators.semilattice_neutr_set.insert_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cBig_Operators.semilattice_neutr_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((cHOL.eq @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ ((cSet.insert @ V3) @ V2))) @ ((V0 @ V3) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V3) @ cOrderings.bot_class.bot))))))))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.union,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V1))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cSet.Bex @ V1) @ (^[V5]: ((cOrderings.ord_class.less_eq @ (V2 @ V5)) @ (V3 @ V4)))))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V3 @ V4))))))))))))))
(TComplete_Lattices.complete_lattice_class.Inf_UNIV,((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ cOrderings.top_class.top)) @ cOrderings.bot_class.bot))
(TComplete_Lattices.complete_lattice_class.Inf_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.Bex @ V1) @ (^[V3]: ((cOrderings.ord_class.less_eq @ V3) @ V2))))))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V1)) @ (cComplete_Lattices.Inf_class.Inf @ V0))))))))
(TComplete_Lattices.complete_lattice_class.SUP_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cSet.Bex @ V1) @ (^[V5]: ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V3 @ V5)))))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4))))))))))))))
(TComplete_Lattices.complete_lattice_class.Sup_UNIV,((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ cOrderings.top_class.top)) @ cOrderings.top_class.top))
(TComplete_Lattices.complete_lattice_class.Sup_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cSet.Bex @ V1) @ (^[V3]: ((cOrderings.ord_class.less_eq @ V2) @ V3))))))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Partial_Order.ccpo.admissible_disj_lemma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V1) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V5]: ((cSet.Bex @ V3) @ (^[V6]: ((cHOL.conj @ ((V1 @ V5) @ V6)) @ (V4 @ V6))))))) @ ((cHOL.eq @ (V0 @ V3)) @ (V0 @ (cSet.Collect @ (^[V5]: ((cHOL.conj @ ((cSet.member @ V5) @ V3)) @ (V4 @ V5))))))))))))))))))))
(TComplete_Partial_Order.ccpo.iteratesp_iterates_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cComplete_Partial_Order.class.ccpo @ V0) @ V1) @ V2)) @ ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.iteratesp @ V0) @ V1) @ V3)) @ (^[V4]: ((cSet.member @ V4) @ (((cComplete_Partial_Order.ccpo.iterates @ V0) @ V1) @ V3))))))))))))))
(TComplete_Partial_Order.ccpo_class.admissible_disj,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ (^[V2]: (V1 @ V2)))) @ (((cComplete_Partial_Order.ccpo.admissible @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq) @ (^[V2]: ((cHOL.disj @ (V0 @ V2)) @ (V1 @ V2)))))))))))
(TComplete_Partial_Order.ccpo_class.fixp_lowerbound,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (((cComplete_Partial_Order.monotone @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V0 @ V1)) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Partial_Order.ccpo_class.fixp @ V0)) @ V1))))))))
(TComplete_Partial_Order.ccpo_class.iterates.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((c==> @ (V2 @ V3)) @ (V2 @ (V1 @ V3))))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cHOL.conj @ ((cSet.member @ V4) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ (V2 @ V4))))) @ (V2 @ (cComplete_Lattices.Sup_class.Sup @ V3))))))) @ (V2 @ V0)))))))))))
(TComplete_Partial_Order.ccpo_class.iterates.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.member @ V2) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))))) @ ((cSet.member @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1)))))))))
(TComplete_Partial_Order.ccpo_class.iterates.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((cSet.member @ (V1 @ V0)) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ (V0 @ V3))) @ ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V3)) @ V2))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V3))) @ ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V4)))) @ V2)))))) @ V2))))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (V0 @ V2))) @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V2))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V2))) @ ((cHOL.conj @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V2)) @ ((cSet.Ball @ V2) @ (^[V3]: ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V3))))))))))))))
(TDivides.classrel_ring_div_ring_1_no_zero_divisors,(cRings.ring_1_no_zero_divisors_class @ cTYPE))
(TDivides.semiring_numeral_div.le_add_diff_inverse2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V9) @ V10)) @ ((cHOL.eq @ ((V3 @ ((V6 @ V10) @ V9)) @ V9)) @ V10))))))))))))))))))))))))))
(TDivides.semiring_numeral_div.mod_less_eq_dividend,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((((cDivides.class.semiring_numeral_div @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8)) @ ((c==> @ ((V7 @ V4) @ V9)) @ ((V7 @ ((V2 @ V9) @ V10)) @ V9))))))))))))))))))))))))))
(TDivides.semiring_numeral_div_class.divmod_digit_0_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ ((cDivides.div_class.mod @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ V0)) @ ((cHOL.eq @ ((cDivides.div_class.mod @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ ((cDivides.div_class.mod @ V1) @ V0)))))))))
(TDivides.semiring_numeral_div_class.divmod_digit_0_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ ((cDivides.div_class.mod @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0))) @ V0)) @ ((cHOL.eq @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cDivides.div_class.div @ V1) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V0)))) @ ((cDivides.div_class.div @ V1) @ V0)))))))))
(TDivides.semiring_numeral_div_class.divmod_digit_1_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cDivides.div_class.mod @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cDivides.div_class.mod @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ V1)) @ ((cDivides.div_class.mod @ V0) @ V1))))))))))
(TDivides.semiring_numeral_div_class.divmod_digit_1_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cDivides.div_class.mod @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ ((cDivides.div_class.div @ V0) @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))) @ cGroups.one_class.one)) @ ((cDivides.div_class.div @ V0) @ V1))))))))))
(TDivides.semiring_numeral_div_class.divmod_step_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod_step @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ V2)) @ ((cProduct_Type.Pair @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)) @ cGroups.one_class.one)) @ ((cGroups.minus_class.minus @ V2) @ (cNum.numeral_class.numeral @ V0)))) @ ((cProduct_Type.Pair @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)) @ V2))))))))))
(TExtraction.sumbool.size_sumbool_inst.size_sumbool,((c== @ cExtraction.sumbool.size_sumbool_inst.size_sumbool) @ cExtraction.sumbool.size_sumbool_inst.size_sumbool))
(TFields.class.linordered_field_inverse_zero.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)))))))))))))))))))))))))))
(TFields.class.linordered_field_inverse_zero.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))))))))))
(TFields.division_ring.nonzero_inverse_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ (V0 @ ((V3 @ V8) @ V9))) @ ((V3 @ (V0 @ V9)) @ (V0 @ V8)))))))))))))))))))))))))))
(TFields.field.nonzero_mult_divide_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V9) @ V10)) @ ((V2 @ V9) @ V8))) @ ((V1 @ V10) @ V8))))))))))))))))))))))))))))
(TFields.field_inverse_zero_class.one_eq_divide_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ V1))))))))
(TFields.linordered_field.inverse_less_iff_less_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((cHOL.eq @ ((V10 @ (V0 @ V12)) @ (V0 @ V13))) @ ((V10 @ V13) @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field.inverse_less_imp_less_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ (V0 @ V12)) @ (V0 @ V13))) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V10 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field.less_imp_inverse_less_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((c==> @ ((V10 @ V13) @ V5)) @ ((V10 @ (V0 @ V13)) @ (V0 @ V12))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.mult_imp_div_pos_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ V2) @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2))))))))))
(TFields.linordered_field_class.mult_imp_le_div_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V1) @ V0)) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0)))))))))))
(TFields.linordered_field_class.nonzero_abs_inverse,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cGroups.abs_class.abs @ (cFields.inverse_class.inverse @ V0))) @ (cFields.inverse_class.inverse @ (cGroups.abs_class.abs @ V0)))))))
(TFields.linordered_field_inverse_zero.divide_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V12) @ V13)) @ V14)) @ (((cHOL.If @ ((V10 @ V5) @ V13)) @ ((V9 @ V12) @ ((V2 @ V14) @ V13))) @ (((cHOL.If @ ((V10 @ V13) @ V5)) @ ((V9 @ ((V2 @ V14) @ V13)) @ V12)) @ ((V9 @ V5) @ V14))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.le_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ V12) @ ((V1 @ V13) @ V14))) @ (((cHOL.If @ ((V10 @ V5) @ V14)) @ ((V9 @ ((V2 @ V12) @ V14)) @ V13)) @ (((cHOL.If @ ((V10 @ V14) @ V5)) @ ((V9 @ V13) @ ((V2 @ V12) @ V14))) @ ((V9 @ V12) @ V5))))))))))))))))))))))))))))))))))))
(TFinite_Set.comp_fun_commute.comp_comp_fun_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ (cFinite_Set.comp_fun_commute @ ((cFun.comp @ V0) @ V1))))))))
(TGroups.cancel_semigroup_add_class.add_left_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2)))))))))
(TGroups.cancel_semigroup_add_class.add_left_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cHOL.eq @ V1) @ V2)))))))))
(TGroups.class.cancel_ab_semigroup_add_axioms.intro,(call @ (^[V0]: ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((cHOL.eq @ V2) @ V3))))))))) @ (cGroups.class.cancel_ab_semigroup_add_axioms @ V0)))))
(TGroups.linordered_ab_group_add.less_eq_neg_nonpos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V6) @ (V3 @ V6))) @ ((V4 @ V6) @ V1))))))))))))))))))
(TGroups.linordered_ab_group_add.neg_less_eq_nonneg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ (V3 @ V6)) @ V6)) @ ((V4 @ V1) @ V6))))))))))))))))))
(TGroups.ordered_ab_group_add.max_diff_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ (((cOrderings.ord.max @ V4) @ V6) @ V7)) @ V8)) @ (((cOrderings.ord.max @ V4) @ ((V2 @ V6) @ V8)) @ ((V2 @ V7) @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add.min_diff_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V2 @ (((cOrderings.ord.min @ V4) @ V6) @ V7)) @ V8)) @ (((cOrderings.ord.min @ V4) @ ((V2 @ V6) @ V8)) @ ((V2 @ V7) @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_ge_minus_self,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ (V4 @ V7)) @ (V0 @ V7))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_minus_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ (V0 @ ((V3 @ V7) @ V8))) @ (V0 @ ((V3 @ V8) @ V7)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_minus_le_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ (V4 @ (V0 @ V7))) @ V2)))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_not_less_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (cHOL.Not @ ((V6 @ (V0 @ V7)) @ V2))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_triangle_ineq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ (V0 @ ((V1 @ V7) @ V8))) @ ((V1 @ (V0 @ V7)) @ (V0 @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.zero_less_abs_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.eq @ ((V6 @ V2) @ (V0 @ V7))) @ (cHOL.Not @ ((cHOL.eq @ V7) @ V2)))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_add_abs,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cGroups.plus_class.plus @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1)))) @ ((cGroups.plus_class.plus @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_ge_self,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ V0) @ (cGroups.abs_class.abs @ V0)))))
(TGroups.ordered_ab_group_add_abs_class.abs_ge_zero,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cGroups.abs_class.abs @ V0)))))
(TGroups.ordered_ab_group_add_class.neg_0_le_iff_le,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cGroups.uminus_class.uminus @ V0))) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_group_add_class.neg_le_0_iff_le,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)))))
(TGroups.ordered_cancel_comm_monoid_diff.le_iff_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.eq @ ((V3 @ V5) @ V6)) @ (cHOL.Ex @ (^[V7]: ((cHOL.eq @ V6) @ ((V0 @ V5) @ V7)))))))))))))))))))))
(TGroups.semigroup_mult_class.mult.semigroup_axioms,(cGroups.semigroup @ cGroups.times_class.times))
(TGroups.semigroup_mult_class.semigroup_mult_axioms,(cGroups.class.semigroup_mult @ cGroups.times_class.times))
(TLattices.boolean_algebra_class.compl_eq_compl_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TLattices.boolean_algebra_class.compl_le_compl_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TLattices.bounded_lattice_bot_class.bot_eq_sup_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))))))
(TLattices.bounded_lattice_bot_class.sup_eq_bot_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))))))))
(TLattices.bounded_lattice_top_class.inf_eq_top_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.top_class.top)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ V1) @ cOrderings.top_class.top))))))))
(TLattices.class.bounded_semilattice_inf_top.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.bounded_semilattice_inf_top @ V0) @ V1) @ V2) @ V3)) @ (((cOrderings.class.order_top @ V1) @ V2) @ V3)))))))))))
(TLattices.class.bounded_semilattice_inf_top.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.bounded_semilattice_inf_top @ V0) @ V1) @ V2) @ V3)) @ (((cLattices.class.semilattice_inf @ V0) @ V1) @ V2)))))))))))
(TLattices.class.bounded_semilattice_sup_bot.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.bounded_semilattice_sup_bot @ V0) @ V1) @ V2) @ V3)) @ (((cOrderings.class.order_bot @ V3) @ V1) @ V2)))))))))))
(TLattices.class.bounded_semilattice_sup_bot.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cLattices.class.bounded_semilattice_sup_bot @ V0) @ V1) @ V2) @ V3)) @ (((cLattices.class.semilattice_sup @ V0) @ V1) @ V2)))))))))))
(TLattices.linorder_class.max.abel_semigroup_axioms,(cGroups.abel_semigroup @ cOrderings.ord_class.max))
(TLattices.linorder_class.min.abel_semigroup_axioms,(cGroups.abel_semigroup @ cOrderings.ord_class.min))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rec_def,((c== @ cLazy_Sequence.lazy_sequence.lazy_sequence_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cLazy_Sequence.lazy_sequence.lazy_sequence_rec_set @ V0) @ V1) @ V2)))))))
(TList.comm_monoid_add.distinct_listsum_conv_Setsum,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (cList.distinct @ V2)) @ ((cHOL.eq @ (((cList.monoid_add.listsum @ V0) @ V1) @ V2)) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V3]: V3)) @ (cList.set @ V2))))))))))))
(TList.linorder_class.finite_sorted_distinct_unique,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ (cHOL.Ex1 @ (^[V1]: ((cHOL.conj @ ((cHOL.eq @ (cList.set @ V1)) @ V0)) @ ((cHOL.conj @ (cList.linorder_class.sorted @ V1)) @ (cList.distinct @ V1)))))))))
(TList.linorder_class.sorted_list_of_set_eq_Nil_iff,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ V0)) @ cList.list.Nil)) @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))))))
(TNat.linordered_semidom_class.less_imp_of_nat_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((cOrderings.ord_class.less @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))))))))
(TNat.linordered_semidom_class.of_nat_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ (cNat.semiring_1_class.of_nat @ V0)) @ (cNat.semiring_1_class.of_nat @ V1))) @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)))))))
(TNat.semiring_1_class.semiring_1_class.of_nat_dict,((c== @ cNat.semiring_1_class.of_nat) @ (((cNat.semiring_1.of_nat @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))
(TNitpick.pair_box.size_pair_box_inst.size_pair_box,((c== @ cNitpick.pair_box.size_pair_box_inst.size_pair_box) @ cNitpick.pair_box.size_pair_box_inst.size_pair_box))
(TNum.linordered_idom_class.not_zero_le_neg_numeral,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.linordered_semidom_class.not_numeral_less_one,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.one_class.one)))))
(TNum.linordered_semidom_class.one_less_numeral_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.numeral_class.numeral @ V0))) @ ((cNum.ord_num_inst.less_num @ cNum.num.One) @ V0)))))
(TOrderings.order_bot_class.bot.ordering_top_axioms,(((cOrderings.ordering_top @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cOrderings.bot_class.bot))
(TOrderings.order_class.dual_order.order_iff_strict,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ V1) @ V0))))))))
(TOrderings.order_class.dual_order.strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0)))))))))
(TOrderings.order_class.order.strict_implies_not_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))))))))
(TOrderings.order_top_class.top.ordering_top_axioms,(((cOrderings.ordering_top @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cOrderings.top_class.top))
(TPartial_Function.partial_function_definitions_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V2]: ((V0 @ V2) @ V2)))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((V0 @ V2) @ V4))))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.implies @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((cHOL.implies @ ((cSet.member @ V3) @ V2)) @ ((V0 @ V3) @ (V1 @ V2))))))))) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((cHOL.implies @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cSet.member @ V4) @ V2)) @ ((V0 @ V4) @ V3))))) @ ((V0 @ (V1 @ V2)) @ V3))))))))))))))))
(TPower.linordered_semidom.power_less_imp_less_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V8) @ V7))) @ ((c==> @ ((V4 @ V1) @ V8)) @ ((V5 @ V6) @ V8)))))))))))))))))))))))
(TPower.linordered_semidom_class.power_Suc_less_one,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))) @ cGroups.one_class.one))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_graph_def,((c== @ cQuickcheck_Exhaustive.check_all_n_lists_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V4 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V6]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ (cHOL.induct_forall @ (^[V6]: (cHOL.induct_forall @ (^[V7]: ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.check_all_n_lists_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.check_all_n_lists_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: (V2 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V4) @ V6)) @ (^[V8]: ((cList.list.Cons @ (V5 @ cProduct_Type.Unity)) @ (V7 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_graph_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil))) @ ((cHOL.eq @ V2) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((V0 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6))))))))))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ V2))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.check_all_subsets_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V5]: (((cOption.option.option_case @ (V2 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V3) @ V5))) @ cOption.option.Some) @ (V2 @ V5)))) @ V4))) @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cList.list.Cons @ V3) @ V4))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (V1 @ (((cFun.fun_upd @ V4) @ V5) @ V6)))) @ V3))) @ V3))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ V3))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_fun'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (V4 @ (^[V8]: V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (V3 @ (^[V7]: V6)))) @ V5)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V3 @ (((cFun.fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ cOption.option.None)))) @ ((cHOL.implies @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V3 @ (((cFun.fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V3 @ (((cFun.fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_fun'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: (V3 @ (((cFun.fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V2) @ V3))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_int'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_int'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ (((V3 @ V4) @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_rel_def,((c== @ cQuickcheck_Exhaustive.exhaustive_integer'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ (((V3 @ V4) @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_rel_def,((c== @ cQuickcheck_Exhaustive.exhaustive_natural'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_set_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cOrderings.bot_class.bot)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_set_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ V4) @ V3)) @ cOption.option.None) @ (V1 @ ((cSet.insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ V4) @ V3)) @ cOption.option.None) @ (V1 @ ((cSet.insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ ((cProduct_Type.Pair @ V1) @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V1 @ cOrderings.bot_class.bot)) @ (V2 @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ V4) @ V3)) @ cOption.option.None) @ (V1 @ ((cSet.insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))
(TQuickcheck_Exhaustive.fast_exhaustive_class.intro,((c==> @ (cCode_Evaluation.term_of_class @ cTYPE)) @ (cQuickcheck_Exhaustive.fast_exhaustive_class @ cTYPE)))
(TQuickcheck_Exhaustive.fast_exhaustive_class.super,((c==> @ (cQuickcheck_Exhaustive.fast_exhaustive_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TQuickcheck_Exhaustive.full_exhaustive_class.intro,((c==> @ (cCode_Evaluation.term_of_class @ cTYPE)) @ (cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE)))
(TQuickcheck_Exhaustive.full_exhaustive_class.super,((c==> @ (cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE)) @ (cCode_Evaluation.term_of_class @ cTYPE)))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (((V0 @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V5 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V8)))) @ V7)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V6)) @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V10]: (V5 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V8) @ V9) @ V10)))) @ V7))) @ V7))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)) @ V7)) @ cOption.option.None)))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ V0) @ V1) @ V2)) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V3]: (V0 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V3)))) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V1)) @ (((cQuickcheck_Exhaustive.full_exhaustive_fun' @ (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: (V0 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V3) @ V4) @ V5)))) @ V2))) @ V2))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)) @ cOption.option.None)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ (((V0 @ V4) @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V6) @ V7)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V5) @ V6) @ ((cInt.plus_int_inst.plus_int @ V7) @ cInt.one_int_inst.one_int))) @ cOption.option.Some) @ (V5 @ ((cProduct_Type.Pair @ V7) @ (^[V8]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V7)))))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V1) @ V2)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_int' @ V0) @ V1) @ ((cInt.plus_int_inst.plus_int @ V2) @ cInt.one_int_inst.one_int))) @ cOption.option.Some) @ (V0 @ ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V2)))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_integer_inst.full_exhaustive_integer @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V0) @ (cCode_Numeral.integer_of_natural @ V1)) @ (cCode_Numeral.uminus_integer_inst.uminus_integer @ (cCode_Numeral.integer_of_natural @ V1)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_natural_inst.full_exhaustive_natural @ V0) @ V1)) @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V0) @ V1) @ cCode_Numeral.zero_natural_inst.zero_natural)))))))
(TQuickcheck_Exhaustive.full_exhaustive_set.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_set_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_set_rel) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((V2 @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_rel_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_set_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ V4))) @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))
(TQuickcheck_Exhaustive.random_aux_three_valued_def,((c== @ cQuickcheck_Exhaustive.random_aux_three_valued) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.Value) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.No_value) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ cList.list.Nil))))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.Value) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V5)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.No_value) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ cList.list.Nil))))) @ V4)))))) @ V0))))
(TQuickcheck_Exhaustive.three_valued.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V2) @ V3) @ V4) @ V0)) @ ((((cQuickcheck_Exhaustive.three_valued.three_valued_case @ V2) @ V3) @ V4) @ V1))))))))))))))
(TQuickcheck_Exhaustive.unknown.Abs_unknown_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.unknown.unknown_rep_set))) @ ((cHOL.eq @ (cQuickcheck_Exhaustive.Rep_unknown @ (cQuickcheck_Exhaustive.Abs_unknown @ V0))) @ V0)))))
(TQuickcheck_Exhaustive.unknown.Rep_unknown_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.Abs_unknown @ (cQuickcheck_Exhaustive.Rep_unknown @ V0))) @ V0))))
(TQuickcheck_Exhaustive.unknown.unknown_rec_set_def,((c== @ cQuickcheck_Exhaustive.unknown.unknown_rec_set) @ (^[V0]: (^[V1]: (cInductive.complete_lattice_class.lfp @ (^[V2]: (^[V3]: (^[V4]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((cHOL.eq @ V4) @ V0))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Exhaustive.unknown.Known @ V5))) @ ((cHOL.eq @ V4) @ (V1 @ V5))))))))))))))
(TQuickcheck_Exhaustive.unknown.unknown_rep_set_def,((c== @ cQuickcheck_Exhaustive.unknown.unknown_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.Leaf @ V2)))))))))))
(TQuickcheck_Narrowing.arity_narrowing_three_valued,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_itself,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_nibble,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_option,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_term_of_narrowing_cons,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_term_of_narrowing_term,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_term_of_narrowing_type,(cCode_Evaluation.term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_typerep_narrowing_cons,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Narrowing.arity_typerep_narrowing_term,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Narrowing.arity_typerep_narrowing_type,(cTyperep.typerep_class @ cTYPE))
(TQuickcheck_Narrowing.partial_term_of_integer_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_integer_inst.partial_term_of_integer @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_natural_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_natural_inst.partial_term_of_natural @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_typerep_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_typerep_inst.partial_term_of_typerep @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_unknown_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.property.Abs_property_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set))) @ (V0 @ (cQuickcheck_Narrowing.Abs_property @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.property.Abs_property_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_property @ V0)) @ (cQuickcheck_Narrowing.Abs_property @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.property.Rep_property_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Narrowing.Rep_property @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.property.Rep_property_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_property @ V0)) @ (cQuickcheck_Narrowing.Rep_property @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.random_cfun_inst.random_cfun,((c== @ cQuickcheck_Narrowing.random_cfun_inst.random_cfun) @ cQuickcheck_Narrowing.random_cfun_inst.random_cfun))
(TQuickcheck_Narrowing.random_ffun_inst.random_ffun,((c== @ cQuickcheck_Narrowing.random_ffun_inst.random_ffun) @ cQuickcheck_Narrowing.random_ffun_inst.random_ffun))
(TRings.class.linordered_comm_semiring_strict.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ (((cRings.class.comm_semiring_0 @ V0) @ V3) @ V4)) @ ((c==> @ (((cRings.class.linordered_comm_semiring_strict_axioms @ V2) @ V3) @ V4)) @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))
(TRings.class.linordered_semiring_strict_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.linordered_semiring_strict_axioms @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V1 @ V3) @ V4)) @ ((cHOL.implies @ ((V1 @ V0) @ V5)) @ ((V1 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V1 @ V3) @ V4)) @ ((cHOL.implies @ ((V1 @ V0) @ V5)) @ ((V1 @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V5)))))))))))))))))))
(TRings.classrel_comm_ring_1_comm_semiring_1_cancel,(cRings.comm_semiring_1_cancel_class @ cTYPE))
(TRings.classrel_linordered_idom_linordered_semidom,(cRings.linordered_semidom_class @ cTYPE))
(TRings.comm_ring_class.square_diff_square_factored,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cGroups.times_class.times @ V1) @ V1))) @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.minus_class.minus @ V0) @ V1))))))))
(TRings.linordered_comm_semiring_strict_class.intro,((c==> @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cRings.comm_semiring_0_class @ cTYPE)) @ ((c==> @ (((cRings.class.linordered_comm_semiring_strict_axioms @ cOrderings.ord_class.less) @ cGroups.zero_class.zero) @ cGroups.times_class.times)) @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)))))
(TRings.linordered_comm_semiring_strict_class.super_2,((c==> @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)) @ (cRings.comm_semiring_0_class @ cTYPE)))
(TRings.linordered_comm_semiring_strict_class.super_1,((c==> @ (cRings.linordered_comm_semiring_strict_class @ cTYPE)) @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)))
(TRings.linordered_idom_class.mult_le_cancel_right1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.one_class.one)))))))))
(TRings.linordered_idom_class.mult_le_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V0)))))))))
(TRings.linordered_ring_strict.mult_le_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ ((V7 @ V8) @ V9)) @ ((V7 @ V10) @ V9))) @ ((cHOL.conj @ ((cHOL.implies @ ((V5 @ V3) @ V9)) @ ((V4 @ V8) @ V10))) @ ((cHOL.implies @ ((V5 @ V9) @ V3)) @ ((V4 @ V10) @ V8))))))))))))))))))))))))))))
(TRings.linordered_semiring.mult_left_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ ((V4 @ V5) @ V6)) @ ((V4 @ V5) @ V7))) @ ((c==> @ ((V1 @ V3) @ V5)) @ ((V2 @ V6) @ V7)))))))))))))))))))))
(TRings.linordered_semiring_1_class.convex_bound_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V4)) @ ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V3) @ V4)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V0)) @ ((cGroups.times_class.times @ V4) @ V2))) @ V1)))))))))))))))))
(TRings.linordered_semiring_strict.mult_strict_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((c==> @ ((V3 @ V7) @ V8)) @ ((c==> @ ((V3 @ V1) @ V6)) @ ((c==> @ ((V2 @ V1) @ V7)) @ ((V3 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V8))))))))))))))))))))))))))
(TRings.ordered_cancel_semiring.mult_nonneg_nonpos2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.ordered_cancel_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((c==> @ ((V2 @ V6) @ V1)) @ ((V2 @ ((V4 @ V6) @ V5)) @ V1)))))))))))))))))))
(TSet_Interval.complete_lattice.Inf_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ V8) @ V9)) @ ((cHOL.eq @ (V0 @ ((((cSet_Interval.ord.atLeastLessThan @ V3) @ V4) @ V8) @ V9))) @ V8))))))))))))))))))))))))
(TSet_Interval.linorder.greaterThan_Int_greaterThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord.lessThan @ V1) @ V2)) @ ((cSet_Interval.ord.lessThan @ V1) @ V3))) @ ((cSet_Interval.ord.lessThan @ V1) @ (((cOrderings.ord.min @ V0) @ V2) @ V3)))))))))))))
(TSet_Interval.linorder_class.Int_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V2) @ V3))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V3))))))))))))
(TSet_Interval.linorder_class.lessThan_Int_lessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.greaterThan @ V0)) @ (cSet_Interval.ord_class.greaterThan @ V1))) @ (cSet_Interval.ord_class.greaterThan @ ((cOrderings.ord_class.max @ V0) @ V1))))))))
(TSet_Interval.ord_class.ord_class.greaterThan_dict,((c== @ cSet_Interval.ord_class.greaterThan) @ (cSet_Interval.ord.greaterThan @ cOrderings.ord_class.less)))
(TSet_Interval.order_class.atLeastAtMost_singleton',(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))))))))
(TSet_Interval.order_class.atLeastatMost_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))))))))
(TSet_Interval.order_class.atLeastatMost_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ V3))) @ ((cHOL.disj @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))))
(TTransitive_Closure.rtrancl_Un_separator_converseE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ ((cLattices.sup_class.sup @ V2) @ V3)))) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V4) @ V1)) @ (cTransitive_Closure.rtrancl @ V2))) @ ((cHOL.implies @ ((cSet.member @ ((cProduct_Type.Pair @ V5) @ V4)) @ V3)) @ ((cHOL.eq @ V5) @ V4)))))))) @ ((cSet.member @ ((cProduct_Type.Pair @ V0) @ V1)) @ (cTransitive_Closure.rtrancl @ V2)))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cGroups.plus_class.plus @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V2))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ (((cFinite_Set.fold @ ((cFun.comp @ cGroups.plus_class.plus) @ V0)) @ cGroups.zero_class.zero) @ V1)))))))
(TBig_Operators.comm_monoid_add_class.setsum.neutral,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ cGroups.zero_class.zero)))))))
(TBig_Operators.comm_monoid_add_class.setsum.reindex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet.image @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ ((cFun.comp @ V2) @ V0)) @ V1))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.related,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ cGroups.zero_class.zero) @ cGroups.zero_class.zero)) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cHOL.conj @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V7))) @ ((V0 @ ((cGroups.plus_class.plus @ V4) @ V5)) @ ((cGroups.plus_class.plus @ V6) @ V7)))))))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V4]: ((V0 @ (V2 @ V4)) @ (V3 @ V4))))) @ ((V0 @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1)))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: ((V0 @ V3) @ V4))) @ V1))) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: ((V0 @ V4) @ V3))) @ V2))) @ V1)))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.Sigma,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cBig_Operators.comm_monoid_mult_class.setprod @ (V2 @ V3)) @ (V1 @ V3)))) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (cProduct_Type.prod.prod_case @ V2)) @ ((cProduct_Type.Sigma @ V0) @ (^[V3]: (V1 @ V3))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.delta,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V3) @ V1)) @ (V2 @ V3)) @ cGroups.one_class.one))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.one_class.one))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.empty,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ cOrderings.bot_class.bot)) @ cGroups.one_class.one))))
(TBig_Operators.linorder_class.min_max.inf_left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.min @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.sup_left_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.max @ V0) @ V1)))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.closed,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cSet.member @ ((cLattices.inf_class.inf @ V1) @ V2)) @ ((cSet.insert @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))) @ ((cSet.member @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ V0)))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cSet.insert @ V1) @ V0))) @ ((cLattices.inf_class.inf @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cLattices.inf_class.inf @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V1)) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))))))))))
(TBig_Operators.semilattice_order_neutr_set.antimono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V4) @ V5)) @ ((c==> @ (cFinite_Set.finite @ V5)) @ ((V2 @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V5)) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V4))))))))))))))))))
(TBig_Operators.semilattice_order_neutr_set.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ ((V2 @ V5) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V4))) @ ((c==> @ ((c==> @ (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ V4)) @ ((V2 @ V5) @ V7))))) @ V6)) @ V6)))))))))))))))))))
(TBig_Operators.semilattice_order_neutr_set.boundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V4)) @ ((V2 @ V5) @ V6))))) @ ((V2 @ V5) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V4))))))))))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.closed,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((cSet.member @ ((cLattices.sup_class.sup @ V1) @ V2)) @ ((cSet.insert @ V1) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))) @ ((cSet.member @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ V0)))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.insert,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cSet.insert @ V1) @ V0))) @ ((cLattices.sup_class.sup @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cLattices.sup_class.sup @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.subset,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V1)) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0))) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0))))))))))
(TCode_Evaluation.term_of_itself_inst.term_of_itself,((c== @ cCode_Evaluation.term_of_itself_inst.term_of_itself) @ cCode_Evaluation.term_of_itself_inst.term_of_itself))
(TCode_Evaluation.term_of_nibble_inst.term_of_nibble,((c== @ cCode_Evaluation.term_of_nibble_inst.term_of_nibble) @ cCode_Evaluation.term_of_nibble_inst.term_of_nibble))
(TCode_Evaluation.term_of_option_inst.term_of_option,((c== @ cCode_Evaluation.term_of_option_inst.term_of_option) @ cCode_Evaluation.term_of_option_inst.term_of_option))
(TComplete_Lattices.complete_distrib_lattice.INF_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (V9 @ V11)))) @ V10)) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: ((V5 @ (V9 @ V11)) @ V10))))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.Inf_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ (V0 @ V8)) @ V9)) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V10]: ((V5 @ V10) @ V9))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.SUP_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (V9 @ V11)))) @ V10)) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: ((V2 @ (V9 @ V11)) @ V10))))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.Sup_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ (V1 @ V8)) @ V9)) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V10]: ((V2 @ V10) @ V9))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.inf_SUP,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V8) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: (V10 @ V11))))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V11]: ((V2 @ V8) @ (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.inf_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ V8) @ (V1 @ V9))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V10]: ((V2 @ V8) @ V10))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.sup_INF,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ V8) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: (V10 @ V11))))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V11]: ((V5 @ V8) @ (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.sup_Inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ V8) @ (V0 @ V9))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V10]: ((V5 @ V8) @ V10))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.INF_inf_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (V9 @ V11)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: (V10 @ V11))))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V11]: ((V2 @ (V9 @ V11)) @ (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_subset_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V8) @ V9)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((V3 @ (V10 @ V12)) @ (V11 @ V12)))))) @ ((V3 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: (V10 @ V12)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V9) @ (^[V12]: (V11 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_sup_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (V9 @ V11)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: (V10 @ V11))))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V11]: ((V5 @ (V9 @ V11)) @ (V10 @ V11)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_subset_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V8) @ V9)) @ ((V3 @ (V1 @ V8)) @ (V1 @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_const,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: V1))) @ V1)))))))
(TComplete_Lattices.complete_lattice_class.INF_empty,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ cOrderings.bot_class.bot) @ (^[V1]: (V0 @ V1)))) @ cOrderings.top_class.top))))
(TComplete_Lattices.complete_lattice_class.INF_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cSet.image @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ (V0 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_lower,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3)))) @ (V2 @ V0))))))))))
(TComplete_Lattices.complete_lattice_class.INF_union,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.Inf_empty,((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top))
(TComplete_Lattices.complete_lattice_class.Inf_lower,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V1)) @ V0)))))))
(TComplete_Lattices.complete_lattice_class.SUP_const,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: V1))) @ V1)))))))
(TComplete_Lattices.complete_lattice_class.SUP_empty,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.bot_class.bot) @ (^[V1]: (V0 @ V1)))) @ cOrderings.bot_class.bot))))
(TComplete_Lattices.complete_lattice_class.SUP_image,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet.image @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ (V0 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V2))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)))))))))
(TComplete_Lattices.complete_lattice_class.SUP_lessD,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V1 @ V4)))) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less @ (V1 @ V3)) @ V2))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_union,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cLattices.sup_class.sup @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_upper,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.Sup_empty,((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))
(TComplete_Lattices.complete_lattice_class.Sup_least,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)))))))
(TComplete_Lattices.complete_lattice_class.Sup_upper,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.complete_linorder.INF_eq_bot_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V10]: (V9 @ V10)))) @ V6)) @ (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V4 @ V6) @ V10)) @ ((cSet.Bex @ V8) @ (^[V11]: ((V4 @ (V9 @ V11)) @ V10)))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.Inf_eq_bot_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V8)) @ V6)) @ (cHOL.All @ (^[V9]: ((cHOL.implies @ ((V4 @ V6) @ V9)) @ ((cSet.Bex @ V8) @ (^[V10]: ((V4 @ V10) @ V9)))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.SUP_eq_top_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V10]: (V9 @ V10)))) @ V7)) @ (cHOL.All @ (^[V10]: ((cHOL.implies @ ((V4 @ V10) @ V7)) @ ((cSet.Bex @ V8) @ (^[V11]: ((V4 @ V10) @ (V9 @ V11))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_linorder.Sup_eq_top_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V1 @ V8)) @ V7)) @ (cHOL.All @ (^[V9]: ((cHOL.implies @ ((V4 @ V9) @ V7)) @ ((cSet.Bex @ V8) @ (^[V10]: ((V4 @ V9) @ V10)))))))))))))))))))))))))))
(TComplete_Partial_Order.ccpo_class.iterates.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ ((c==> @ (V2 @ V3)) @ (V2 @ (V1 @ V3))))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cHOL.conj @ ((cSet.member @ V4) @ (cComplete_Partial_Order.ccpo_class.iterates @ V1))) @ (V2 @ V4))))) @ (V2 @ (cComplete_Lattices.Sup_class.Sup @ V3))))))) @ (V2 @ V0)))))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V3)) @ ((c==> @ (V2 @ V3)) @ (V2 @ (V0 @ V3))))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cHOL.conj @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V4)) @ (V2 @ V4))))) @ (V2 @ (cComplete_Lattices.Sup_class.Sup @ V3))))))) @ (V2 @ V1)))))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cComplete_Partial_Order.ccpo_class.iteratesp @ V1) @ V2)))) @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V1)) @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ (V0 @ V1))))))))
(TDivides.semiring_numeral_div_class.divmod_step_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod_step @ V0) @ V1)) @ ((cHOL.Let @ V1) @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (((cHOL.If @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ V3)) @ ((cProduct_Type.Pair @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V2)) @ cGroups.one_class.one)) @ ((cGroups.minus_class.minus @ V3) @ (cNum.numeral_class.numeral @ V0)))) @ ((cProduct_Type.Pair @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V2)) @ V3))))))))))))
(TDivides.semiring_numeral_div_class.mult_div_cancel,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cDivides.div_class.div @ V1) @ V0))) @ ((cGroups.minus_class.minus @ V1) @ ((cDivides.div_class.mod @ V1) @ V0))))))))
(TFields.class.division_ring_inverse_zero_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cFields.class.division_ring_inverse_zero_axioms @ V0) @ V1)) @ ((cHOL.eq @ (V0 @ V1)) @ V1)))))))
(TFields.division_ring_inverse_zero.inverse_minus_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ (V7 @ V8))) @ (V7 @ (V0 @ V8)))))))))))))))))))))))
(TFields.field.nonzero_mult_divide_mult_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V9) @ V10)) @ ((V2 @ V8) @ V9))) @ ((V1 @ V10) @ V8))))))))))))))))))))))))))))
(TFields.field.nonzero_mult_divide_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V10) @ V9)) @ ((V2 @ V8) @ V9))) @ ((V1 @ V10) @ V8))))))))))))))))))))))))))))
(TFields.field_class.nonzero_divide_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V1)))))))))
(TFields.field_class.nonzero_mult_divide_cancel_left,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ V1)))))))
(TFields.field_inverse_zero_class.divide_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cFields.inverse_class.divide @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TFields.field_inverse_zero_class.divide_minus_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ (cGroups.uminus_class.uminus @ V1))) @ (cGroups.uminus_class.uminus @ ((cFields.inverse_class.divide @ V0) @ V1))))))))
(TFields.field_inverse_zero_class.field_inverse_zero,((cHOL.eq @ (cFields.inverse_class.inverse @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TFields.field_inverse_zero_class.minus_divide_right,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cFields.inverse_class.divide @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TFinite_Set.comp_fun_commute.fold_graph_insertE_aux,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ ((c==> @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ ((V0 @ V4) @ V5))) @ ((((cFinite_Set.fold_graph @ V0) @ V1) @ ((cGroups.minus_class.minus @ V2) @ ((cSet.insert @ V4) @ cOrderings.bot_class.bot))) @ V5))))))))))))))))))
(TFinite_Set.complete_lattice_class.inf_INF_fold_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V2))) @ (((cFinite_Set.fold @ ((cFun.comp @ cLattices.inf_class.inf) @ V2)) @ V1) @ V0))))))))))
(TFinite_Set.complete_lattice_class.inf_Inf_fold_inf,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1)) @ (((cFinite_Set.fold @ cLattices.inf_class.inf) @ V1) @ V0))))))))
(TFinite_Set.complete_lattice_class.sup_SUP_fold_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V2))) @ (((cFinite_Set.fold @ ((cFun.comp @ cLattices.sup_class.sup) @ V2)) @ V1) @ V0))))))))))
(TFinite_Set.complete_lattice_class.sup_Sup_fold_sup,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ (((cFinite_Set.fold @ cLattices.sup_class.sup) @ V1) @ V0))))))))
(TFinite_Set.semilattice_inf_class.comp_fun_idem_inf,(cFinite_Set.comp_fun_idem @ cLattices.inf_class.inf))
(TFinite_Set.semilattice_sup_class.comp_fun_idem_sup,(cFinite_Set.comp_fun_idem @ cLattices.sup_class.sup))
(TGroups.cancel_semigroup_add_class.add_right_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V1))) @ ((cHOL.eq @ V0) @ V2)))))))))
(TGroups.cancel_semigroup_add_class.add_right_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V1))) @ ((cHOL.eq @ V0) @ V2)))))))))
(TGroups.class.ordered_ab_group_add_abs_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: ((V0 @ V1) @ (V2 @ V5))))) @ ((c==> @ (call @ (^[V5]: ((V0 @ V5) @ (V2 @ V5))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((V0 @ V5) @ V6)) @ ((c==> @ ((V0 @ (V3 @ V5)) @ V6)) @ ((V0 @ (V2 @ V5)) @ V6)))))))) @ ((c==> @ (call @ (^[V5]: ((cHOL.eq @ (V2 @ (V3 @ V5))) @ (V2 @ V5))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((V0 @ (V2 @ ((V4 @ V5) @ V6))) @ ((V4 @ (V2 @ V5)) @ (V2 @ V6)))))))) @ (((((cGroups.class.ordered_ab_group_add_abs_axioms @ V2) @ V4) @ V1) @ V3) @ V0)))))))))))))))))
(TGroups.class.ordered_ab_semigroup_add_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V2) @ V3)) @ ((V0 @ ((V1 @ V4) @ V2)) @ ((V1 @ V4) @ V3)))))))))) @ ((cGroups.class.ordered_ab_semigroup_add_axioms @ V1) @ V0)))))))
(TGroups.class.ordered_ab_semigroup_add_imp_le.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ V0) @ V1)) @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2))))))))))
(TGroups.class.ordered_cancel_ab_semigroup_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cGroups.class.cancel_ab_semigroup_add @ V0)) @ ((c==> @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2))))))))))
(TGroups.class.ordered_cancel_comm_monoid_diff.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)) @ ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V3) @ V4)) @ ((c==> @ ((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ V0) @ V3)) @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))))
(TGroups.comm_monoid_diff_class.add_diff_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cGroups.minus_class.minus @ V1) @ V2)))))))))
(TGroups.ordered_ab_group_add_abs.abs_triangle_ineq2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ ((V3 @ (V0 @ V7)) @ (V0 @ V8))) @ (V0 @ ((V3 @ V7) @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_triangle_ineq3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ (V0 @ ((V3 @ (V0 @ V7)) @ (V0 @ V8)))) @ (V0 @ ((V3 @ V7) @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_triangle_ineq4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ (V0 @ ((V3 @ V7) @ V8))) @ ((V1 @ (V0 @ V7)) @ (V0 @ V8)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_class.diff_le_0_iff_le,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TGroups.ordered_ab_group_add_class.le_iff_diff_le_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cGroups.zero_class.zero)))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.intro,((c==> @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ ((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq)) @ (cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.super,((c==> @ (cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE)) @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)))
(TGroups.ordered_cancel_ab_semigroup_add_class.intro,((c==> @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE))))
(TGroups.ordered_cancel_ab_semigroup_add_class.super_2,((c==> @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_class @ cTYPE)))
(TGroups.ordered_cancel_ab_semigroup_add_class.super_1,((c==> @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ (cGroups.cancel_ab_semigroup_add_class @ cTYPE)))
(TGroups.ordered_cancel_comm_monoid_diff.le_add_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((V3 @ V7) @ ((V2 @ ((V0 @ V6) @ V7)) @ V5)))))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.intro,((c==> @ (cGroups.comm_monoid_diff_class @ cTYPE)) @ ((c==> @ (cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE)) @ ((c==> @ ((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq)) @ (cGroups.ordered_cancel_comm_monoid_diff_class @ cTYPE)))))
(TGroups.ordered_cancel_comm_monoid_diff_class.super_2,((c==> @ (cGroups.ordered_cancel_comm_monoid_diff_class @ cTYPE)) @ (cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE)))
(TGroups.ordered_cancel_comm_monoid_diff_class.super_1,((c==> @ (cGroups.ordered_cancel_comm_monoid_diff_class @ cTYPE)) @ (cGroups.comm_monoid_diff_class @ cTYPE)))
(TGroups.ordered_comm_monoid_add.add_nonneg_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ V1)) @ ((cHOL.eq @ V5) @ V1)))))))))))))))))))
(TLattices.semilattice_inf_class.inf.strict_boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ ((cLattices.inf_class.inf @ V1) @ V2))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V2)) @ V3))) @ V3)))))))))))
(TLattices.semilattice_sup_class.sup.strict_boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ ((cLattices.sup_class.sup @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ V3))) @ V3)))))))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_case_def,((c== @ cLazy_Sequence.lazy_sequence.lazy_sequence_case) @ (^[V0]: (cLazy_Sequence.lazy_sequence.lazy_sequence_rec @ (^[V1]: (V0 @ V1))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_size_def,(call @ (^[V0]: ((c== @ (cLazy_Sequence.lazy_sequence.lazy_sequence_size @ V0)) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_rec @ (^[V1]: ((cNat.plus_nat_inst.plus_nat @ ((cList.list.list_size @ V0) @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))))
(TLazy_Sequence.small_lazy_list_inst.small_lazy_list,((c== @ cLazy_Sequence.small_lazy_list_inst.small_lazy_list) @ cLazy_Sequence.small_lazy_list_inst.small_lazy_list))
(TLazy_Sequence.small_lazy_prod_inst.small_lazy_prod,((c== @ cLazy_Sequence.small_lazy_prod_inst.small_lazy_prod) @ cLazy_Sequence.small_lazy_prod_inst.small_lazy_prod))
(TLazy_Sequence.small_lazy_unit_inst.small_lazy_unit,((c== @ cLazy_Sequence.small_lazy_unit_inst.small_lazy_unit) @ cLazy_Sequence.small_lazy_unit_inst.small_lazy_unit))
(TList.linorder_class.linorder_class.insort_key_dict,((c== @ cList.linorder_class.insort_key) @ (cList.linorder.insort_key @ cOrderings.ord_class.less_eq)))
(TList.linorder_class.map_sorted_distinct_set_unique,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ ((cLattices.sup_class.sup @ (cList.set @ V1)) @ (cList.set @ V2)))) @ ((c==> @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ V1))) @ ((c==> @ (cList.distinct @ ((cList.map @ V0) @ V1))) @ ((c==> @ (cList.linorder_class.sorted @ ((cList.map @ V0) @ V2))) @ ((c==> @ (cList.distinct @ ((cList.map @ V0) @ V2))) @ ((c==> @ ((cHOL.eq @ (cList.set @ V1)) @ (cList.set @ V2))) @ ((cHOL.eq @ V1) @ V2))))))))))))))
(TList.monoid_add.interv_listsum_conv_setsum_set_int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V2) @ ((cList.upto @ V3) @ V4)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ (cList.set @ ((cList.upto @ V3) @ V4))))))))))))))))
(TList.monoid_add.interv_listsum_conv_setsum_set_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.monoid_add @ V0) @ V1)) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V2) @ ((cList.upt @ V3) @ V4)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ (cList.set @ ((cList.upt @ V3) @ V4))))))))))))))))
(TNitpick.narrowing_pair_box_inst.narrowing_pair_box,((c== @ cNitpick.narrowing_pair_box_inst.narrowing_pair_box) @ cNitpick.narrowing_pair_box_inst.narrowing_pair_box))
(TNum.linordered_idom_class.neg_numeral_less_numeral,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less @ (cNum.neg_numeral_class.neg_numeral @ V0)) @ (cNum.numeral_class.numeral @ V1)))))))
(TNum.linordered_idom_class.not_one_less_neg_numeral,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.linordered_semidom_class.not_numeral_less_zero,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ cGroups.zero_class.zero)))))
(TNum.semiring_numeral_class.semiring_numeral_axioms,(((cNum.class.semiring_numeral @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus))
(TOrderings.order_class.order_class.strict_mono_dict,((c== @ cOrderings.order_class.strict_mono) @ (cOrderings.order.strict_mono @ cOrderings.ord_class.less)))
(TPartial_Function.partial_function_definitions.ccpo,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ (((cComplete_Partial_Order.class.ccpo @ (cPartial_Function.fun_lub @ V1)) @ (cPartial_Function.fun_ord @ V0)) @ (cPartial_Function.mk_less @ (cPartial_Function.fun_ord @ V0)))))))))
(TPower.linordered_idom_class.not_sum_power2_lt_zero,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ cGroups.zero_class.zero)))))))
(TPower.linordered_idom_class.sum_power2_eq_zero_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ cGroups.zero_class.zero)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))
(TPower.linordered_idom_class.sum_power2_gt_zero_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))) @ ((cHOL.disj @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)))))))))
(TPower.linordered_idom_class.sum_power2_le_zero_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ cGroups.zero_class.zero)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))
(TPower.linordered_semidom_class.power_le_imp_le_exp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2))))))))))
(TPower.ring_1_no_zero_divisors.field_power_not_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.ring_1_no_zero_divisors @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ V3))) @ (cHOL.Not @ ((cHOL.eq @ ((((cPower.power.power @ V0) @ V1) @ V6) @ V7)) @ V3)))))))))))))))))))))
(TPower.ring_1_no_zero_divisors_class.zero_eq_power2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TQuickcheck_Exhaustive.arity_full_exhaustive_nibble,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_option,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_n_lists_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.check_all_n_lists_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.check_all_n_lists_rel @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V1 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V4)) @ (^[V6]: ((cList.list.Cons @ (V3 @ cProduct_Type.Unity)) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V0))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ ((cProduct_Type.Pair @ (^[V3]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V3))) @ cOption.option.Some) @ (V0 @ V3)))) @ V2)) @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (V4 @ (^[V8]: V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (V1 @ (((cFun.fun_upd @ V4) @ V5) @ V6)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2))) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (V1 @ (((cFun.fun_upd @ V4) @ V5) @ V6)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)))))) @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V0) @ V2))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V4]: (V1 @ (^[V5]: V4)))) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V6]: (V1 @ (((cFun.fun_upd @ V4) @ V5) @ V6)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)))) @ cOption.option.None)))))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))))))) @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V2 @ V1)) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_sumC_def,((c== @ cQuickcheck_Exhaustive.exhaustive_integer'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_sumC_def,((c== @ cQuickcheck_Exhaustive.exhaustive_natural'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.exhaustive_set_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cOrderings.bot_class.bot)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ V7) @ V6)) @ cOption.option.None) @ (V4 @ ((cSet.insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_fun'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (((V3 @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_rel_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_fun'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V3 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_int'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ (((V3 @ V4) @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_rel_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_int'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V5))))) @ cOption.option.None))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_integer') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.full_exhaustive_integer'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_natural') @ (^[V0]: (^[V1]: (^[V2]: (cQuickcheck_Exhaustive.full_exhaustive_natural'_sumC @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_sumC_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_set_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.term_syntax.termify_pair_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.term_syntax.termify_pair @ cTYPE) @ cTYPE) @ V0) @ V1)) @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ V0)) @ V1)))))))
(TQuickcheck_Exhaustive.type_definition_three_valued,(((cTypedef.type_definition @ cQuickcheck_Exhaustive.Rep_three_valued) @ cQuickcheck_Exhaustive.Abs_three_valued) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set)))
(TQuickcheck_Narrowing.arity_narrowing_lazy_sequence,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_integer,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_natural,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_typerep,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_unknown,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.cfun.cfun_size_overloaded_def,((c== @ cNat.size_class.size) @ (cQuickcheck_Narrowing.cfun.cfun_rec @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Narrowing.cfun.size_cfun_inst.size_cfun,((c== @ cQuickcheck_Narrowing.cfun.size_cfun_inst.size_cfun) @ cQuickcheck_Narrowing.cfun.size_cfun_inst.size_cfun))
(TQuickcheck_Narrowing.ffun.ffun_size_overloaded_def,((c== @ cNat.size_class.size) @ ((cQuickcheck_Narrowing.ffun.ffun_rec @ (^[V0]: cNat.zero_nat_inst.zero_nat)) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ V3) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TQuickcheck_Narrowing.ffun.size_ffun_inst.size_ffun,((c== @ cQuickcheck_Narrowing.ffun.size_ffun_inst.size_ffun) @ cQuickcheck_Narrowing.ffun.size_ffun_inst.size_ffun))
(TQuickcheck_Narrowing.narrowing_cons.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V2) @ V0)) @ ((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case @ V2) @ V1))))))))))
(TQuickcheck_Narrowing.narrowing_dummy_narrowing_def,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_dummy_narrowing) @ cQuickcheck_Narrowing.narrowing_class.narrowing))
(TQuickcheck_Narrowing.narrowing_term.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V2) @ V3) @ V0)) @ (((cQuickcheck_Narrowing.narrowing_term.narrowing_term_case @ V2) @ V3) @ V1))))))))))))
(TQuickcheck_Narrowing.narrowing_type.weak_case_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V2) @ V0)) @ ((cQuickcheck_Narrowing.narrowing_type.narrowing_type_case @ V2) @ V1))))))))))
(TQuickcheck_Narrowing.nibble.narrowing_nibble.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_nibble_inst.narrowing_nibble) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble0)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble1)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble2)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble3)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble4)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble5)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble6)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble7)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble8)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.Nibble9)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.NibbleA)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.NibbleB)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.NibbleC)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.NibbleD)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cString.nibble.NibbleE)) @ (cQuickcheck_Narrowing.cons @ cString.nibble.NibbleF))))))))))))))))))
(TQuickcheck_Narrowing.option.narrowing_option.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cOption.option.None)) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cOption.option.Some)) @ cQuickcheck_Narrowing.narrowing_class.narrowing))))
(TQuickcheck_Narrowing.partial_term_of_finite_1_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_finite_1_inst.partial_term_of_finite_1 @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_finite_2_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_finite_2_inst.partial_term_of_finite_2 @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_finite_3_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_finite_3_inst.partial_term_of_finite_3 @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_finite_4_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_finite_4_inst.partial_term_of_finite_4 @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_finite_5_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_finite_5_inst.partial_term_of_finite_5 @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_property_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_property_inst.partial_term_of_property @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.property.Abs_property_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.property.property_rep_set))) @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_property @ (cQuickcheck_Narrowing.Abs_property @ V0))) @ V0)))))
(TQuickcheck_Narrowing.property.Rep_property_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_property @ (cQuickcheck_Narrowing.Rep_property @ V0))) @ V0))))
(TQuickcheck_Narrowing.property.property_rec_set_def,((c== @ cQuickcheck_Narrowing.property.property_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (cInductive.complete_lattice_class.lfp @ (^[V3]: (^[V4]: (^[V5]: ((cHOL.disj @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Universal @ V8) @ V6) @ V9))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ ((((V0 @ V8) @ V6) @ V9) @ V7))) @ (cHOL.All @ (^[V10]: ((V3 @ (V6 @ V10)) @ (V7 @ V10))))))))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (((cQuickcheck_Narrowing.property.Existential @ V8) @ V6) @ V9))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ ((((V1 @ V8) @ V6) @ V9) @ V7))) @ (cHOL.All @ (^[V10]: ((V3 @ (V6 @ V10)) @ (V7 @ V10))))))))))))))) @ (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cQuickcheck_Narrowing.property.Property @ V6))) @ ((cHOL.eq @ V5) @ (V2 @ V6))))))))))))))))
(TQuickcheck_Narrowing.property.property_rep_set_def,((c== @ cQuickcheck_Narrowing.property.property_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ (^[V5]: (V2 @ V5)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4)))))))) @ (cHOL.induct_forall @ (^[V5]: (V0 @ (V2 @ V5)))))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ (^[V5]: (V2 @ V5)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4))))))))) @ (cHOL.induct_forall @ (^[V5]: (V0 @ (V2 @ V5)))))))))))) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.Leaf @ (cSum_Type.Inl @ V2))))))))))))))
(TQuickcheck_Narrowing.random_aux_narrowing_cons_def,((c== @ cQuickcheck_Narrowing.random_aux_narrowing_cons) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ cList.list.Nil))) @ V4)))))) @ V0))))
(TQuickcheck_Random.random_itself_inst.random_itself,((c== @ cQuickcheck_Random.random_itself_inst.random_itself) @ cQuickcheck_Random.random_itself_inst.random_itself))
(TQuickcheck_Random.random_nibble_inst.random_nibble,((c== @ cQuickcheck_Random.random_nibble_inst.random_nibble) @ cQuickcheck_Random.random_nibble_inst.random_nibble))
(TQuickcheck_Random.random_option_inst.random_option,((c== @ cQuickcheck_Random.random_option_inst.random_option) @ cQuickcheck_Random.random_option_inst.random_option))
(TQuickcheck_Random.term_syntax.valterm_emptyset_def,((cHOL.eq @ cQuickcheck_Random.term_syntax.valterm_emptyset) @ ((cProduct_Type.Pair @ cOrderings.bot_class.bot) @ (^[V0]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rec_def,((c== @ cRecord.tuple_isomorphism.tuple_isomorphism_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cRecord.tuple_isomorphism.tuple_isomorphism_rec_set @ V0) @ V1) @ V2)))))))
(TRings.class.linordered_comm_semiring_strict.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cRings.class.linordered_comm_semiring_strict_axioms @ V2) @ V3) @ V4)))))))))))))
(TRings.class.linordered_comm_semiring_strict.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cRings.class.comm_semiring_0 @ V0) @ V3) @ V4)))))))))))))
(TRings.class.linordered_comm_semiring_strict.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)))))))))))))
(TRings.classrel_semiring_1_cancel_semiring_0_cancel,(cRings.semiring_0_cancel_class @ cTYPE))
(TRings.comm_semiring_0_class.comm_semiring_0_axioms,(((cRings.class.comm_semiring_0 @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.comm_semiring_1_class.comm_semiring_1_axioms,((((cRings.class.comm_semiring_1 @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TRings.linordered_comm_semiring_strict_class.axioms,(((cRings.class.linordered_comm_semiring_strict_axioms @ cOrderings.ord_class.less) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.linordered_idom_class.linordered_idom_axioms,((((((((((cRings.class.linordered_idom @ cGroups.abs_class.abs) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.plus_class.plus) @ cGroups.one_class.one) @ cGroups.sgn_class.sgn) @ cGroups.times_class.times))
(TRings.linordered_idom_class.mult_less_cancel_left1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.one_class.one)))))))))
(TRings.linordered_idom_class.mult_less_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V1)))))))))
(TRings.linordered_ring_class.linordered_ring_axioms,((((((((cRings.class.linordered_ring @ cGroups.abs_class.abs) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.plus_class.plus) @ cGroups.times_class.times))
(TRings.linordered_ring_strict.mult_less_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ ((V7 @ V8) @ V9)) @ ((V7 @ V8) @ V10))) @ ((cHOL.conj @ ((cHOL.implies @ ((V4 @ V3) @ V8)) @ ((V5 @ V9) @ V10))) @ ((cHOL.implies @ ((V4 @ V8) @ V3)) @ ((V5 @ V10) @ V9))))))))))))))))))))))))))))
(TRings.linordered_ring_strict_class.mult_less_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)))))))))
(TRings.linordered_semiring.mult_right_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ ((V4 @ V5) @ V6)) @ ((V4 @ V7) @ V6))) @ ((c==> @ ((V1 @ V3) @ V6)) @ ((V2 @ V5) @ V7)))))))))))))))))))))
(TRings.linordered_semiring_1_strict.convex_bound_lt,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((cRings.class.linordered_semiring_1_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V3 @ V6) @ V7)) @ ((c==> @ ((V3 @ V8) @ V7)) @ ((c==> @ ((V2 @ V1) @ V9)) @ ((c==> @ ((V2 @ V1) @ V10)) @ ((c==> @ ((cHOL.eq @ ((V0 @ V9) @ V10)) @ V5)) @ ((V3 @ ((V0 @ ((V4 @ V9) @ V6)) @ ((V4 @ V10) @ V8))) @ V7))))))))))))))))))))))))))))))
(TRings.linordered_semiring_strict.mult_strict_mono',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((c==> @ ((V3 @ V7) @ V8)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((c==> @ ((V2 @ V1) @ V7)) @ ((V3 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V8))))))))))))))))))))))))))
(TRings.ring_no_zero_divisors_class.mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TSemiring_Normalization.field.normalizing_field_ops_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (cPure.term @ (V0 @ V8))))))))))))))))))))))
(TSemiring_Normalization.field.normalizing_field_ops_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ (cPure.term @ ((V1 @ V8) @ V9))))))))))))))))))))))))
(TSet_Interval.image_minus_const_atLeastLessThan_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cSet.image @ (^[V3]: ((cNat.minus_nat_inst.minus_nat @ V3) @ V0))) @ ((cSet_Interval.ord_class.atLeastLessThan @ V1) @ V2))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V0) @ V2)) @ ((cSet_Interval.ord_class.atLeastLessThan @ ((cNat.minus_nat_inst.minus_nat @ V1) @ V0)) @ ((cNat.minus_nat_inst.minus_nat @ V2) @ V0))) @ (((cHOL.If @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2)) @ ((cSet.insert @ cNat.zero_nat_inst.zero_nat) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot))))))))))
(TSet_Interval.order_class.atLeastLessThan_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TSet_Interval.order_class.atLeastatMost_psubset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ V3))) @ ((cHOL.conj @ ((cHOL.disj @ (cHOL.Not @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V1) @ V3)) @ ((cHOL.disj @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V3)))))) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))))))))))))
(TSet_Interval.order_class.greaterThanLessThan_empty,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanLessThan @ V1) @ V0)) @ cOrderings.bot_class.bot)))))))
(TSet_Interval.order_class.not_empty_eq_Ici_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (cSet_Interval.ord_class.atLeast @ V0))))))
(TSet_Interval.order_class.not_empty_eq_Iic_eq_empty,(call @ (^[V0]: (cHOL.Not @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (cSet_Interval.ord_class.atMost @ V0))))))
(TTransitive_Closure.converse_rtranclp_into_rtranclp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V1) @ V2)) @ ((c==> @ (((cTransitive_Closure.rtranclp @ V0) @ V2) @ V3)) @ (((cTransitive_Closure.rtranclp @ V0) @ V1) @ V3))))))))))))
(TBig_Operators.comm_monoid_add.setsum_Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: (cFinite_Set.finite @ V4)))) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V4) @ V5)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V3) @ (cComplete_Lattices.Sup_class.Sup @ V2))) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V3)) @ V2))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.If_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (((cHOL.If @ (V1 @ V4)) @ (V2 @ V4)) @ (V3 @ V4)))) @ V0)) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.inf_class.inf @ V0) @ (cSet.Collect @ (^[V4]: (V1 @ V4)))))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ ((cLattices.inf_class.inf @ V0) @ (cGroups.uminus_class.uminus @ (cSet.Collect @ (^[V4]: (V1 @ V4))))))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.infinite,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V0)) @ cGroups.zero_class.zero)))))))
(TBig_Operators.comm_monoid_mult.setprod_reindex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ V4) @ ((cSet.image @ V2) @ V3))) @ ((c==> @ ((cHOL.eq @ V5) @ ((cFun.comp @ V6) @ V2))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V6) @ V4)) @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V5) @ V3)))))))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.delta',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: (((cHOL.If @ ((cHOL.eq @ V1) @ V3)) @ (V2 @ V3)) @ cGroups.one_class.one))) @ V0)) @ (((cHOL.If @ ((cSet.member @ V1) @ V0)) @ (V2 @ V1)) @ cGroups.one_class.one))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cSet.insert @ V1) @ V0))) @ ((cGroups.times_class.times @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cGroups.times_class.times @ (V2 @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))))
(TBig_Operators.linorder_class.min_max.distrib_inf_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V0) @ V2))) @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.distrib_sup_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_Sup_absorb,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Max @ V0))) @ V1))))))))
(TBig_Operators.linorder_class.min_max.inf_right_idem,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V1)) @ ((cOrderings.ord_class.min @ V0) @ V1)))))))
(TBig_Operators.linorder_class.min_max.inf_sup_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.max @ V0) @ V1))) @ V0))))))
(TBig_Operators.linorder_class.min_max.lattice_axioms,((((cLattices.class.lattice @ cOrderings.ord_class.min) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cOrderings.ord_class.max))
(TBig_Operators.linorder_class.min_max.sup_Inf_absorb,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ V1))))))))
(TBig_Operators.linorder_class.min_max.sup_inf_absorb,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.min @ V0) @ V1))) @ V0))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cSet.insert @ V1) @ V0))) @ (((cFinite_Set.fold @ cLattices.inf_class.inf) @ V1) @ V0))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.in_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cSet.insert @ V1) @ V0))) @ (((cFinite_Set.fold @ cLattices.sup_class.sup) @ V1) @ V0))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.in_idem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0))) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)))))))))
(TCode_Numeral.natural.size_natural_inst.size_natural,((c== @ cCode_Numeral.natural.size_natural_inst.size_natural) @ cCode_Numeral.natural.size_natural_inst.size_natural))
(TComplete_Lattices.class.complete_lattice_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c== @ (((((cComplete_Lattices.class.complete_lattice_axioms @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.conj @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cSet.member @ V5) @ V6)) @ ((V2 @ (V0 @ V6)) @ V5))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cSet.member @ V7) @ V5)) @ ((V2 @ V6) @ V7))))) @ ((V2 @ V6) @ (V0 @ V5)))))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ ((cSet.member @ V5) @ V6)) @ ((V2 @ V5) @ (V1 @ V6)))))))))) @ ((cHOL.conj @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cSet.member @ V7) @ V5)) @ ((V2 @ V7) @ V6))))) @ ((V2 @ (V1 @ V5)) @ V6))))))) @ ((cHOL.conj @ ((cHOL.eq @ (V0 @ cOrderings.bot_class.bot)) @ V4)) @ ((cHOL.eq @ (V1 @ cOrderings.bot_class.bot)) @ V3))))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ ((cSet.insert @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.inf_class.inf @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ V2))))))))))
(TComplete_Lattices.complete_lattice_class.INF_le_SUP,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))))))))
(TComplete_Lattices.complete_lattice_class.INF_lower2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (V2 @ V0)) @ V3)) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V2 @ V4)))) @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.Inf_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cSet.insert @ V0) @ V1))) @ ((cLattices.inf_class.inf @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))))))))
(TComplete_Lattices.complete_lattice_class.Inf_le_Sup,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V0))))))
(TComplete_Lattices.complete_lattice_class.Inf_lower2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V2)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V1)) @ V2))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_absorb,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_insert,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ ((cSet.insert @ V0) @ V1)) @ (^[V3]: (V2 @ V3)))) @ ((cLattices.sup_class.sup @ (V2 @ V0)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V2))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cSet.Ball @ V0) @ (^[V3]: ((cOrderings.ord_class.less_eq @ (V1 @ V3)) @ V2)))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_upper2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ (V3 @ V0))) @ ((cOrderings.ord_class.less_eq @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.complete_lattice_class.Sup_insert,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.insert @ V0) @ V1))) @ ((cLattices.sup_class.sup @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.complete_lattice_class.Sup_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))
(TComplete_Lattices.complete_lattice_class.Sup_upper2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cSet.member @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ (cComplete_Lattices.Sup_class.Sup @ V1)))))))))))
(TComplete_Lattices.complete_lattice_class.le_INF_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cSet.Ball @ V1) @ (^[V3]: ((cOrderings.ord_class.less_eq @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.le_Inf_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ ((cSet.Ball @ V1) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V0) @ V2)))))))))
(TComplete_Lattices.complete_lattice_class.less_INF_D,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V2 @ V4))))) @ ((c==> @ ((cSet.member @ V3) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ (V2 @ V3)))))))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V3)) @ ((c==> @ (V2 @ V3)) @ (V2 @ (V0 @ V3))))))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cHOL.conj @ ((cComplete_Partial_Order.ccpo_class.iteratesp @ V0) @ V4)) @ (V2 @ V4))))) @ (V2 @ (cComplete_Lattices.Sup_class.Sup @ V3))))))) @ (V2 @ V1)))))))))))
(TDivides.semiring_numeral_div_class.diff_invert_add1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cHOL.eq @ V0) @ ((cGroups.minus_class.minus @ V2) @ V1))))))))))
(TFields.division_ring_class.nonzero_inverse_minus_eq,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cFields.inverse_class.inverse @ (cGroups.uminus_class.uminus @ V0))) @ (cGroups.uminus_class.uminus @ (cFields.inverse_class.inverse @ V0)))))))
(TFields.division_ring_inverse_zero.inverse_eq_iff_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V8)) @ (V0 @ V9))) @ ((cHOL.eq @ V8) @ V9))))))))))))))))))))))))
(TFields.division_ring_inverse_zero.inverse_eq_imp_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cHOL.eq @ (V0 @ V8)) @ (V0 @ V9))) @ ((cHOL.eq @ V8) @ V9))))))))))))))))))))))))
(TFields.division_ring_inverse_zero_class.divide_zero,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TFields.field.nonzero_mult_divide_mult_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V9) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V10) @ V9)) @ ((V2 @ V9) @ V8))) @ ((V1 @ V10) @ V8))))))))))))))))))))))))))))
(TFields.field_class.nonzero_divide_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V1) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0)))))))))
(TFields.field_class.nonzero_mult_divide_cancel_right,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V1) @ V0)) @ V0)) @ V1)))))))
(TFields.field_inverse_zero_class.divide_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cFields.inverse_class.divide @ V2) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ V2))))))))))
(TFields.field_inverse_zero_class.minus_divide_divide,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFields.inverse_class.divide @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cFields.inverse_class.divide @ V0) @ V1)))))))
(TFields.linordered_field.divide_strict_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((c==> @ ((V10 @ V14) @ V5)) @ ((c==> @ ((V10 @ V5) @ ((V2 @ V12) @ V13))) @ ((V10 @ ((V1 @ V14) @ V12)) @ ((V1 @ V14) @ V13)))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.inverse_le_iff_le_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))))
(TFields.linordered_field_class.inverse_le_imp_le_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TFields.linordered_field_class.inverse_less_iff_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))))
(TFields.linordered_field_class.inverse_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TFields.linordered_field_class.le_imp_inverse_le_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V1)) @ (cFields.inverse_class.inverse @ V0)))))))))
(TFields.linordered_field_class.less_imp_inverse_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V1)) @ (cFields.inverse_class.inverse @ V0)))))))))
(TFields.linordered_field_class.mult_imp_div_pos_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ V2) @ V0))) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V1) @ V0)) @ V2))))))))))
(TFields.linordered_field_class.mult_imp_less_div_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V1) @ V0)) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ ((cFields.inverse_class.divide @ V2) @ V0)))))))))))
(TFields.linordered_field_inverse_zero.divide_eq_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V12) @ V13)) @ V3)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V13) @ V5))) @ ((cHOL.eq @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_le_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V12) @ V13)) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V13)) @ ((V9 @ V12) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V13) @ V5)) @ ((V9 @ V13) @ V12))) @ ((cHOL.eq @ V13) @ V5))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V12) @ V13)) @ V14)) @ (((cHOL.If @ ((V10 @ V5) @ V13)) @ ((V10 @ V12) @ ((V2 @ V14) @ V13))) @ (((cHOL.If @ ((V10 @ V13) @ V5)) @ ((V10 @ ((V2 @ V14) @ V13)) @ V12)) @ ((V10 @ V5) @ V14))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.eq_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ V3) @ ((V1 @ V12) @ V13))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V13) @ V5))) @ ((cHOL.eq @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.inverse_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ (V0 @ V12)) @ (V0 @ V13))) @ ((cHOL.conj @ ((cHOL.implies @ ((V10 @ V5) @ ((V2 @ V12) @ V13))) @ ((V9 @ V13) @ V12))) @ ((cHOL.implies @ ((V9 @ ((V2 @ V12) @ V13)) @ V5)) @ ((V9 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.le_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ V3) @ ((V1 @ V12) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V13)) @ ((V9 @ V13) @ V12))) @ ((cHOL.conj @ ((V10 @ V13) @ V5)) @ ((V9 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.less_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V12) @ ((V1 @ V13) @ V14))) @ (((cHOL.If @ ((V10 @ V5) @ V14)) @ ((V10 @ ((V2 @ V12) @ V14)) @ V13)) @ (((cHOL.If @ ((V10 @ V14) @ V5)) @ ((V10 @ V13) @ ((V2 @ V12) @ V14))) @ ((V10 @ V12) @ V5))))))))))))))))))))))))))))))))))))
(TFinite_Set.comp_fun_commute.comp_fun_commute_funpow,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.comp_fun_commute @ V0)) @ (cFinite_Set.comp_fun_commute @ (^[V2]: ((cNat.compow @ (V1 @ V2)) @ (V0 @ V2))))))))))
(TGroups.class.linordered_cancel_ab_semigroup_add_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cHOL.conj @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cOrderings.class.linorder @ V1) @ V2))))))))))
(TGroups.class.ordered_ab_semigroup_add_imp_le.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ V0) @ V1)))))))))
(TGroups.class.ordered_ab_semigroup_add_imp_le.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)))))))))
(TGroups.class.ordered_cancel_ab_semigroup_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ (((cGroups.class.ordered_ab_semigroup_add @ V0) @ V1) @ V2)))))))))
(TGroups.class.ordered_cancel_ab_semigroup_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ (cGroups.class.cancel_ab_semigroup_add @ V0)))))))))
(TGroups.class.ordered_cancel_comm_monoid_diff.axioms_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ V0) @ V3)))))))))))))
(TGroups.class.ordered_cancel_comm_monoid_diff.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V3) @ V4)))))))))))))
(TGroups.class.ordered_cancel_comm_monoid_diff.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ (((cGroups.class.comm_monoid_diff @ V0) @ V1) @ V2)))))))))))))
(TGroups.classrel_ab_group_add_cancel_comm_monoid_add,(cGroups.cancel_comm_monoid_add_class @ cTYPE))
(TGroups.comm_monoid_add_class.add.comm_monoid_axioms,((cGroups.comm_monoid @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.comm_monoid_add_class.comm_monoid_add_axioms,((cGroups.class.comm_monoid_add @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.comm_monoid_diff_class.add_diff_cancel_left',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V0)) @ V1))))))
(TGroups.comm_monoid_diff_class.add_diff_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V1))) @ ((cGroups.minus_class.minus @ V0) @ V2)))))))))
(TGroups.linordered_ab_group_add_class.equal_neg_zero,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_ab_group_add_class.neg_equal_zero,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_cancel_ab_semigroup_add_class_def,((c== @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((cPure.conjunction @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE))))
(TGroups.ordered_ab_group_add_abs_class.abs_of_nonneg,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ V0)))))
(TGroups.ordered_ab_group_add_abs_class.abs_of_nonpos,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ (cGroups.abs_class.abs @ V0)) @ (cGroups.uminus_class.uminus @ V0))))))
(TGroups.ordered_ab_group_add_class.diff_eq_diff_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.minus_class.minus @ V2) @ V3))) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V2) @ V3))))))))))))
(TGroups.ordered_ab_group_add_class.neg_less_iff_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TGroups.ordered_ab_semigroup_add_class.add_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V2) @ V0)) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.axioms,((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq))
(TGroups.ordered_cancel_comm_monoid_diff_class.axioms,((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq))
(TGroups.ordered_comm_monoid_add_class.add_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))))
(TGroups.ordered_comm_monoid_add_class.add_neg_nonpos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TGroups.ordered_comm_monoid_add_class.add_nonneg_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TGroups.ordered_comm_monoid_add_class.add_nonpos_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TGroups.ordered_comm_monoid_add_class.add_pos_nonneg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TLattices.boolean_algebra_class.compl_less_compl_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))
(TLattices.boolean_algebra_class.dual_boolean_algebra,((((((((cLattices.class.boolean_algebra @ (^[V0]: (^[V1]: ((cLattices.sup_class.sup @ V0) @ (cGroups.uminus_class.uminus @ V1))))) @ cGroups.uminus_class.uminus) @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot))
(TLattices.bounded_lattice_class.dual_bounded_lattice,((((((cLattices.class.bounded_lattice @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot))
(TLattices.distrib_lattice_class.dual_distrib_lattice,((((cLattices.class.distrib_lattice @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf))
(TLattices.semilattice_inf_class.inf.semigroup_axioms,(cGroups.semigroup @ cLattices.inf_class.inf))
(TLattices.semilattice_sup_class.sup.semigroup_axioms,(cGroups.semigroup @ cLattices.sup_class.sup))
(TLazy_Sequence.lazy_sequence.Abs_lazy_sequence_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cLazy_Sequence.Abs_lazy_sequence @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set))) @ V1))))) @ V1))))))
(TLazy_Sequence.lazy_sequence.Rep_lazy_sequence_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cLazy_Sequence.Rep_lazy_sequence @ V2))) @ V1)))) @ V1)))))))
(TList.linorder_class.sorted_list_of_set_sort_remdups,(call @ (^[V0]: ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ (cList.set @ V0))) @ ((cList.linorder_class.sort_key @ (^[V1]: V1)) @ (cList.remdups @ V0))))))
(TList.monoid_add_class.monoid_add_class.listsum_dict,((c== @ cList.monoid_add_class.listsum) @ ((cList.monoid_add.listsum @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))
(TNat_Transfer.transfer_int_nat_set_function_closures_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ (cNat_Transfer.is_nat @ V1))))))))
(TNat_Transfer.transfer_int_nat_set_function_closures_5,(call @ (^[V0]: (cNat_Transfer.nat_set @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0)))))
(TNat_Transfer.transfer_int_nat_set_function_closures_4,(call @ (^[V0]: (cNat_Transfer.nat_set @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ V1))))))))
(TNat_Transfer.transfer_int_nat_set_function_closures_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ (cNat_Transfer.nat_set @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TNat_Transfer.transfer_int_nat_set_function_closures_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ (cNat_Transfer.nat_set @ ((cLattices.sup_class.sup @ V0) @ V1)))))))))
(TNat_Transfer.transfer_int_nat_set_function_closures_1,(cNat_Transfer.nat_set @ cOrderings.bot_class.bot))
(TNat_Transfer.transfer_nat_int_set_function_closures_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1))))))))
(TNat_Transfer.transfer_nat_int_set_function_closures_5,(call @ (^[V0]: (cNat_Transfer.nat_set @ ((cSet.image @ cNat.semiring_1_class.of_nat) @ V0)))))
(TNat_Transfer.transfer_nat_int_set_function_closures_4,(call @ (^[V0]: (cNat_Transfer.nat_set @ (cSet.Collect @ (^[V1]: ((cHOL.conj @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V1)) @ (V0 @ V1))))))))
(TNat_Transfer.transfer_nat_int_set_function_closures_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ (cNat_Transfer.nat_set @ ((cLattices.inf_class.inf @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_set_function_closures_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.nat_set @ V0)) @ ((c==> @ (cNat_Transfer.nat_set @ V1)) @ (cNat_Transfer.nat_set @ ((cLattices.sup_class.sup @ V0) @ V1)))))))))
(TNat_Transfer.transfer_nat_int_set_function_closures_1,(cNat_Transfer.nat_set @ cOrderings.bot_class.bot))
(TNum.linordered_idom_class.not_zero_less_neg_numeral,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cNum.neg_numeral_class.neg_numeral @ V0))))))
(TNum.neg_numeral_class.neg_numeral_class.is_num_dict,((c== @ cNum.neg_numeral_class.is_num) @ (((cNum.neg_numeral.is_num @ cGroups.plus_class.plus) @ cGroups.uminus_class.uminus) @ cGroups.one_class.one)))
(TPartial_Function.partial_function_definitions.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((V0 @ V2) @ V2)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V2) @ V4)))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((V0 @ V3) @ (V1 @ V2))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((V0 @ V4) @ V3))))) @ ((V0 @ (V1 @ V2)) @ V3)))))))) @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)))))))))))
(TPower.linordered_idom_class.odd_0_le_power_imp_0_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)))))))
(TPower.linordered_idom_class.zero_less_power_abs_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cPower.power_class.power @ (cGroups.abs_class.abs @ V0)) @ V1))) @ ((cHOL.disj @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V1) @ cNat.zero_nat_inst.zero_nat))))))))
(TPower.linordered_ring_class.not_sum_squares_lt_zero,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cGroups.times_class.times @ V1) @ V1))) @ cGroups.zero_class.zero)))))))
(TPower.linordered_semidom_class.power2_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ ((cPower.power_class.power @ V1) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TPower.linordered_semidom_class.power_eq_imp_eq_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V2) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cNat.ord_nat_inst.less_nat @ cNat.zero_nat_inst.zero_nat) @ V1)) @ ((cHOL.eq @ V0) @ V2))))))))))))
(TPower.linordered_semidom_class.power_increasing_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2))))))))))
(TPower.linordered_semidom_class.power_le_imp_le_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))) @ ((cPower.power_class.power @ V2) @ (cNat.Suc @ V1)))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TPower.linordered_semidom_class.power_less_power_Suc,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1)))))))))
(TPower.ring_1_no_zero_divisors_class.power2_eq_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)))))))
(TQuickcheck_Exhaustive.arity_full_exhaustive_integer,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_natural,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_unknown,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_n_lists.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (V1 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V5)) @ (^[V7]: ((cList.list.Cons @ (V4 @ cProduct_Type.Unity)) @ (V6 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.check_all_n_lists_rel) @ V1))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V4 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V6]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V3 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V5]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.check_all_n_lists_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V7]: (^[V8]: (V3 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V5) @ V7)) @ (^[V9]: ((cList.list.Cons @ (V6 @ cProduct_Type.Unity)) @ (V8 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.check_all_subsets.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V1 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V2) @ V4))) @ cOption.option.Some) @ (V1 @ V4)))) @ V3)) @ ((cProduct_Type.Pair @ V1) @ ((cList.list.Cons @ V2) @ V3)))) @ V0)))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ V1))))))))
(TQuickcheck_Exhaustive.check_all_subsets_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ V1) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ V2))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ V2)))))))))))) @ V2))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ cList.list.Nil))) @ ((cHOL.eq @ V1) @ (V3 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5))))))))))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_fun'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((cQuickcheck_Exhaustive.exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V7]: (V4 @ (^[V8]: V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.exhaustive_class.exhaustive @ (^[V9]: (V4 @ (((cFun.fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_int'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_int'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_graph_def,((c== @ cQuickcheck_Exhaustive.exhaustive_integer'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_integer'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_integer'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V4) @ cCode_Numeral.one_integer_inst.one_integer))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V3) @ V4))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_graph_def,((c== @ cQuickcheck_Exhaustive.exhaustive_natural'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_natural'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_natural'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V3) @ V4))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_sumC_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_fun'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_sumC_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_int'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_graph_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_set_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V0 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_set_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ V2)))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_set_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.orelse @ (V2 @ V4)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V5)) @ (cProduct_Type.fst @ V4))) @ cOption.option.None) @ (V2 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V4))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ V3))) @ (cHOL.Not @ ((cHOL.eq @ V3) @ cCode_Numeral.zero_natural_inst.zero_natural))))))))))))))
(TQuickcheck_Exhaustive.num.full_exhaustive_num.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_num_inst.full_exhaustive_num @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cNum.num.One) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_num_inst.full_exhaustive_num @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cNum.num.Bit0 @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_num_inst.full_exhaustive_num @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cNum.num.Bit1 @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))) @ cList.list.Nil)) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.seq.full_exhaustive_seq.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cPredicate.seq.Empty) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cPredicate.seq.Insert @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cPredicate.seq.Join @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.sum.full_exhaustive_sum.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cSum_Type.Inl @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cSum_Type.Inr @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.term_syntax.term_emptyset_def,((cHOL.eq @ (cQuickcheck_Exhaustive.term_syntax.term_emptyset @ cTYPE)) @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))
(TQuickcheck_Exhaustive.three_valued.Rep_three_valued,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Exhaustive.Rep_three_valued @ V0)) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set)))))
(TQuickcheck_Exhaustive.three_valued.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.random_aux_three_valued @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.Value) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ V3)))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.No_value) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))))))) @ cList.list.Nil))))) @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.unknown_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cQuickcheck_Exhaustive.unknown.unknown_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V2) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((c==> @ ((cHOL.eq @ V3) @ V0)) @ V4))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V2) @ (cQuickcheck_Exhaustive.unknown.Known @ V5))) @ ((c==> @ ((cHOL.eq @ V3) @ (V1 @ V5))) @ V4))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.unknown.unknown_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((((cQuickcheck_Exhaustive.unknown.unknown_rec_set @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V2) @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((cHOL.eq @ V3) @ V0))) @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cQuickcheck_Exhaustive.unknown.Known @ V4))) @ ((cHOL.eq @ V3) @ (V1 @ V4))))))))))))))))
(TQuickcheck_Narrowing.arity_narrowing_narrowing_type,(cQuickcheck_Narrowing.narrowing_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_finite_1,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_finite_2,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_finite_3,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_finite_4,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_finite_5,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_property,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.term_of_cfun_inst.term_of_cfun,((c== @ cQuickcheck_Narrowing.term_of_cfun_inst.term_of_cfun) @ cQuickcheck_Narrowing.term_of_cfun_inst.term_of_cfun))
(TQuickcheck_Narrowing.term_of_ffun_inst.term_of_ffun,((c== @ cQuickcheck_Narrowing.term_of_ffun_inst.term_of_ffun) @ cQuickcheck_Narrowing.term_of_ffun_inst.term_of_ffun))
(TQuickcheck_Narrowing.type_definition_narrowing_cons,(((cTypedef.type_definition @ cQuickcheck_Narrowing.Rep_narrowing_cons) @ cQuickcheck_Narrowing.Abs_narrowing_cons) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set)))
(TQuickcheck_Narrowing.type_definition_narrowing_term,(((cTypedef.type_definition @ cQuickcheck_Narrowing.Rep_narrowing_term) @ cQuickcheck_Narrowing.Abs_narrowing_term) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1)))
(TQuickcheck_Narrowing.type_definition_narrowing_type,(((cTypedef.type_definition @ cQuickcheck_Narrowing.Rep_narrowing_type) @ cQuickcheck_Narrowing.Abs_narrowing_type) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1)))
(TQuickcheck_Narrowing.typerep_cfun_inst.typerep_cfun,((c== @ cQuickcheck_Narrowing.typerep_cfun_inst.typerep_cfun) @ cQuickcheck_Narrowing.typerep_cfun_inst.typerep_cfun))
(TQuickcheck_Narrowing.typerep_ffun_inst.typerep_ffun,((c== @ cQuickcheck_Narrowing.typerep_ffun_inst.typerep_ffun) @ cQuickcheck_Narrowing.typerep_ffun_inst.typerep_ffun))
(TQuickcheck_Random.term_syntax.valtermify_insert_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V0) @ V1)) @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSet.insert) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)) @ V1)))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_case_def,((c== @ cRecord.tuple_isomorphism.tuple_isomorphism_case) @ (^[V0]: (cRecord.tuple_isomorphism.tuple_isomorphism_rec @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2)))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_size_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRecord.tuple_isomorphism.tuple_isomorphism_size @ V0) @ V1) @ V2)) @ (cRecord.tuple_isomorphism.tuple_isomorphism_rec @ (^[V3]: (^[V4]: cNat.zero_nat_inst.zero_nat)))))))))))
(TRings.class.linordered_semiring_strict_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V5))))))))))) @ (((cRings.class.linordered_semiring_strict_axioms @ V1) @ V0) @ V2))))))))))
(TRings.linordered_idom.linorder_neqE_linordered_idom,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((cRings.class.linordered_idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V10) @ V11))) @ ((c==> @ ((c==> @ ((V5 @ V10) @ V11)) @ V12)) @ ((c==> @ ((c==> @ ((V5 @ V11) @ V10)) @ V12)) @ V12)))))))))))))))))))))))))))))))
(TRings.linordered_idom_class.mult_less_cancel_right1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V1))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.one_class.one)))))))))
(TRings.linordered_idom_class.mult_less_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.one_class.one))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)))))))))
(TRings.linordered_ring_strict.mult_less_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ ((V7 @ V8) @ V9)) @ ((V7 @ V10) @ V9))) @ ((cHOL.conj @ ((cHOL.implies @ ((V4 @ V3) @ V9)) @ ((V5 @ V8) @ V10))) @ ((cHOL.implies @ ((V4 @ V9) @ V3)) @ ((V5 @ V10) @ V8))))))))))))))))))))))))))))
(TRings.linordered_ring_strict_class.zero_le_mult_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)))))))))
(TRings.linordered_semiring_strict.zero_less_mult_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V1) @ ((V4 @ V5) @ V6))) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((V3 @ V1) @ V6)))))))))))))))))))
(TRings.linordered_semiring_strict_class.mult_neg_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.linordered_semiring_strict_class.mult_pos_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.linordered_semiring_strict_class.mult_pos_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.ring_1_no_zero_divisors_class.square_eq_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V0)) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.one_class.one)) @ ((cHOL.eq @ V0) @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)))))))
(TRings.ring_no_zero_divisors_class.mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ V2))))))))))
(TSemiring_Normalization.idom.normalizing_idom_axioms,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cRings.class.idom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))
(TSet_Interval.atLeastSucLessThan_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ (cNat.Suc @ V0)) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)))))))
(TSet_Interval.complete_lattice.Sup_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ V8) @ V9)) @ ((cHOL.eq @ (V1 @ ((((cSet_Interval.ord.greaterThanAtMost @ V3) @ V4) @ V8) @ V9))) @ V9))))))))))))))))))))))))
(TSet_Interval.linorder_class.Int_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V2) @ V3))) @ ((cSet_Interval.ord_class.greaterThanLessThan @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V3))))))))))))
(TSet_Interval.ord_class.ord_class.atLeastAtMost_dict,((c== @ cSet_Interval.ord_class.atLeastAtMost) @ (cSet_Interval.ord.atLeastAtMost @ cOrderings.ord_class.less_eq)))
(TSet_Interval.order_class.atLeastLessThan_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TSet_Interval.transfer_int_nat_set_function_closures,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cNat_Transfer.is_nat @ V0)) @ (cNat_Transfer.nat_set @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TSet_Interval.transfer_nat_int_set_function_closures,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cInt.ord_int_inst.less_eq_int @ cInt.zero_int_inst.zero_int) @ V0)) @ (cNat_Transfer.nat_set @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))))))))
(TTyperep.typerep_class.typerep_class.typerep_of_dict,((c== @ cTyperep.typerep_class.typerep_of) @ (cTyperep.typerep.typerep_of @ cTyperep.typerep_class.typerep)))
(TBig_Operators.comm_monoid_add.setsum_reindex_nonzero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ V5) @ V2)) @ ((c==> @ ((cSet.member @ V6) @ V2)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V3 @ V5)) @ (V3 @ V6))) @ ((cHOL.eq @ (V4 @ (V3 @ V5))) @ V1)))))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ V4) @ ((cSet.image @ V3) @ V2))) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ ((cFun.comp @ V4) @ V3)) @ V2))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cGroups.times_class.times @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V2))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.eq_fold,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1)) @ (((cFinite_Set.fold @ ((cFun.comp @ cGroups.times_class.times) @ V0)) @ cGroups.one_class.one) @ V1)))))))
(TBig_Operators.comm_monoid_mult_class.setprod.neutral,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ cGroups.one_class.one)))))))
(TBig_Operators.comm_monoid_mult_class.setprod.reindex,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cSet.image @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ ((cFun.comp @ V2) @ V0)) @ V1))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.related,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((V0 @ cGroups.one_class.one) @ cGroups.one_class.one)) @ ((c==> @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: (cHOL.All @ (^[V6]: (cHOL.All @ (^[V7]: ((cHOL.implies @ ((cHOL.conj @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V7))) @ ((V0 @ ((cGroups.times_class.times @ V4) @ V5)) @ ((cGroups.times_class.times @ V6) @ V7)))))))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V4]: ((V0 @ (V2 @ V4)) @ (V3 @ V4))))) @ ((V0 @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)))))))))))))))
(TBig_Operators.comm_monoid_set.mono_neutral_cong_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V2) @ V3)) @ (^[V6]: ((cHOL.eq @ (V4 @ V6)) @ V1)))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V3)) @ ((cHOL.eq @ (V5 @ V6)) @ (V4 @ V6)))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V5) @ V3)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2))))))))))))))))))))
(TBig_Operators.distrib_lattice_class.inf_Sup1_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0))) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cLattices.inf_class.inf @ V1) @ V3))) @ ((cSet.member @ V3) @ V0)))))))))))))))
(TBig_Operators.distrib_lattice_class.inf_Sup2_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V1))) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cLattices.inf_class.inf @ V3) @ V4))) @ ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ V4) @ V1))))))))))))))))))))
(TBig_Operators.distrib_lattice_class.sup_Inf1_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cLattices.sup_class.sup @ V1) @ V3))) @ ((cSet.member @ V3) @ V0)))))))))))))))
(TBig_Operators.distrib_lattice_class.sup_Inf2_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V1))) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cLattices.sup_class.sup @ V3) @ V4))) @ ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ V4) @ V1))))))))))))))))))))
(TBig_Operators.linorder_class.linorder_class.Max_dict,((c== @ cBig_Operators.linorder_class.Max) @ (cBig_Operators.linorder.Max @ cOrderings.ord_class.less_eq)))
(TBig_Operators.linorder_class.linorder_class.Min_dict,((c== @ cBig_Operators.linorder_class.Min) @ (cBig_Operators.linorder.Min @ cOrderings.ord_class.less_eq)))
(TBig_Operators.linorder_class.min_max.inf_sup_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_sup_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_inf_distrib_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_inf_distrib_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.antimono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V1)) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))) @ ((c==> @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3))))) @ V2)) @ V2)))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.boundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.eq_fold',(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ (cOption.the @ (((cFinite_Set.fold @ (^[V1]: (^[V2]: (cOption.option.Some @ (((cOption.option.option_case @ V1) @ (^[V3]: ((cLattices.inf_class.inf @ V1) @ V3))) @ V2))))) @ cOption.option.None) @ V0))))))
(TBig_Operators.semilattice_order_neutr_set.coboundedI,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((c==> @ ((cSet.member @ V5) @ V4)) @ ((V2 @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V4)) @ V5)))))))))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.antimono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V1))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.boundedE,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ V1)) @ ((c==> @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V3) @ V1))))) @ V2)) @ V2)))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.boundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ V1)))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.eq_fold',(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ (cOption.the @ (((cFinite_Set.fold @ (^[V1]: (^[V2]: (cOption.option.Some @ (((cOption.option.option_case @ V1) @ (^[V3]: ((cLattices.sup_class.sup @ V1) @ V3))) @ V2))))) @ cOption.option.None) @ V0))))))
(TCode_Evaluation.term_of_integer_inst.term_of_integer,((c== @ cCode_Evaluation.term_of_integer_inst.term_of_integer) @ cCode_Evaluation.term_of_integer_inst.term_of_integer))
(TCode_Evaluation.term_of_literal_inst.term_of_literal,((c== @ cCode_Evaluation.term_of_literal_inst.term_of_literal) @ cCode_Evaluation.term_of_literal_inst.term_of_literal))
(TCode_Evaluation.term_of_natural_inst.term_of_natural,((c== @ cCode_Evaluation.term_of_natural_inst.term_of_natural) @ cCode_Evaluation.term_of_natural_inst.term_of_natural))
(TCode_Evaluation.term_of_typerep_inst.term_of_typerep,((c== @ cCode_Evaluation.term_of_typerep_inst.term_of_typerep) @ cCode_Evaluation.term_of_typerep_inst.term_of_typerep))
(TComplete_Lattices.arity_complete_boolean_algebra_fun,(cComplete_Lattices.complete_boolean_algebra_class @ cTYPE))
(TComplete_Lattices.arity_complete_boolean_algebra_set,(cComplete_Lattices.complete_boolean_algebra_class @ cTYPE))
(TComplete_Lattices.arity_complete_distrib_lattice_fun,(cComplete_Lattices.complete_distrib_lattice_class @ cTYPE))
(TComplete_Lattices.class.complete_boolean_algebra_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c== @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.conj @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cLattices.class.boolean_algebra @ V8) @ V9) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7))))))))))))))))))))))))
(TComplete_Lattices.class.complete_distrib_lattice_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c== @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.conj @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ V0) @ V1) @ V2) @ V5))))))))))))))))))))
(TComplete_Lattices.complete_boolean_algebra_class_def,((c== @ (cComplete_Lattices.complete_boolean_algebra_class @ cTYPE)) @ ((cPure.conjunction @ (cComplete_Lattices.complete_distrib_lattice_class @ cTYPE)) @ (cLattices.boolean_algebra_class @ cTYPE))))
(TComplete_Lattices.complete_distrib_lattice_class_def,((c== @ (cComplete_Lattices.complete_distrib_lattice_class @ cTYPE)) @ ((cPure.conjunction @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ ((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cLattices.inf_class.inf) @ cLattices.sup_class.sup))))
(TComplete_Lattices.complete_lattice.INF_superset_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V8) @ V9)) @ ((c==> @ (call @ (^[V12]: ((c==> @ ((cSet.member @ V12) @ V8)) @ ((V3 @ (V10 @ V12)) @ (V11 @ V12)))))) @ ((V3 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V9) @ (^[V12]: (V10 @ V12)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V12]: (V11 @ V12))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_superset_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V8) @ V9)) @ ((V3 @ (V0 @ V9)) @ (V0 @ V8)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Inf_union_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ ((cLattices.sup_class.sup @ V8) @ V9))) @ ((V2 @ (V0 @ V8)) @ (V0 @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_inter_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((V3 @ (V1 @ ((cLattices.inf_class.inf @ V8) @ V9))) @ ((V2 @ (V1 @ V8)) @ (V1 @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.Sup_union_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V1 @ ((cLattices.sup_class.sup @ V8) @ V9))) @ ((V5 @ (V1 @ V8)) @ (V1 @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.less_eq_Inf_inter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((V3 @ ((V5 @ (V0 @ V8)) @ (V0 @ V9))) @ (V0 @ ((cLattices.inf_class.inf @ V8) @ V9)))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: ((V2 @ V3) @ V4)))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: ((V2 @ V4) @ V3)))))))))))))
(TComplete_Lattices.complete_lattice_class.Inf_less_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1))))))))
(TComplete_Lattices.complete_lattice_class.SUP_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: ((V2 @ V3) @ V4)))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: ((V2 @ V4) @ V3)))))))))))))
(TComplete_Lattices.complete_lattice_class.less_eq_Sup,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0)))))))))
(TComplete_Lattices.complete_linorder_class.INF_le_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ V1)) @ V2)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cSet.Bex @ V0) @ (^[V4]: ((cOrderings.ord_class.less @ (V1 @ V4)) @ V3))))))))))))))
(TComplete_Lattices.complete_linorder_class.Inf_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cSet.Bex @ V0) @ (^[V3]: ((cOrderings.ord_class.less @ V3) @ V2))))))))))))
(TComplete_Lattices.complete_linorder_class.le_SUP_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ V2))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V3) @ V0)) @ ((cSet.Bex @ V1) @ (^[V4]: ((cOrderings.ord_class.less @ V3) @ (V2 @ V4)))))))))))))))
(TComplete_Lattices.complete_linorder_class.le_Sup_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ V0)) @ ((cSet.Bex @ V1) @ (^[V3]: ((cOrderings.ord_class.less @ V2) @ V3))))))))))))
(TDivides.semiring_numeral_div_class.divmod_step_simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ V1)) @ ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod_step @ V0) @ ((cProduct_Type.Pair @ V2) @ V1))) @ ((cProduct_Type.Pair @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V2)) @ cGroups.one_class.one)) @ ((cGroups.minus_class.minus @ V1) @ (cNum.numeral_class.numeral @ V0))))))))))))
(TDivides.semiring_numeral_div_class.divmod_step_simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ (cNum.numeral_class.numeral @ V1))) @ ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod_step @ V1) @ ((cProduct_Type.Pair @ V2) @ V0))) @ ((cProduct_Type.Pair @ ((cGroups.times_class.times @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V2)) @ V0))))))))))
(TFields.class.division_ring_inverse_zero_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (V0 @ V1)) @ V1)) @ ((cFields.class.division_ring_inverse_zero_axioms @ V0) @ V1)))))))
(TFields.division_ring_class.division_ring_inverse_add,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ (cFields.inverse_class.inverse @ V0)) @ ((cGroups.plus_class.plus @ V0) @ V1))) @ (cFields.inverse_class.inverse @ V1))))))))))
(TFields.division_ring_class.nonzero_inverse_eq_divide,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0))))))
(TFields.division_ring_class.nonzero_inverse_eq_imp_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TFields.division_ring_inverse_zero.inverse_inverse_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ (V0 @ V8))) @ V8)))))))))))))))))))))
(TFields.division_ring_inverse_zero_class.inverse_zero,((cHOL.eq @ (cFields.inverse_class.inverse @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))
(TFields.field_inverse_zero_class.inverse_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cFields.inverse_class.inverse @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cGroups.times_class.times @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))))))))
(TFields.linordered_field.divide_strict_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V13)) @ ((c==> @ ((V10 @ V14) @ V5)) @ ((V10 @ ((V1 @ V13) @ V14)) @ ((V1 @ V12) @ V14))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_class.linordered_field_no_lb,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0))))))
(TFields.linordered_field_class.linordered_field_no_ub,(cHOL.All @ (^[V0]: (cHOL.Ex @ (^[V1]: ((cOrderings.ord_class.less @ V0) @ V1))))))
(TFields.linordered_field_inverse_zero.divide_le_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V12) @ V13)) @ V5)) @ ((cHOL.disj @ ((cHOL.conj @ ((V9 @ V5) @ V12)) @ ((V9 @ V13) @ V5))) @ ((cHOL.conj @ ((V9 @ V12) @ V5)) @ ((V9 @ V5) @ V13))))))))))))))))))))))))))))))))))
(TGroups.comm_monoid_diff_class.add_diff_cancel_right',(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V1)) @ V0))))))
(TGroups.linordered_ab_group_add_class.double_zero_sym,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V0))) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_ab_group_add_class.neg_less_nonneg,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TGroups.ordered_ab_group_add_abs_class.abs_idempotent,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cGroups.abs_class.abs @ V0))) @ (cGroups.abs_class.abs @ V0)))))
(TGroups.ordered_ab_semigroup_add_class.add_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TGroups.ordered_cancel_comm_monoid_diff.le_diff_conv2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V3 @ V7) @ ((V2 @ V6) @ V5))) @ ((V3 @ ((V0 @ V7) @ V5)) @ V6)))))))))))))))))))))
(TGroups.ordered_comm_monoid_add.add_strict_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V3 @ V1) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((V3 @ V5) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TGroups.ordered_comm_monoid_add_class.add_increasing2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.plus_class.plus @ V2) @ V0)))))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_8,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_7,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_6,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TGroups.ordered_comm_monoid_add_class.add_sign_intros_1,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TLattices.linorder_class.max.semilattice_order_axioms,(((cLattices.semilattice_order @ cOrderings.ord_class.max) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TLattices.linorder_class.min.semilattice_order_axioms,(((cLattices.semilattice_order @ cOrderings.ord_class.min) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TLazy_Sequence.lazy_sequence.Abs_lazy_sequence_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set))) @ (V0 @ (cLazy_Sequence.Abs_lazy_sequence @ V2)))))) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence.Abs_lazy_sequence_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cLazy_Sequence.Abs_lazy_sequence @ V0)) @ (cLazy_Sequence.Abs_lazy_sequence @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TLazy_Sequence.lazy_sequence.Rep_lazy_sequence_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cLazy_Sequence.Rep_lazy_sequence @ V2))))) @ (V1 @ V0))))))))
(TLazy_Sequence.lazy_sequence.Rep_lazy_sequence_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cLazy_Sequence.Rep_lazy_sequence @ V0)) @ (cLazy_Sequence.Rep_lazy_sequence @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TLazy_Sequence.lazy_sequence.arity_size_lazy_sequence,(cNat.size_class @ cTYPE))
(TLazy_Sequence.lazy_sequence_of_list_of_lazy_sequence,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ (cLazy_Sequence.list_of_lazy_sequence @ V0))) @ V0))))
(TList.linorder_class.sorted_list_of_set.insert_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cList.linorder_class.sorted_list_of_set @ ((cSet.insert @ V1) @ V0))) @ (((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V1) @ (cList.linorder_class.sorted_list_of_set @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot)))))))))))
(TNum.linordered_idom_class.not_numeral_le_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less_eq @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TNum.neg_numeral_class.neg_numeral_class.dbl_dec_dict,((c== @ cNum.neg_numeral_class.dbl_dec) @ (((cNum.neg_numeral.dbl_dec @ cGroups.minus_class.minus) @ cGroups.plus_class.plus) @ cGroups.one_class.one)))
(TNum.neg_numeral_class.neg_numeral_class.dbl_inc_dict,((c== @ cNum.neg_numeral_class.dbl_inc) @ ((cNum.neg_numeral.dbl_inc @ cGroups.plus_class.plus) @ cGroups.one_class.one)))
(TOrderings.dense_linorder_class.dense_linorder_axioms,((cOrderings.class.dense_linorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TPower.linordered_ring_strict.sum_squares_eq_zero_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V6 @ ((V7 @ V8) @ V8)) @ ((V7 @ V9) @ V9))) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V8) @ V3)) @ ((cHOL.eq @ V9) @ V3)))))))))))))))))))))))))
(TPower.linordered_ring_strict.sum_squares_gt_zero_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ V3) @ ((V6 @ ((V7 @ V8) @ V8)) @ ((V7 @ V9) @ V9)))) @ ((cHOL.disj @ (cHOL.Not @ ((cHOL.eq @ V8) @ V3))) @ (cHOL.Not @ ((cHOL.eq @ V9) @ V3))))))))))))))))))))))))))
(TPower.linordered_ring_strict.sum_squares_le_zero_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V4 @ ((V6 @ ((V7 @ V8) @ V8)) @ ((V7 @ V9) @ V9))) @ V3)) @ ((cHOL.conj @ ((cHOL.eq @ V8) @ V3)) @ ((cHOL.eq @ V9) @ V3)))))))))))))))))))))))))
(TPower.linordered_semidom.power_strict_increasing_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((cRings.class.linordered_semidom @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((V5 @ V3) @ V6)) @ ((cHOL.eq @ ((V5 @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V7)) @ ((((cPower.power.power @ V3) @ V2) @ V6) @ V8))) @ ((cNat.ord_nat_inst.less_nat @ V7) @ V8)))))))))))))))))))))))
(TQuickcheck_Exhaustive.arity_full_exhaustive_finite_1,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_finite_2,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_finite_3,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_finite_4,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.arity_full_exhaustive_finite_5,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_n_lists_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V4 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V6]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.check_all_n_lists_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (V1 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V5)) @ (^[V7]: ((cList.list.Cons @ (V4 @ cProduct_Type.Unity)) @ (V6 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (V1 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V5)) @ (^[V7]: ((cList.list.Cons @ (V4 @ cProduct_Type.Unity)) @ (V6 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ ((cProduct_Type.Pair @ V1) @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V1 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: (V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: (V1 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V3) @ V5)) @ (^[V7]: ((cList.list.Cons @ (V4 @ cProduct_Type.Unity)) @ (V6 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil)) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_graph.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V4))) @ cOption.option.Some) @ (V0 @ V4)))) @ V2)) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V4))) @ cOption.option.Some) @ (V0 @ V4)))) @ V2)))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V4))) @ cOption.option.Some) @ (V0 @ V4)))) @ V2)))))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_graph.intros_1,(call @ (^[V0]: ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil)) @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))
(TQuickcheck_Exhaustive.exhaustive_integer'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_integer'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.exhaustive_integer'_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_natural'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.exhaustive_natural'_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_graph_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_fun'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (V4 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))) @ ((cHOL.induct_implies @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((V0 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V3 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (V2 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V5) @ V6) @ V7)))) @ V4))) @ V4))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)) @ V4)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V3)))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_graph_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_int'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6)))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((cHOL.induct_implies @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V5))))) @ cOption.option.None)) @ V2))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cInt.plus_int_inst.plus_int @ V4) @ cInt.one_int_inst.one_int))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ ((cHOL.conj @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V3) @ V4))) @ ((cHOL.eq @ (V2 @ ((cProduct_Type.Pair @ V4) @ (^[V5]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V4))))) @ cOption.option.None))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V6) @ V7)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V5) @ V6) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V7) @ cCode_Numeral.one_integer_inst.one_integer))) @ cOption.option.Some) @ (V5 @ ((cProduct_Type.Pair @ V7) @ (^[V8]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V7)))))))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V1) @ V2)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V0) @ V1) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V2) @ cCode_Numeral.one_integer_inst.one_integer))) @ cOption.option.Some) @ (V0 @ ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V2))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ V1)))))))) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ ((cProduct_Type.Pair @ V7) @ (^[V8]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V7))))) @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V5) @ V6) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V7) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ V4))))))))))) @ V4)))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V2))))) @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V0) @ V1) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_set_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_rel.intros,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_set_rel @ ((cProduct_Type.Pair @ (^[V2]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V2)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V3]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V3)) @ (cProduct_Type.fst @ V2))) @ cOption.option.None) @ (V1 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V3) @ V2))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V0))))))))
(TQuickcheck_Exhaustive.term_syntax.termify_insert_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.term_syntax.termify_insert @ cTYPE) @ V0) @ V1)) @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ V0)) @ V1)))))))
(TQuickcheck_Exhaustive.term_syntax.valtermify_Inl_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.term_syntax.valtermify_Inl @ V0)) @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inl) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)))))
(TQuickcheck_Exhaustive.term_syntax.valtermify_Inr_def,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.term_syntax.valtermify_Inr @ V0)) @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cSum_Type.Inr) @ (^[V1]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)))))
(TQuickcheck_Exhaustive.three_valued.Unknown_value_def,((c== @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (cQuickcheck_Exhaustive.Abs_three_valued @ (cDatatype.In0 @ cHOL.undefined))))
(TQuickcheck_Exhaustive.unknown.unknown_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Exhaustive.unknown.unknown_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((((cQuickcheck_Exhaustive.unknown.unknown_rec_set @ V0) @ V1) @ (cQuickcheck_Exhaustive.unknown.Known @ V2)) @ (V1 @ V2)))))))))
(TQuickcheck_Exhaustive.unknown.unknown_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: ((((cQuickcheck_Exhaustive.unknown.unknown_rec_set @ V0) @ V1) @ cQuickcheck_Exhaustive.unknown.Unknown) @ V0))))))
(TQuickcheck_Exhaustive.unknown.unknown_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Exhaustive.unknown.unknown_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.Leaf @ V2)))))) @ (V1 @ V0)))))))))
(TQuickcheck_Exhaustive.unknown.unknown_rep_set.intros_2,(call @ (^[V0]: (cQuickcheck_Exhaustive.unknown.unknown_rep_set @ (cDatatype.In1 @ (cDatatype.Leaf @ V0))))))
(TQuickcheck_Exhaustive.unknown.unknown_rep_set.intros_1,(cQuickcheck_Exhaustive.unknown.unknown_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TQuickcheck_Narrowing.cfun.full_exhaustive_cfun.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cQuickcheck_Narrowing.cfun.Constant @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.ffun.full_exhaustive_ffun.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cQuickcheck_Narrowing.ffun.Constant @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: (V0 @ ((cProduct_Type.Pair @ (((cQuickcheck_Narrowing.ffun.Update @ V2) @ V4) @ V6)) @ (^[V8]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))) @ (V7 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.narrowing_cons.random_aux.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_narrowing_cons @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_term.random_aux.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_narrowing_term_list @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_term @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_term_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_term.random_aux.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_narrowing_term @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_integer_inst.random_integer @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_term_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_term.Narrowing_variable) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_type.random_aux.simps_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_narrowing_type_list @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ ((cQuickcheck_Random.beyond @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_type @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_type_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_type.random_aux.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_narrowing_type_list_list @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_type_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_type_list_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_type.random_aux.simps_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.random_aux_narrowing_type @ V0) @ V1) @ V2)) @ ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.scomp @ ((cQuickcheck_Narrowing.random_aux_narrowing_type_list_list @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V1)) @ (^[V3]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products) @ (^[V4]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V3)))))) @ cList.list.Nil))) @ V2)))))))))
(TQuickcheck_Narrowing.natural.narrowing_natural.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_natural_inst.narrowing_natural) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cCode_Numeral.zero_natural_inst.zero_natural)) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cCode_Numeral.Suc)) @ cQuickcheck_Narrowing.narrowing_natural_inst.narrowing_natural))))
(TQuickcheck_Narrowing.property.property_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.property.Universal @ V8) @ V6) @ V9))) @ ((c==> @ ((cHOL.eq @ V4) @ ((((V0 @ V8) @ V6) @ V9) @ V7))) @ ((c==> @ (cHOL.All @ (^[V10]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (V6 @ V10)) @ (V7 @ V10))))) @ V5)))))))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.property.Existential @ V8) @ V6) @ V9))) @ ((c==> @ ((cHOL.eq @ V4) @ ((((V1 @ V8) @ V6) @ V9) @ V7))) @ ((c==> @ (cHOL.All @ (^[V10]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (V6 @ V10)) @ (V7 @ V10))))) @ V5)))))))))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V3) @ (cQuickcheck_Narrowing.property.Property @ V6))) @ ((c==> @ ((cHOL.eq @ V4) @ (V2 @ V6))) @ V5))))) @ V5)))))))))))))))))
(TQuickcheck_Narrowing.property.property_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.property.Universal @ V7) @ V5) @ V8))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((((V0 @ V7) @ V5) @ V8) @ V6))) @ (cHOL.All @ (^[V9]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (V5 @ V9)) @ (V6 @ V9))))))))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (((cQuickcheck_Narrowing.property.Existential @ V7) @ V5) @ V8))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ ((((V1 @ V7) @ V5) @ V8) @ V6))) @ (cHOL.All @ (^[V9]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (V5 @ V9)) @ (V6 @ V9))))))))))))))) @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Narrowing.property.Property @ V5))) @ ((cHOL.eq @ V4) @ (V2 @ V5)))))))))))))))))))
(TQuickcheck_Narrowing.unknown.narrowing_unknown.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Exhaustive.unknown.Unknown)) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Exhaustive.unknown.Known)) @ cQuickcheck_Narrowing.narrowing_class.narrowing))))
(TQuickcheck_Random.random_integer_inst.random_integer,((c== @ cQuickcheck_Random.random_integer_inst.random_integer) @ cQuickcheck_Random.random_integer_inst.random_integer))
(TQuickcheck_Random.random_literal_inst.random_literal,((c== @ cQuickcheck_Random.random_literal_inst.random_literal) @ cQuickcheck_Random.random_literal_inst.random_literal))
(TQuickcheck_Random.random_natural_inst.random_natural,((c== @ cQuickcheck_Random.random_natural_inst.random_natural) @ cQuickcheck_Random.random_natural_inst.random_natural))
(TQuickcheck_Random.random_typerep_inst.random_typerep,((c== @ cQuickcheck_Random.random_typerep_inst.random_typerep) @ cQuickcheck_Random.random_typerep_inst.random_typerep))
(TRecord.tuple_isomorphism.Abs_tuple_isomorphism_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cRecord.Abs_tuple_isomorphism @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set))) @ V1))))) @ V1))))))
(TRecord.tuple_isomorphism.Rep_tuple_isomorphism_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cRecord.Rep_tuple_isomorphism @ V2))) @ V1)))) @ V1)))))))
(TRings.linordered_ring_strict.mult_le_cancel_left_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V5 @ V8) @ V3)) @ ((cHOL.eq @ ((V4 @ ((V7 @ V8) @ V9)) @ ((V7 @ V8) @ V10))) @ ((V4 @ V10) @ V9)))))))))))))))))))))))))))
(TRings.linordered_ring_strict.mult_le_cancel_left_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V5 @ V3) @ V8)) @ ((cHOL.eq @ ((V4 @ ((V7 @ V8) @ V9)) @ ((V7 @ V8) @ V10))) @ ((V4 @ V9) @ V10)))))))))))))))))))))))))))
(TRings.linordered_semiring_strict.mult_left_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ ((V4 @ V5) @ V6)) @ ((V4 @ V5) @ V7))) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((V2 @ V6) @ V7)))))))))))))))))))))
(TRings.linordered_semiring_strict.zero_less_mult_pos2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V1) @ ((V4 @ V5) @ V6))) @ ((c==> @ ((V3 @ V1) @ V6)) @ ((V3 @ V1) @ V5)))))))))))))))))))
(TRings.linordered_semiring_strict_class.mult_pos_neg2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V1) @ V0)) @ cGroups.zero_class.zero))))))))
(TRings.no_zero_divisors_class.no_zero_divisors_axioms,((cRings.class.no_zero_divisors @ cGroups.times_class.times) @ cGroups.zero_class.zero))
(TRings.ordered_ring_abs_class.ordered_ring_abs_axioms,((((((((cRings.class.ordered_ring_abs @ cGroups.abs_class.abs) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.times_class.times))
(TRings.ordered_semiring_class.ordered_semiring_axioms,(((((cRings.class.ordered_semiring @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.times_class.times))
(TSemiring_Normalization.field.normalizing_field_rules_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (V0 @ V8)) @ ((V1 @ V3) @ V8))))))))))))))))))))))
(TSemiring_Normalization.field.normalizing_field_rules_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ V8) @ V9)) @ ((V2 @ V8) @ (V0 @ V9)))))))))))))))))))))))))
(TSet_Interval.complete_lattice.Sup_greaterThanAtLeast,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V4 @ V8) @ V7)) @ ((cHOL.eq @ (V1 @ ((cSet_Interval.ord.greaterThan @ V4) @ V8))) @ V7))))))))))))))))))))))
(TSet_Interval.order_class.atLeastAtMost_singleton_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot))) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ V1)) @ ((cHOL.eq @ V1) @ V2))))))))))
(TSet_Interval.order_class.greaterThanAtMost_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TBig_Operators.comm_monoid_add_class.setsum.eq_general,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.Ball @ V0) @ (^[V5]: (cHOL.Ex1 @ (^[V6]: ((cHOL.conj @ ((cSet.member @ V6) @ V1)) @ ((cHOL.eq @ (V2 @ V6)) @ V5))))))) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V5]: ((cHOL.conj @ ((cSet.member @ (V2 @ V5)) @ V0)) @ ((cHOL.eq @ (V3 @ (V2 @ V5))) @ (V4 @ V5)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V4) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V0)))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_UNION_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ V2)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((c==> @ ((cSet.member @ V3) @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((c==> @ ((cSet.member @ V4) @ V2)) @ ((c==> @ ((cSet.member @ V4) @ V3)) @ ((cHOL.eq @ (V1 @ V4)) @ cGroups.zero_class.zero))))))))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V2]: ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ V2))) @ V0))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_reindex_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ cFun.id) @ ((cSet.image @ V0) @ V1)))))))))
(TBig_Operators.comm_monoid_mult.setprod_Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: (cFinite_Set.finite @ V4)))) @ ((c==> @ ((cSet.Ball @ V2) @ (^[V4]: ((cSet.Ball @ V2) @ (^[V5]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V4) @ V5)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V3) @ (cComplete_Lattices.Sup_class.Sup @ V2))) @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ (((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V3)) @ V2))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.If_cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V4]: (((cHOL.If @ (V1 @ V4)) @ (V2 @ V4)) @ (V3 @ V4)))) @ V0)) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.inf_class.inf @ V0) @ (cSet.Collect @ (^[V4]: (V1 @ V4)))))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ ((cLattices.inf_class.inf @ V0) @ (cGroups.uminus_class.uminus @ (cSet.Collect @ (^[V4]: (V1 @ V4))))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.infinite,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ (cFinite_Set.finite @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ V0)) @ cGroups.one_class.one)))))))
(TBig_Operators.comm_monoid_set.mono_neutral_cong_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cBig_Operators.comm_monoid_set @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V2)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V3) @ V2)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V2) @ V3)) @ (^[V6]: ((cHOL.eq @ (V4 @ V6)) @ V1)))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V3)) @ ((cHOL.eq @ (V4 @ V6)) @ (V5 @ V6)))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V4) @ V2)) @ ((((cBig_Operators.comm_monoid_set.F @ V0) @ V1) @ V5) @ V3))))))))))))))))))))
(TBig_Operators.linorder_class.min_max.dual_semilattice,(((cLattices.class.semilattice_inf @ cOrderings.ord_class.max) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TBig_Operators.linorder_class.min_max.inf_Sup1_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ V1) @ (cBig_Operators.linorder_class.Max @ V0))) @ (cBig_Operators.linorder_class.Max @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cOrderings.ord_class.min @ V1) @ V3))) @ ((cSet.member @ V3) @ V0)))))))))))))))
(TBig_Operators.linorder_class.min_max.inf_Sup2_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.min @ (cBig_Operators.linorder_class.Max @ V0)) @ (cBig_Operators.linorder_class.Max @ V1))) @ (cBig_Operators.linorder_class.Max @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cOrderings.ord_class.min @ V3) @ V4))) @ ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ V4) @ V1))))))))))))))))))))
(TBig_Operators.linorder_class.min_max.inf_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ V1) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_sup_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ ((cOrderings.ord_class.min @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.inf_sup_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V2)) @ ((cOrderings.ord_class.min @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_Inf1_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ (cBig_Operators.linorder_class.Min @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cOrderings.ord_class.max @ V1) @ V3))) @ ((cSet.member @ V3) @ V0)))))))))))))))
(TBig_Operators.linorder_class.min_max.sup_Inf2_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.max @ (cBig_Operators.linorder_class.Min @ V0)) @ (cBig_Operators.linorder_class.Min @ V1))) @ (cBig_Operators.linorder_class.Min @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cOrderings.ord_class.max @ V3) @ V4))) @ ((cHOL.conj @ ((cSet.member @ V3) @ V0)) @ ((cSet.member @ V4) @ V1))))))))))))))))))))
(TBig_Operators.linorder_class.min_max.sup_inf_distrib1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V1)) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_inf_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ ((cOrderings.ord_class.max @ V0) @ V2)) @ ((cOrderings.ord_class.max @ V1) @ V2))))))))))
(TBig_Operators.linorder_class.min_max.sup_left_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.max @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ V1) @ ((cOrderings.ord_class.max @ V0) @ V2))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.singleton,(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0))))
(TBig_Operators.semilattice_order_neutr_set.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cBig_Operators.semilattice_order_neutr_set @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cFinite_Set.finite @ V4)) @ ((cHOL.eq @ ((V2 @ V5) @ (((cBig_Operators.semilattice_neutr_set.F @ V0) @ V1) @ V4))) @ ((cSet.Ball @ V4) @ (^[V6]: ((V2 @ V5) @ V6)))))))))))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.singleton,(call @ (^[V0]: ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cSet.insert @ V0) @ cOrderings.bot_class.bot))) @ V0))))
(TComplete_Lattices.arity_complete_boolean_algebra_bool,(cComplete_Lattices.complete_boolean_algebra_class @ cTYPE))
(TComplete_Lattices.class.complete_lattice_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ V5) @ V6)) @ ((V0 @ (V1 @ V6)) @ V5))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ V5)) @ ((V0 @ V6) @ V7))))) @ ((V0 @ V6) @ (V1 @ V5)))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cSet.member @ V5) @ V6)) @ ((V0 @ V5) @ (V2 @ V6)))))))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ V5)) @ ((V0 @ V7) @ V6))))) @ ((V0 @ (V2 @ V5)) @ V6))))))) @ ((c==> @ ((cHOL.eq @ (V1 @ cOrderings.bot_class.bot)) @ V3)) @ ((c==> @ ((cHOL.eq @ (V2 @ cOrderings.bot_class.bot)) @ V4)) @ (((((cComplete_Lattices.class.complete_lattice_axioms @ V1) @ V2) @ V0) @ V4) @ V3))))))))))))))))))
(TComplete_Lattices.complete_boolean_algebra.uminus_INF,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V9 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V10) @ (^[V12]: (V11 @ V12))))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V10) @ (^[V12]: (V9 @ (V11 @ V12)))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_boolean_algebra.uminus_Inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V9 @ (V0 @ V10))) @ (V1 @ ((cSet.image @ V9) @ V10)))))))))))))))))))))))))))
(TComplete_Lattices.complete_boolean_algebra.uminus_SUP,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V9 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V10) @ (^[V12]: (V11 @ V12))))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V10) @ (^[V12]: (V9 @ (V11 @ V12)))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_boolean_algebra.uminus_Sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((cHOL.eq @ (V9 @ (V1 @ V10))) @ (V0 @ ((cSet.image @ V9) @ V10)))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_constant,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: V1))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.top_class.top) @ V1)))))))
(TComplete_Lattices.complete_lattice_class.INF_greatest,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ (V2 @ V3)))))) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_top_conv_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.top_class.top) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.top_class.top)))))))))
(TComplete_Lattices.complete_lattice_class.INF_top_conv_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2)))) @ cOrderings.top_class.top)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.top_class.top)))))))))
(TComplete_Lattices.complete_lattice_class.Inf_greatest,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))) @ ((cOrderings.ord_class.less_eq @ V1) @ (cComplete_Lattices.Inf_class.Inf @ V0))))))))
(TComplete_Lattices.complete_lattice_class.Inf_top_conv_2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.top_class.top) @ (cComplete_Lattices.Inf_class.Inf @ V0))) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.top_class.top)))))))
(TComplete_Lattices.complete_lattice_class.Inf_top_conv_1,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ cOrderings.top_class.top)) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.top_class.top)))))))
(TComplete_Lattices.complete_lattice_class.SUP_bot_conv_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.bot_class.bot)))))))))
(TComplete_Lattices.complete_lattice_class.SUP_bot_conv_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2)))) @ cOrderings.bot_class.bot)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ (V1 @ V2)) @ cOrderings.bot_class.bot)))))))))
(TComplete_Lattices.complete_lattice_class.SUP_constant,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: V1))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ cOrderings.bot_class.bot) @ V1)))))))
(TComplete_Lattices.complete_lattice_class.Sup_bot_conv_2,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TComplete_Lattices.complete_lattice_class.Sup_bot_conv_1,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ cOrderings.bot_class.bot)) @ ((cSet.Ball @ V0) @ (^[V1]: ((cHOL.eq @ V1) @ cOrderings.bot_class.bot)))))))
(TComplete_Partial_Order.classrel_complete_lattice_ccpo,(cComplete_Partial_Order.ccpo_class @ cTYPE))
(TDivides.semiring_numeral_div_class.divmod_divmod_step,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ V1)) @ (((cHOL.If @ ((cNum.ord_num_inst.less_num @ V0) @ V1)) @ ((cProduct_Type.Pair @ cGroups.zero_class.zero) @ (cNum.numeral_class.numeral @ V0))) @ ((cDivides.semiring_numeral_div_class.divmod_step @ V1) @ ((cDivides.semiring_numeral_div_class.divmod @ V0) @ (cNum.num.Bit0 @ V1))))))))))
(TFields.classrel_division_ring_ring_1_no_zero_divisors,(cRings.ring_1_no_zero_divisors_class @ cTYPE))
(TFields.division_ring_class.division_ring_inverse_diff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ (cFields.inverse_class.inverse @ V0)) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ (cFields.inverse_class.inverse @ V1))))))))))
(TFields.division_ring_class.nonzero_inverse_inverse_eq,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cFields.inverse_class.inverse @ (cFields.inverse_class.inverse @ V0))) @ V0)))))
(TFields.division_ring_class.nonzero_minus_divide_right,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cFields.inverse_class.divide @ V1) @ V0))) @ ((cFields.inverse_class.divide @ V1) @ (cGroups.uminus_class.uminus @ V0)))))))))
(TFields.field_inverse_zero_class.divide_divide_eq_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cFields.inverse_class.divide @ V0) @ V1)) @ V2)) @ ((cFields.inverse_class.divide @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TFields.field_inverse_zero_class.times_divide_times_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cFields.inverse_class.divide @ V2) @ V3))) @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3))))))))))))
(TFields.linordered_field.inverse_negative_imp_negative,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ (V0 @ V12)) @ V5)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V12) @ V5))) @ ((V10 @ V12) @ V5)))))))))))))))))))))))))))))))
(TFields.linordered_field.inverse_positive_imp_positive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ (V0 @ V12))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V12) @ V5))) @ ((V10 @ V5) @ V12)))))))))))))))))))))))))))))))
(TFields.linordered_field.negative_imp_inverse_negative,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((V10 @ (V0 @ V12)) @ V5))))))))))))))))))))))))))))))
(TFields.linordered_field.positive_imp_inverse_positive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((V10 @ V5) @ (V0 @ V12)))))))))))))))))))))))))))))))
(TFields.linordered_field_class.divide_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V2) @ V1)) @ ((cFields.inverse_class.divide @ V2) @ V0))))))))))))
(TFields.linordered_field_class.linordered_field_axioms,((((((((((((cFields.class.linordered_field @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.abs_class.abs) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.sgn_class.sgn))
(TFields.linordered_field_inverse_zero.divide_le_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V12) @ V13)) @ ((V1 @ V14) @ V13))) @ ((cHOL.conj @ ((cHOL.implies @ ((V10 @ V5) @ V13)) @ ((V9 @ V12) @ V14))) @ ((cHOL.implies @ ((V10 @ V13) @ V5)) @ ((V9 @ V14) @ V12))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_less_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V12) @ V13)) @ V3)) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V13)) @ ((V10 @ V12) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V13) @ V5)) @ ((V10 @ V13) @ V12))) @ ((cHOL.eq @ V13) @ V5))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.inverse_le_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ (V0 @ V12)) @ V3)) @ ((cHOL.disj @ ((V9 @ V12) @ V5)) @ ((V9 @ V3) @ V12)))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.inverse_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ (V0 @ V12)) @ (V0 @ V13))) @ ((cHOL.conj @ ((cHOL.implies @ ((V10 @ V5) @ ((V2 @ V12) @ V13))) @ ((V10 @ V13) @ V12))) @ ((cHOL.implies @ ((V9 @ ((V2 @ V12) @ V13)) @ V5)) @ ((V10 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.less_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V3) @ ((V1 @ V12) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V13)) @ ((V10 @ V13) @ V12))) @ ((cHOL.conj @ ((V10 @ V13) @ V5)) @ ((V10 @ V12) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.abs_divide,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cFields.inverse_class.divide @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))))))))
(TGroups.ab_semigroup_add_class.ab_semigroup_add_axioms,(cGroups.class.ab_semigroup_add @ cGroups.plus_class.plus))
(TGroups.class.linordered_cancel_ab_semigroup_add.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((cOrderings.class.linorder @ V1) @ V2)) @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2))))))))))
(TGroups.comm_monoid_diff_class.comm_monoid_diff_axioms,(((cGroups.class.comm_monoid_diff @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus))
(TGroups.comm_monoid_mult_class.comm_monoid_mult_axioms,((cGroups.class.comm_monoid_mult @ cGroups.times_class.times) @ cGroups.one_class.one))
(TGroups.comm_monoid_mult_class.mult.comm_monoid_axioms,((cGroups.comm_monoid @ cGroups.times_class.times) @ cGroups.one_class.one))
(TGroups.linordered_ab_group_add_class.minus_max_eq_min,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cOrderings.ord_class.max @ V0) @ V1))) @ ((cOrderings.ord_class.min @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TGroups.linordered_ab_group_add_class.minus_min_eq_max,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cOrderings.ord_class.min @ V0) @ V1))) @ ((cOrderings.ord_class.max @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.uminus_class.uminus @ V1))))))))
(TGroups.linordered_cancel_ab_semigroup_add_class.intro,((c==> @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)) @ ((c==> @ (cOrderings.linorder_class @ cTYPE)) @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE))))
(TGroups.linordered_cancel_ab_semigroup_add_class.super_2,((c==> @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ (cOrderings.linorder_class @ cTYPE)))
(TGroups.linordered_cancel_ab_semigroup_add_class.super_1,((c==> @ (cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE)) @ (cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE)))
(TGroups.ordered_ab_group_add_abs_class.abs_le_zero_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_group_add_class.neg_0_less_iff_less,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cGroups.uminus_class.uminus @ V0))) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_group_add_class.neg_less_0_iff_less,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cGroups.uminus_class.uminus @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TGroups.ordered_cancel_comm_monoid_diff.add_diff_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V0 @ V7) @ ((V2 @ V6) @ V5))) @ ((V2 @ ((V0 @ V7) @ V6)) @ V5)))))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff.diff_add_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V7) @ V6)) @ V5)) @ ((V0 @ V7) @ ((V2 @ V6) @ V5))))))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.diff_add,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V1) @ V0)) @ V0)) @ V1)))))))
(TGroups.ordered_comm_monoid_add.add_strict_increasing2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cGroups.class.ordered_comm_monoid_add @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((V2 @ V1) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((V3 @ V5) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TLattices.boolean_algebra_class.boolean_algebra_axioms,((((((((cLattices.class.boolean_algebra @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))
(TLattices.bounded_lattice_class.bounded_lattice_axioms,((((((cLattices.class.bounded_lattice @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))
(TLattices.classrel_bounded_lattice_bounded_lattice_bot,(cLattices.bounded_lattice_bot_class @ cTYPE))
(TLattices.classrel_bounded_lattice_bounded_lattice_top,(cLattices.bounded_lattice_top_class @ cTYPE))
(TLattices.distrib_lattice_class.distrib_lattice_axioms,((((cLattices.class.distrib_lattice @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup))
(TLattices.semilattice_inf_class.inf.semilattice_axioms,(cLattices.semilattice @ cLattices.inf_class.inf))
(TLattices.semilattice_inf_class.semilattice_inf_axioms,(((cLattices.class.semilattice_inf @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TLattices.semilattice_sup_class.semilattice_sup_axioms,(((cLattices.class.semilattice_sup @ cLattices.sup_class.sup) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TLattices.semilattice_sup_class.sup.semilattice_axioms,(cLattices.semilattice @ cLattices.sup_class.sup))
(TLazy_Sequence.lazy_sequence.Abs_lazy_sequence_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set))) @ ((cHOL.eq @ (cLazy_Sequence.Rep_lazy_sequence @ (cLazy_Sequence.Abs_lazy_sequence @ V0))) @ V0)))))
(TLazy_Sequence.lazy_sequence.Rep_lazy_sequence_inverse,(call @ (^[V0]: ((cHOL.eq @ (cLazy_Sequence.Abs_lazy_sequence @ (cLazy_Sequence.Rep_lazy_sequence @ V0))) @ V0))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_of_list_def,(call @ (^[V0]: ((c== @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V0)) @ (cLazy_Sequence.Abs_lazy_sequence @ (cDatatype.Leaf @ V0))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rec_set_def,((c== @ cLazy_Sequence.lazy_sequence.lazy_sequence_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V2) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V4))) @ ((cHOL.eq @ V3) @ (V0 @ V4))))))))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rep_set_def,((c== @ cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.Leaf @ V2)))))))))
(TList.linorder_class.sorted_list_of_set.folding_axioms,(cFinite_Set.folding @ (cList.linorder_class.insort_key @ (^[V0]: V0))))
(TNat.semiring_1_class.semiring_1_class.of_nat_aux_dict,((c== @ cNat.semiring_1.of_nat_aux) @ cNat.semiring_1.of_nat_aux))
(TOrderings.order_class.dual_order.strict_implies_order,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.bool.full_exhaustive_bool.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_bool_inst.full_exhaustive_bool @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cHOL.True) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cHOL.False) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil))))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.char.full_exhaustive_char.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_char_inst.full_exhaustive_char @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_nibble_inst.full_exhaustive_nibble @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_nibble_inst.full_exhaustive_nibble @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cString.char.Char @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.check_all_n_lists_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.check_all_n_lists_graph @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ (V4 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V6]: cList.list.Nil)))) @ (cQuickcheck_Exhaustive.check_all_class.check_all @ (cProduct_Type.prod.prod_case @ (^[V6]: (^[V7]: (V3 @ ((cProduct_Type.Pair @ (cProduct_Type.prod.prod_case @ (^[V8]: (^[V9]: (V4 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V6) @ V8)) @ (^[V10]: ((cList.list.Cons @ (V7 @ cProduct_Type.Unity)) @ (V9 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.check_all_subsets_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil)) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V2) @ V3))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V3) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_integer'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer))))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_integer'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ V3))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.exhaustive_natural'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_natural'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V3 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_rel @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: (V1 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V3) @ V4) @ V5)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V0) @ V2)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V5))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ (V2 @ ((cProduct_Type.Pair @ V1) @ (^[V3]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V1))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ (((V0 @ V4) @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V6) @ V7)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V5) @ V6) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V7) @ cCode_Numeral.one_integer_inst.one_integer))) @ cOption.option.Some) @ (V5 @ ((cProduct_Type.Pair @ V7) @ (^[V8]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V7)))))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V1) @ V2)) @ cOption.option.None) @ (((cOption.option.option_case @ (((cQuickcheck_Exhaustive.full_exhaustive_integer' @ V0) @ V1) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V2) @ cCode_Numeral.one_integer_inst.one_integer))) @ cOption.option.Some) @ (V0 @ ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V2)))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ (((V0 @ V4) @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (((V0 @ V4) @ V5) @ V6))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V0) @ V1) @ V2)) @ V3)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((cHOL.eq @ V0) @ V5)) @ ((c==> @ ((cHOL.eq @ V1) @ V6)) @ ((c==> @ ((cHOL.eq @ V2) @ V7)) @ ((c==> @ ((cHOL.eq @ V3) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V6) @ V7)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V5 @ ((cProduct_Type.Pair @ V7) @ (^[V8]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V7))))) @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V5) @ V6) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V7) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V5) @ ((cProduct_Type.Pair @ V6) @ V7)))) @ V4)))))))))))) @ V4))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.psimps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((cHOL.eq @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V0) @ V1) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V1) @ V2)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ V2) @ (^[V3]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V2))))) @ (((cQuickcheck_Exhaustive.full_exhaustive_natural' @ V0) @ V1) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V2) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V4)) @ (cProduct_Type.fst @ V3))) @ cOption.option.None) @ (V1 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V1) @ V2))) @ V0))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_set_rel) @ V1))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ V4))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V3 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ (V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_set_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V5]: ((cQuickcheck_Exhaustive.orelse @ (V3 @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V6)) @ (cProduct_Type.fst @ V5))) @ cOption.option.None) @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V6) @ V5))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cProduct_Type.Pair @ V3) @ V4)))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.list.full_exhaustive_list.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.pred.full_exhaustive_pred.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cPredicate.pred.Pred @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil)))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.term.full_exhaustive_term.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_term_inst.full_exhaustive_term @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ (V0 @ ((cProduct_Type.Pair @ cCode_Evaluation.term.dummy_term) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.term_syntax.termify_fun_upd_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((((cQuickcheck_Exhaustive.term_syntax.termify_fun_upd @ cTYPE) @ cTYPE) @ V0) @ V1) @ V2)) @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ V0)) @ V1)) @ V2)))))))))
(TQuickcheck_Exhaustive.term_syntax.valtermify_pair_def,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.valtermify_pair @ V0) @ V1)) @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cProduct_Type.Pair) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)) @ V1)))))))
(TQuickcheck_Exhaustive.unit.full_exhaustive_unit.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_unit_inst.full_exhaustive_unit @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ (V0 @ ((cProduct_Type.Pair @ cProduct_Type.Unity) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ cList.list.Nil)))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.unknown.unknown_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Exhaustive.unknown.unknown_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.Leaf @ V2)))))) @ (V1 @ V0)))))))))
(TQuickcheck_Narrowing.narrowing_int_inst.narrowing_int,((c== @ cQuickcheck_Narrowing.narrowing_int_inst.narrowing_int) @ cQuickcheck_Narrowing.narrowing_int_inst.narrowing_int))
(TQuickcheck_Narrowing.narrowing_nat_inst.narrowing_nat,((c== @ cQuickcheck_Narrowing.narrowing_nat_inst.narrowing_nat) @ cQuickcheck_Narrowing.narrowing_nat_inst.narrowing_nat))
(TQuickcheck_Narrowing.narrowing_num_inst.narrowing_num,((c== @ cQuickcheck_Narrowing.narrowing_num_inst.narrowing_num) @ cQuickcheck_Narrowing.narrowing_num_inst.narrowing_num))
(TQuickcheck_Narrowing.narrowing_set_inst.narrowing_set,((c== @ cQuickcheck_Narrowing.narrowing_set_inst.narrowing_set) @ cQuickcheck_Narrowing.narrowing_set_inst.narrowing_set))
(TQuickcheck_Narrowing.narrowing_sum_inst.narrowing_sum,((c== @ cQuickcheck_Narrowing.narrowing_sum_inst.narrowing_sum) @ cQuickcheck_Narrowing.narrowing_sum_inst.narrowing_sum))
(TQuickcheck_Narrowing.property.property_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Narrowing.property.property_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (cQuickcheck_Narrowing.property.Property @ V3)) @ (V2 @ V3)))))))))))
(TQuickcheck_Narrowing.property.property_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.All @ (^[V7]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (V3 @ V7)) @ (V4 @ V7))))) @ (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Existential @ V5) @ V3) @ V6)) @ ((((V1 @ V5) @ V3) @ V6) @ V4))))))))))))))))))
(TQuickcheck_Narrowing.property.property_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (cHOL.All @ (^[V7]: (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (V3 @ V7)) @ (V4 @ V7))))) @ (((((cQuickcheck_Narrowing.property.property_rec_set @ V0) @ V1) @ V2) @ (((cQuickcheck_Narrowing.property.Universal @ V5) @ V3) @ V6)) @ ((((V0 @ V5) @ V3) @ V6) @ V4))))))))))))))))))
(TQuickcheck_Narrowing.property.property_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.property.property_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (cQuickcheck_Narrowing.property.property_rep_set @ (V2 @ V5))))) @ ((c==> @ (call @ (^[V5]: (V1 @ (V2 @ V5))))) @ (V1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ V2)) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4)))))))))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (cQuickcheck_Narrowing.property.property_rep_set @ (V2 @ V5))))) @ ((c==> @ (call @ (^[V5]: (V1 @ (V2 @ V5))))) @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ V2)) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4))))))))))))))))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.Leaf @ (cSum_Type.Inl @ V2)))))))) @ (V1 @ V0))))))))))
(TQuickcheck_Narrowing.property.property_rep_set.intros_3,(call @ (^[V0]: (cQuickcheck_Narrowing.property.property_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.Leaf @ (cSum_Type.Inl @ V0))))))))
(TQuickcheck_Narrowing.property.property_rep_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (cQuickcheck_Narrowing.property.property_rep_set @ (V0 @ V3))))) @ (cQuickcheck_Narrowing.property.property_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V1)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ (^[V3]: (V0 @ V3)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V2))))))))))))))))
(TQuickcheck_Narrowing.property.property_rep_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (cQuickcheck_Narrowing.property.property_rep_set @ (V0 @ V3))))) @ (cQuickcheck_Narrowing.property.property_rep_set @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V1)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ (^[V3]: (V0 @ V3)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V2)))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_update_swap_fst_fst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ ((cFun.comp @ (V3 @ V4)) @ (V1 @ V2)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2))))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_update_swap_fst_snd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_update_swap_snd_fst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_update_swap_snd_snd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ ((cFun.comp @ (V3 @ V4)) @ (V1 @ V2)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4))) @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2))))))))))))))))
(TRecord.tuple_isomorphism.Abs_tuple_isomorphism_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set))) @ (V0 @ (cRecord.Abs_tuple_isomorphism @ V2)))))) @ (V0 @ V1)))))))
(TRecord.tuple_isomorphism.Abs_tuple_isomorphism_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cRecord.Abs_tuple_isomorphism @ V0)) @ (cRecord.Abs_tuple_isomorphism @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TRecord.tuple_isomorphism.Rep_tuple_isomorphism_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cRecord.Rep_tuple_isomorphism @ V2))))) @ (V1 @ V0))))))))
(TRecord.tuple_isomorphism.Rep_tuple_isomorphism_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cRecord.Rep_tuple_isomorphism @ V0)) @ (cRecord.Rep_tuple_isomorphism @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TRecord.tuple_isomorphism.arity_size_tuple_isomorphism,(cNat.size_class @ cTYPE))
(TRings.classrel_comm_semiring_0_cancel_comm_semiring_0,(cRings.comm_semiring_0_class @ cTYPE))
(TRings.classrel_comm_semiring_1_cancel_comm_semiring_1,(cRings.comm_semiring_1_class @ cTYPE))
(TRings.classrel_linordered_idom_linordered_ring_strict,(cRings.linordered_ring_strict_class @ cTYPE))
(TRings.classrel_linordered_ring_strict_linordered_ring,(cRings.linordered_ring_class @ cTYPE))
(TRings.classrel_ordered_comm_semiring_ordered_semiring,(cRings.ordered_semiring_class @ cTYPE))
(TRings.linordered_ring_strict_class.zero_less_mult_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)))))))))
(TRings.linordered_semiring_strict.mult_right_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ ((V4 @ V5) @ V6)) @ ((V4 @ V7) @ V6))) @ ((c==> @ ((V3 @ V1) @ V6)) @ ((V2 @ V5) @ V7)))))))))))))))))))))
(TRings.ordered_cancel_semiring_class.split_mult_neg_le,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)))))))
(TRings.ordered_comm_semiring_class.comm_mult_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V2) @ V0)) @ ((cGroups.times_class.times @ V2) @ V1)))))))))))
(TRings.ring_1_no_zero_divisors_class.mult_cancel_left1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.one_class.one))))))))
(TRings.ring_1_no_zero_divisors_class.mult_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V0)) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.one_class.one))))))))
(TSemiring_Normalization.field.normalizing_field_axioms,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cFields.class.field @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TSet_Interval.atLeastLessThanPlusOne_atLeastAtMost_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)))))))
(TSet_Interval.complete_lattice_class.Inf_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ V0)))))))
(TSet_Interval.complete_lattice_class.Sup_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ V1)))))))
(TSet_Interval.ord_class.ord_class.atLeastLessThan_dict,((c== @ cSet_Interval.ord_class.atLeastLessThan) @ ((cSet_Interval.ord.atLeastLessThan @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less)))
(TSet_Interval.order_class.greaterThanAtMost_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ (cHOL.Not @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TSet_Interval.ordered_ab_group_add.image_uminus_atMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ ((cSet_Interval.ord.atMost @ V4) @ V6))) @ ((cSet_Interval.ord.atLeast @ V4) @ (V3 @ V6)))))))))))))))))))
(TBig_Operators.comm_monoid_add.setsum_cartesian_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_add @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V5]: ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (^[V6]: ((V2 @ V5) @ V6))) @ V3))) @ V4)) @ ((((cBig_Operators.comm_monoid_add.setsum @ V0) @ V1) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((V2 @ V5) @ V6))))) @ ((cProduct_Type.Sigma @ V4) @ (^[V5]: V3))))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.strong_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (V2 @ V4))) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: (V3 @ V4))) @ V1)))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.subset_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.union_inter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1)))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1))))))))))))
(TBig_Operators.linorder_class.min_max.comp_fun_idem_inf,(cFinite_Set.comp_fun_idem @ cOrderings.ord_class.min))
(TBig_Operators.linorder_class.min_max.comp_fun_idem_sup,(cFinite_Set.comp_fun_idem @ cOrderings.ord_class.max))
(TBig_Operators.linordered_ab_group_add.minus_Max_eq_Min,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cFinite_Set.finite @ V6)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V3 @ ((cBig_Operators.linorder.Max @ V4) @ V6))) @ ((cBig_Operators.linorder.Min @ V4) @ ((cSet.image @ V3) @ V6)))))))))))))))))))))
(TBig_Operators.linordered_ab_group_add.minus_Min_eq_Max,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (cFinite_Set.finite @ V6)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V6) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V3 @ ((cBig_Operators.linorder.Min @ V4) @ V6))) @ ((cBig_Operators.linorder.Max @ V4) @ ((cSet.image @ V3) @ V6)))))))))))))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.coboundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)) @ V1))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.coboundedI,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.member @ V1) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)))))))))
(TCode_Evaluation.term_of_finite_1_inst.term_of_finite_1,((c== @ cCode_Evaluation.term_of_finite_1_inst.term_of_finite_1) @ cCode_Evaluation.term_of_finite_1_inst.term_of_finite_1))
(TCode_Evaluation.term_of_finite_2_inst.term_of_finite_2,((c== @ cCode_Evaluation.term_of_finite_2_inst.term_of_finite_2) @ cCode_Evaluation.term_of_finite_2_inst.term_of_finite_2))
(TCode_Evaluation.term_of_finite_3_inst.term_of_finite_3,((c== @ cCode_Evaluation.term_of_finite_3_inst.term_of_finite_3) @ cCode_Evaluation.term_of_finite_3_inst.term_of_finite_3))
(TCode_Evaluation.term_of_finite_4_inst.term_of_finite_4,((c== @ cCode_Evaluation.term_of_finite_4_inst.term_of_finite_4) @ cCode_Evaluation.term_of_finite_4_inst.term_of_finite_4))
(TCode_Evaluation.term_of_finite_5_inst.term_of_finite_5,((c== @ cCode_Evaluation.term_of_finite_5_inst.term_of_finite_5) @ cCode_Evaluation.term_of_finite_5_inst.term_of_finite_5))
(TComplete_Lattices.class.complete_boolean_algebra.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((((((((cLattices.class.boolean_algebra @ V8) @ V9) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9))))))))))))))))))))))))
(TComplete_Lattices.class.complete_distrib_lattice.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ V0) @ V1) @ V2) @ V5)) @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7))))))))))))))))))))
(TComplete_Lattices.complete_boolean_algebra_class.intro,((c==> @ (cComplete_Lattices.complete_distrib_lattice_class @ cTYPE)) @ ((c==> @ (cLattices.boolean_algebra_class @ cTYPE)) @ (cComplete_Lattices.complete_boolean_algebra_class @ cTYPE))))
(TComplete_Lattices.complete_boolean_algebra_class.super_2,((c==> @ (cComplete_Lattices.complete_boolean_algebra_class @ cTYPE)) @ (cLattices.boolean_algebra_class @ cTYPE)))
(TComplete_Lattices.complete_boolean_algebra_class.super_1,((c==> @ (cComplete_Lattices.complete_boolean_algebra_class @ cTYPE)) @ (cComplete_Lattices.complete_distrib_lattice_class @ cTYPE)))
(TComplete_Lattices.complete_distrib_lattice_class.intro,((c==> @ (cComplete_Lattices.complete_lattice_class @ cTYPE)) @ ((c==> @ ((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cLattices.inf_class.inf) @ cLattices.sup_class.sup)) @ (cComplete_Lattices.complete_distrib_lattice_class @ cTYPE))))
(TComplete_Lattices.complete_distrib_lattice_class.super,((c==> @ (cComplete_Lattices.complete_distrib_lattice_class @ cTYPE)) @ (cComplete_Lattices.complete_lattice_class @ cTYPE)))
(TComplete_Lattices.complete_lattice.INF_foundation_dual,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (cComplete_Lattices.complete_lattice.SUPR @ V0)) @ (cComplete_Lattices.complete_lattice.INFI @ V0))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_foundation_dual,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (cComplete_Lattices.complete_lattice.INFI @ V1)) @ (cComplete_Lattices.complete_lattice.SUPR @ V1))))))))))))))))))))
(TComplete_Lattices.complete_linorder_class.INF_less_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cSet.Bex @ V0) @ (^[V3]: ((cOrderings.ord_class.less @ (V1 @ V3)) @ V2)))))))))))
(TComplete_Lattices.complete_linorder_class.Inf_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1)) @ ((cSet.Bex @ V0) @ (^[V2]: ((cOrderings.ord_class.less @ V2) @ V1)))))))))
(TComplete_Lattices.complete_linorder_class.less_SUP_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cSet.Bex @ V1) @ (^[V3]: ((cOrderings.ord_class.less @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.complete_linorder_class.less_Sup_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((cSet.Bex @ V1) @ (^[V2]: ((cOrderings.ord_class.less @ V0) @ V2)))))))))
(TComplete_Partial_Order.ccpo_class.ccpo_class.fixp_dict,((c== @ cComplete_Partial_Order.ccpo_class.fixp) @ ((cComplete_Partial_Order.ccpo.fixp @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq)))
(TFields.division_ring_class.nonzero_imp_inverse_nonzero,(call @ (^[V0]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ (cHOL.Not @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ cGroups.zero_class.zero))))))
(TFields.division_ring_class.nonzero_minus_divide_divide,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))) @ ((cFields.inverse_class.divide @ V1) @ V0))))))))
(TFields.division_ring_inverse_zero_class.divide_self_if,(call @ (^[V0]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero) @ cGroups.one_class.one)))))
(TFields.field_inverse_zero.mult_divide_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V8) @ V9)) @ ((V2 @ V8) @ V10))) @ ((V1 @ V9) @ V10)))))))))))))))))))))))))))
(TFields.field_inverse_zero_class.divide_divide_eq_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)))))))))
(TFields.linordered_field_class.divide_strict_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V2)) @ ((cFields.inverse_class.divide @ V1) @ V2)))))))))))
(TFields.linordered_field_inverse_zero.divide_le_0_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V3) @ V12)) @ V5)) @ ((V9 @ V12) @ V5))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_less_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V12) @ V13)) @ V5)) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V12)) @ ((V10 @ V13) @ V5))) @ ((cHOL.conj @ ((V10 @ V12) @ V5)) @ ((V10 @ V5) @ V13))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V9 @ V5) @ V14)) @ ((V9 @ ((V1 @ V12) @ V14)) @ ((V1 @ V13) @ V14))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.abs_div_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ (cGroups.abs_class.abs @ V1)) @ V0)) @ (cGroups.abs_class.abs @ ((cFields.inverse_class.divide @ V1) @ V0)))))))))
(TFields.linordered_field_inverse_zero_class.abs_inverse,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cFields.inverse_class.inverse @ V0))) @ (cFields.inverse_class.inverse @ (cGroups.abs_class.abs @ V0))))))
(TGroups.class.linordered_cancel_ab_semigroup_add.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((cOrderings.class.linorder @ V1) @ V2)))))))))
(TGroups.class.linordered_cancel_ab_semigroup_add.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (((cGroups.class.linordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)))))))))
(TGroups.linordered_ab_group_add_class.le_minus_self_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_ab_group_add_class.minus_le_self_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)))))
(TGroups.ordered_ab_group_add_abs.abs_diff_triangle_ineq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ (V0 @ ((V3 @ ((V1 @ V7) @ V8)) @ ((V1 @ V9) @ V10)))) @ ((V1 @ (V0 @ ((V3 @ V7) @ V9))) @ (V0 @ ((V3 @ V8) @ V10))))))))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs.abs_triangle_ineq2_sym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cGroups.class.ordered_ab_group_add_abs @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((V5 @ ((V3 @ (V0 @ V7)) @ (V0 @ V8))) @ (V0 @ ((V3 @ V8) @ V7)))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_minus_cancel,(call @ (^[V0]: ((cHOL.eq @ (cGroups.abs_class.abs @ (cGroups.uminus_class.uminus @ V0))) @ (cGroups.abs_class.abs @ V0)))))
(TGroups.ordered_ab_group_add_class.diff_eq_diff_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.minus_class.minus @ V2) @ V3))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ V3))))))))))))
(TGroups.ordered_ab_group_add_class.diff_less_0_iff_less,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ V1)))))))
(TGroups.ordered_ab_group_add_class.less_iff_diff_less_0,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cGroups.minus_class.minus @ V0) @ V1)) @ cGroups.zero_class.zero)))))))
(TGroups.ordered_cancel_ab_semigroup_add.add_strict_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((V2 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff.add_diff_assoc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V0 @ ((V2 @ V6) @ V5)) @ V7)) @ ((V2 @ ((V0 @ V6) @ V7)) @ V5)))))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff.diff_add_assoc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V6) @ V7)) @ V5)) @ ((V0 @ ((V2 @ V6) @ V5)) @ V7)))))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff.diff_diff_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V2 @ V7) @ ((V2 @ V6) @ V5))) @ ((V2 @ ((V0 @ V7) @ V5)) @ V6)))))))))))))))))))))
(TGroups.ordered_comm_monoid_add_class.add_nonneg_nonneg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V1)))))))))
(TGroups.ordered_comm_monoid_add_class.add_nonpos_nonpos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TList.linorder_class.filter_equals_takeWhile_sorted_rev,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cList.linorder_class.sorted @ (cList.rev @ ((cList.map @ V0) @ V1)))) @ ((cHOL.eq @ ((cList.filter @ (^[V3]: ((cOrderings.ord_class.less @ V2) @ (V0 @ V3)))) @ V1)) @ ((cList.takeWhile @ (^[V3]: ((cOrderings.ord_class.less @ V2) @ (V0 @ V3)))) @ V1))))))))))
(TList.monoid_add_class.listsum_distinct_conv_setsum_set,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V1) @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ (cList.set @ V0)))))))))
(TNitpick.full_exhaustive_word_inst.full_exhaustive_word,((c== @ cNitpick.full_exhaustive_word_inst.full_exhaustive_word) @ cNitpick.full_exhaustive_word_inst.full_exhaustive_word))
(TNitpick.partial_term_of_word_inst.partial_term_of_word,((c== @ cNitpick.partial_term_of_word_inst.partial_term_of_word) @ cNitpick.partial_term_of_word_inst.partial_term_of_word))
(TNum.linordered_idom_class.not_numeral_less_neg_numeral,(call @ (^[V0]: (call @ (^[V1]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cNum.numeral_class.numeral @ V0)) @ (cNum.neg_numeral_class.neg_numeral @ V1))))))))
(TOrderings.order_class.dual_order.strict_implies_not_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0))))))))
(TPartial_Function.partial_function_definitions.leq_refl,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((V0 @ V2) @ V2)))))))))
(TPower.linordered_semidom_class.power_less_imp_less_exp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TPower.linordered_semidom_class.power_strict_decreasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V2) @ V1)) @ ((cPower.power_class.power @ V2) @ V0))))))))))))
(TPower.linordered_semidom_class.power_strict_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cNat.ord_nat_inst.less_nat @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V2)) @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V2) @ V0)) @ ((cPower.power_class.power @ V2) @ V1)))))))))))
(TQuickcheck_Exhaustive.check_all_class.check_all_axioms,(((cQuickcheck_Exhaustive.class.check_all @ cEnum.enum_class.enum) @ cEnum.enum_class.enum_all) @ cEnum.enum_class.enum_ex))
(TQuickcheck_Exhaustive.check_all_fun_inst.check_all_fun,((c== @ cQuickcheck_Exhaustive.check_all_fun_inst.check_all_fun) @ cQuickcheck_Exhaustive.check_all_fun_inst.check_all_fun))
(TQuickcheck_Exhaustive.check_all_set_inst.check_all_set,((c== @ cQuickcheck_Exhaustive.check_all_set_inst.check_all_set) @ cQuickcheck_Exhaustive.check_all_set_inst.check_all_set))
(TQuickcheck_Exhaustive.check_all_sum_inst.check_all_sum,((c== @ cQuickcheck_Exhaustive.check_all_sum_inst.check_all_sum) @ cQuickcheck_Exhaustive.check_all_sum_inst.check_all_sum))
(TQuickcheck_Exhaustive.equal_unknown_inst.equal_unknown,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Exhaustive.exhaustive_integer'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer))))))) @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ V1)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V2 @ V1)) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer)))))))))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V2 @ V1)) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V2)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (V1 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V4) @ V5) @ V6)))) @ V3))) @ V3))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V2) @ cCode_Numeral.one_natural_inst.one_natural)) @ V3))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_fun'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (V4 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (V3 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V6)))) @ V5)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V3 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))) @ cOption.option.None)))) @ ((cHOL.implies @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V3 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V3 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5)))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V4)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: (V3 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V6) @ V7) @ V8)))) @ V5))) @ V5))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural)) @ V5))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V2) @ V3))) @ ((c==> @ ((cHOL.eq @ (V1 @ ((cProduct_Type.Pair @ V3) @ (^[V4]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V3))))) @ cOption.option.None)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cInt.plus_int_inst.plus_int @ V3) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0)))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_int'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V4) @ V5)) @ cOption.option.None) @ (((cOption.option.option_case @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int))))) @ cOption.option.Some) @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V5)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((cHOL.implies @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V5))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V5))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cInt.plus_int_inst.plus_int @ V5) @ cInt.one_int_inst.one_int)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_integer'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ (((V3 @ V4) @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_rel_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_integer'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V5))))) @ cOption.option.None))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V0) @ ((cProduct_Type.Pair @ V1) @ V2)))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_natural'_rel) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ (((V3 @ V4) @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (((V3 @ V4) @ V5) @ V6)))))))))) @ (((V3 @ V0) @ V1) @ V2))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_rel_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_natural'_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V4)) @ (cProduct_Type.fst @ V3))) @ cOption.option.None) @ (V1 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V2 @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V4)) @ (cProduct_Type.fst @ V3))) @ cOption.option.None) @ (V1 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ ((cProduct_Type.Pair @ V1) @ V0)) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V1 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ (V2 @ ((cProduct_Type.Pair @ (^[V3]: ((cQuickcheck_Exhaustive.orelse @ (V1 @ V3)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V4)) @ (cProduct_Type.fst @ V3))) @ cOption.option.None) @ (V1 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V3))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))
(TQuickcheck_Narrowing.finite_1.narrowing_finite_1.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_finite_1_inst.narrowing_finite_1) @ (cQuickcheck_Narrowing.cons @ cEnum.finite_1.a\<__caret__sub>1)))
(TQuickcheck_Narrowing.finite_2.narrowing_finite_2.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_finite_2_inst.narrowing_finite_2) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_2.a\<__caret__sub>1)) @ (cQuickcheck_Narrowing.cons @ cEnum.finite_2.a\<__caret__sub>2))))
(TQuickcheck_Narrowing.finite_3.narrowing_finite_3.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_finite_3_inst.narrowing_finite_3) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_3.a\<__caret__sub>1)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_3.a\<__caret__sub>2)) @ (cQuickcheck_Narrowing.cons @ cEnum.finite_3.a\<__caret__sub>3)))))
(TQuickcheck_Narrowing.finite_4.narrowing_finite_4.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_finite_4_inst.narrowing_finite_4) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_4.a\<__caret__sub>1)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_4.a\<__caret__sub>2)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_4.a\<__caret__sub>3)) @ (cQuickcheck_Narrowing.cons @ cEnum.finite_4.a\<__caret__sub>4))))))
(TQuickcheck_Narrowing.finite_5.narrowing_finite_5.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_finite_5_inst.narrowing_finite_5) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_5.a\<__caret__sub>1)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_5.a\<__caret__sub>2)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_5.a\<__caret__sub>3)) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cEnum.finite_5.a\<__caret__sub>4)) @ (cQuickcheck_Narrowing.cons @ cEnum.finite_5.a\<__caret__sub>5)))))))
(TQuickcheck_Narrowing.narrowing_cons.Narrowing_cons_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V0) @ V1)) @ (cQuickcheck_Narrowing.Abs_narrowing_cons @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1))))))))))
(TQuickcheck_Narrowing.narrowing_cons.Rep_narrowing_cons,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Narrowing.Rep_narrowing_cons @ V0)) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set)))))
(TQuickcheck_Narrowing.narrowing_term.Rep_narrowing_term,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Narrowing.Rep_narrowing_term @ V0)) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1)))))
(TQuickcheck_Narrowing.narrowing_type.Rep_narrowing_type,(call @ (^[V0]: ((cSet.member @ (cQuickcheck_Narrowing.Rep_narrowing_type @ V0)) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1)))))
(TQuickcheck_Narrowing.partial_term_of_three_valued_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.property.property_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.property.property_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (cQuickcheck_Narrowing.property.property_rep_set @ (V2 @ V5))))) @ ((c==> @ (call @ (^[V5]: (V1 @ (V2 @ V5))))) @ (V1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ V2)) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4)))))))))))))))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (call @ (^[V5]: (cQuickcheck_Narrowing.property.property_rep_set @ (V2 @ V5))))) @ ((c==> @ (call @ (^[V5]: (V1 @ (V2 @ V5))))) @ (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ ((cDatatype.Scons @ (cDatatype.Lim @ V2)) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4))))))))))))))))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ (cDatatype.Leaf @ (cSum_Type.Inl @ V2)))))))) @ (V1 @ V0))))))))))
(TQuickcheck_Random.random_finite_1_inst.random_finite_1,((c== @ cQuickcheck_Random.random_finite_1_inst.random_finite_1) @ cQuickcheck_Random.random_finite_1_inst.random_finite_1))
(TQuickcheck_Random.random_finite_2_inst.random_finite_2,((c== @ cQuickcheck_Random.random_finite_2_inst.random_finite_2) @ cQuickcheck_Random.random_finite_2_inst.random_finite_2))
(TQuickcheck_Random.random_finite_3_inst.random_finite_3,((c== @ cQuickcheck_Random.random_finite_3_inst.random_finite_3) @ cQuickcheck_Random.random_finite_3_inst.random_finite_3))
(TQuickcheck_Random.random_finite_4_inst.random_finite_4,((c== @ cQuickcheck_Random.random_finite_4_inst.random_finite_4) @ cQuickcheck_Random.random_finite_4_inst.random_finite_4))
(TQuickcheck_Random.random_finite_5_inst.random_finite_5,((c== @ cQuickcheck_Random.random_finite_5_inst.random_finite_5) @ cQuickcheck_Random.random_finite_5_inst.random_finite_5))
(TRecord.tuple_isomorphism.Abs_tuple_isomorphism_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set))) @ ((cHOL.eq @ (cRecord.Rep_tuple_isomorphism @ (cRecord.Abs_tuple_isomorphism @ V0))) @ V0)))))
(TRecord.tuple_isomorphism.Rep_tuple_isomorphism_inverse,(call @ (^[V0]: ((cHOL.eq @ (cRecord.Abs_tuple_isomorphism @ (cRecord.Rep_tuple_isomorphism @ V0))) @ V0))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rec_set_def,((c== @ cRecord.tuple_isomorphism.tuple_isomorphism_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V4) @ V5))) @ ((cHOL.eq @ V3) @ ((V0 @ V4) @ V5))))))))))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rep_set_def,((c== @ cRecord.tuple_isomorphism.tuple_isomorphism_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V1) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3)))))))))))))
(TRings.class.linordered_comm_semiring_strict_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c== @ (((cRings.class.linordered_comm_semiring_strict_axioms @ V0) @ V1) @ V2)) @ (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.implies @ ((V0 @ V3) @ V4)) @ ((cHOL.implies @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))))))))))
(TRings.linordered_ring_strict.mult_less_cancel_left_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V5 @ V8) @ V3)) @ ((cHOL.eq @ ((V5 @ ((V7 @ V8) @ V9)) @ ((V7 @ V8) @ V10))) @ ((V5 @ V10) @ V9)))))))))))))))))))))))))))
(TRings.linordered_ring_strict.mult_less_cancel_left_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V5 @ V3) @ V8)) @ ((cHOL.eq @ ((V5 @ ((V7 @ V8) @ V9)) @ ((V7 @ V8) @ V10))) @ ((V5 @ V9) @ V10)))))))))))))))))))))))))))
(TRings.linordered_ring_strict.mult_strict_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V5 @ V8) @ V9)) @ ((c==> @ ((V5 @ V10) @ V3)) @ ((V5 @ ((V7 @ V10) @ V9)) @ ((V7 @ V10) @ V8))))))))))))))))))))))))))))
(TRings.linordered_ring_strict_class.mult_le_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))))
(TRings.linordered_semiring_strict.mult_le_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((c==> @ ((V3 @ V7) @ V8)) @ ((c==> @ ((V3 @ V1) @ V5)) @ ((c==> @ ((V2 @ V1) @ V7)) @ ((V3 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V8))))))))))))))))))))))))))
(TRings.linordered_semiring_strict.mult_less_le_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((c==> @ ((V2 @ V7) @ V8)) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((c==> @ ((V3 @ V1) @ V7)) @ ((V3 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V8))))))))))))))))))))))))))
(TRings.linordered_semiring_strict.mult_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((c==> @ ((V3 @ V1) @ V7)) @ ((V3 @ ((V4 @ V7) @ V5)) @ ((V4 @ V7) @ V6))))))))))))))))))))))
(TRings.ordered_cancel_semiring_class.mult_nonneg_nonneg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1)))))))))
(TRings.ordered_cancel_semiring_class.mult_nonneg_nonpos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.ordered_cancel_semiring_class.mult_nonpos_nonneg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TRings.ordered_comm_ring_class.ordered_comm_ring_axioms,(((((((cRings.class.ordered_comm_ring @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.times_class.times) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TRings.ring_1_no_zero_divisors_class.mult_cancel_right1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.one_class.one))))))))
(TRings.ring_1_no_zero_divisors_class.mult_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ ((cHOL.disj @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.one_class.one))))))))
(TRings.semiring_0_cancel_class.semiring_0_cancel_axioms,(((cRings.class.semiring_0_cancel @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.semiring_1_cancel_class.semiring_1_cancel_axioms,((((cRings.class.semiring_1_cancel @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cGroups.times_class.times))
(TSet_Interval.bounded_lattice.atLeastAtMost_eq_UNIV_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cLattices.class.bounded_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.atLeastAtMost @ V1) @ V6) @ V7)) @ cOrderings.top_class.top)) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ V4)) @ ((cHOL.eq @ V7) @ V5)))))))))))))))))))))
(TSet_Interval.complete_lattice_class.Inf_atMostLessThan,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cOrderings.top_class.top) @ V0)) @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ (cSet_Interval.ord_class.lessThan @ V0))) @ cOrderings.bot_class.bot)))))
(TSet_Interval.linorder_class.atLeastLessThan_subset_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))))
(TSet_Interval.ordered_ab_group_add.image_uminus_atLeast,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ ((cSet_Interval.ord.atLeast @ V4) @ V6))) @ ((cSet_Interval.ord.atMost @ V4) @ (V3 @ V6)))))))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_reindex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ ((cSet.image @ V0) @ V1))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V1)) @ ((cHOL.eq @ (V3 @ V5)) @ (V4 @ (V0 @ V5))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V4) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1))))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_restrict_set,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ ((cLattices.inf_class.inf @ V0) @ V2))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: (((cHOL.If @ ((cSet.member @ V3) @ V2)) @ (V1 @ V3)) @ cGroups.zero_class.zero))) @ V0))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.eq_general,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.Ball @ V0) @ (^[V5]: (cHOL.Ex1 @ (^[V6]: ((cHOL.conj @ ((cSet.member @ V6) @ V1)) @ ((cHOL.eq @ (V2 @ V6)) @ V5))))))) @ ((c==> @ ((cSet.Ball @ V1) @ (^[V5]: ((cHOL.conj @ ((cSet.member @ (V2 @ V5)) @ V0)) @ ((cHOL.eq @ (V3 @ (V2 @ V5))) @ (V4 @ V5)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V4) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V0)))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod_reindex_id,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V0) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ cFun.id) @ ((cSet.image @ V0) @ V1)))))))))
(TBig_Operators.linorder_class.Max.semilattice_set_axioms,(cBig_Operators.semilattice_set @ cOrderings.ord_class.max))
(TBig_Operators.linorder_class.Min.semilattice_set_axioms,(cBig_Operators.semilattice_set @ cOrderings.ord_class.min))
(TBig_Operators.linorder_class.finite_linorder_max_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (V1 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cOrderings.ord_class.less @ V4) @ V2)))) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cSet.insert @ V2) @ V3)))))))))) @ (V1 @ V0)))))))))
(TBig_Operators.linorder_class.finite_linorder_min_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (V1 @ cOrderings.bot_class.bot)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ ((cSet.Ball @ V3) @ (^[V4]: ((cOrderings.ord_class.less @ V2) @ V4)))) @ ((c==> @ (V1 @ V3)) @ (V1 @ ((cSet.insert @ V2) @ V3)))))))))) @ (V1 @ V0)))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0))) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V1) @ V2)))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.hom_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ ((cLattices.inf_class.inf @ V2) @ V3))) @ ((cLattices.inf_class.inf @ (V0 @ V2)) @ (V0 @ V3)))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V1))) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cSet.image @ V0) @ V1)))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.bounded_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)) @ V1)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cOrderings.ord_class.less_eq @ V2) @ V1)))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.hom_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ (V0 @ ((cLattices.sup_class.sup @ V2) @ V3))) @ ((cLattices.sup_class.sup @ (V0 @ V2)) @ (V0 @ V3)))))))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (V0 @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V1))) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cSet.image @ V0) @ V1)))))))))))
(TComplete_Lattices.class.complete_boolean_algebra.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((((((((cLattices.class.boolean_algebra @ V8) @ V9) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))))))
(TComplete_Lattices.class.complete_boolean_algebra.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))))))
(TComplete_Lattices.class.complete_distrib_lattice.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ V0) @ V1) @ V2) @ V5)))))))))))))))))))
(TComplete_Lattices.class.complete_distrib_lattice.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.axioms,((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cLattices.inf_class.inf) @ cLattices.sup_class.sup))
(TComplete_Lattices.complete_lattice.INF_UNIV_bool_expand,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ cOrderings.top_class.top) @ (^[V9]: (V8 @ V9)))) @ ((V2 @ (V8 @ cHOL.True)) @ (V8 @ cHOL.False)))))))))))))))))))))))
(TComplete_Lattices.complete_lattice.SUP_UNIV_bool_expand,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ cOrderings.top_class.top) @ (^[V9]: (V8 @ V9)))) @ ((V5 @ (V8 @ cHOL.True)) @ (V8 @ cHOL.False)))))))))))))))))))))))
(TComplete_Partial_Order.ccpo_class.admissible_disj_lemma,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cComplete_Partial_Order.chain @ cOrderings.ord_class.less_eq) @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Bex @ V0) @ (^[V3]: ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ (V1 @ V3))))))) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ (cSet.Collect @ (^[V2]: ((cHOL.conj @ ((cSet.member @ V2) @ V0)) @ (V1 @ V2)))))))))))))
(TComplete_Partial_Order.ccpo_class.iteratesp_iterates_eq,(call @ (^[V0]: ((cHOL.eq @ (cComplete_Partial_Order.ccpo_class.iteratesp @ V0)) @ (^[V1]: ((cSet.member @ V1) @ (cComplete_Partial_Order.ccpo_class.iterates @ V0)))))))
(TDivides.semiring_numeral_div_class.le_add_diff_inverse2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V1) @ V0)) @ V0)) @ V1)))))))
(TDivides.semiring_numeral_div_class.mod_less_eq_dividend,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ ((cDivides.div_class.mod @ V0) @ V1)) @ V0)))))))
(TFields.division_ring_class.nonzero_inverse_mult_distrib,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ (cFields.inverse_class.inverse @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cGroups.times_class.times @ (cFields.inverse_class.inverse @ V1)) @ (cFields.inverse_class.inverse @ V0))))))))))
(TFields.field_class.nonzero_mult_divide_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V1) @ V2)) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cFields.inverse_class.divide @ V2) @ V0)))))))))))
(TFields.field_inverse_zero.mult_divide_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V8) @ V5))) @ ((cHOL.eq @ ((V1 @ ((V2 @ V9) @ V8)) @ ((V2 @ V10) @ V8))) @ ((V1 @ V9) @ V10)))))))))))))))))))))))))))
(TFields.linordered_field_class.inverse_less_iff_less_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0)))))))))
(TFields.linordered_field_class.inverse_less_imp_less_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TFields.linordered_field_class.less_imp_inverse_less_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V1)) @ (cFields.inverse_class.inverse @ V0)))))))))
(TFields.linordered_field_inverse_zero.divide_le_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V13) @ V12)) @ V3)) @ ((V9 @ V12) @ V13)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_le_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V9 @ ((V1 @ V13) @ V12)) @ V3)) @ ((V9 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_less_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V12) @ V13)) @ ((V1 @ V14) @ V13))) @ ((cHOL.conj @ ((cHOL.implies @ ((V10 @ V5) @ V13)) @ ((V10 @ V12) @ V14))) @ ((cHOL.conj @ ((cHOL.implies @ ((V10 @ V13) @ V5)) @ ((V10 @ V14) @ V12))) @ (cHOL.Not @ ((cHOL.eq @ V13) @ V5)))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.inverse_less_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ (V0 @ V12)) @ V3)) @ ((cHOL.disj @ ((V9 @ V12) @ V5)) @ ((V10 @ V3) @ V12)))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.le_divide_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V9 @ V3) @ ((V1 @ V13) @ V12))) @ ((V9 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.le_divide_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V9 @ V3) @ ((V1 @ V13) @ V12))) @ ((V9 @ V12) @ V13)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.one_le_inverse_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ V3) @ (V0 @ V12))) @ ((cHOL.conj @ ((V10 @ V5) @ V12)) @ ((V9 @ V12) @ V3)))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.zero_le_divide_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ V5) @ ((V1 @ V12) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((V9 @ V5) @ V12)) @ ((V9 @ V5) @ V13))) @ ((cHOL.conj @ ((V9 @ V12) @ V5)) @ ((V9 @ V13) @ V5))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.divide_le_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ V2)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ ((cGroups.times_class.times @ V2) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V2) @ V1)) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)))))))))))
(TFields.linordered_field_inverse_zero_class.le_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)))))))))))
(TGroups.ab_semigroup_add_class.add.abel_semigroup_axioms,(cGroups.abel_semigroup @ cGroups.plus_class.plus))
(TGroups.ab_semigroup_mult_class.ab_semigroup_mult_axioms,(cGroups.class.ab_semigroup_mult @ cGroups.times_class.times))
(TGroups.class.ordered_ab_semigroup_add_imp_le_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: ((cHOL.implies @ ((V1 @ ((V0 @ V2) @ V3)) @ ((V0 @ V2) @ V4))) @ ((V1 @ V3) @ V4))))))))))))))
(TGroups.class.ordered_cancel_comm_monoid_diff_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: ((cHOL.eq @ ((V1 @ V2) @ V3)) @ (cHOL.Ex @ (^[V4]: ((cHOL.eq @ V3) @ ((V0 @ V2) @ V4)))))))))))))))
(TGroups.linordered_ab_group_add_class.less_eq_neg_nonpos,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ (cGroups.uminus_class.uminus @ V0))) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_ab_group_add_class.neg_less_eq_nonneg,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)))))
(TGroups.ordered_ab_group_add_abs_class.abs_ge_minus_self,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ V0)) @ (cGroups.abs_class.abs @ V0)))))
(TGroups.ordered_ab_group_add_abs_class.abs_minus_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V0) @ V1))) @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V1) @ V0))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_minus_le_zero,(call @ (^[V0]: ((cOrderings.ord_class.less_eq @ (cGroups.uminus_class.uminus @ (cGroups.abs_class.abs @ V0))) @ cGroups.zero_class.zero))))
(TGroups.ordered_ab_group_add_abs_class.abs_not_less_zero,(call @ (^[V0]: (cHOL.Not @ ((cOrderings.ord_class.less @ (cGroups.abs_class.abs @ V0)) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_group_add_abs_class.abs_triangle_ineq,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ ((cGroups.plus_class.plus @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))))))))
(TGroups.ordered_ab_group_add_abs_class.zero_less_abs_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cGroups.abs_class.abs @ V0))) @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))))))
(TGroups.ordered_ab_group_add_class.max_diff_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ ((cGroups.minus_class.minus @ V0) @ V2)) @ ((cGroups.minus_class.minus @ V1) @ V2))))))))))
(TGroups.ordered_ab_group_add_class.min_diff_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ ((cGroups.minus_class.minus @ V0) @ V2)) @ ((cGroups.minus_class.minus @ V1) @ V2))))))))))
(TGroups.ordered_cancel_ab_semigroup_add.add_le_less_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((V2 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TGroups.ordered_cancel_ab_semigroup_add.add_less_le_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((c==> @ ((V1 @ V5) @ V6)) @ ((V2 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff.add_diff_inverse,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((V0 @ V5) @ ((V2 @ V6) @ V5))) @ V6))))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.le_iff_add,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TLattices.semilattice_order.semilattice_strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cLattices.semilattice_order @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ V3) @ V4)) @ ((cHOL.conj @ ((V1 @ V3) @ V4)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))))))))))))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cLazy_Sequence.lazy_sequence.lazy_sequence_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V1) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V4))) @ ((c==> @ ((cHOL.eq @ V2) @ (V0 @ V4))) @ V3))))) @ V3)))))))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cLazy_Sequence.lazy_sequence.lazy_sequence_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V1) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V3))) @ ((cHOL.eq @ V2) @ (V0 @ V3)))))))))))))
(TList.comm_monoid_add_class.distinct_listsum_conv_Setsum,(call @ (^[V0]: ((c==> @ (cList.distinct @ V0)) @ ((cHOL.eq @ (cList.monoid_add_class.listsum @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V1]: V1)) @ (cList.set @ V0)))))))
(TList.linorder_class.sorted_list_of_set.comp_fun_commute,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFun.comp @ ((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V0)) @ ((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V1))) @ ((cFun.comp @ ((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V1)) @ ((cList.linorder_class.insort_key @ (^[V2]: V2)) @ V0))))))))
(TOrderings.order_class.order.not_eq_order_implies_strict,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TPartial_Function.partial_function_definitions.leq_trans,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V2) @ V4)))))))))))))))
(TPartial_Function.partial_function_definitions.lub_least,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V2)) @ ((V0 @ V4) @ V3))))) @ ((V0 @ (V1 @ V2)) @ V3)))))))))))))
(TPartial_Function.partial_function_definitions.lub_upper,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ ((cComplete_Partial_Order.chain @ V0) @ V2)) @ ((c==> @ ((cSet.member @ V3) @ V2)) @ ((V0 @ V3) @ (V1 @ V2))))))))))))))
(TPower.linordered_semidom_class.power_less_imp_less_base,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V2) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TQuickcheck_Exhaustive.exhaustive_integer'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.exhaustive_natural'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (V4 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (V1 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V4) @ V5) @ V6)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2))) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (V1 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V4) @ V5) @ V6)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V0) @ V2))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V4]: (V1 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V4)))) @ V2)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V0)) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V5]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V6]: (V1 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V4) @ V5) @ V6)))) @ V2))) @ V2))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V0) @ cCode_Numeral.one_natural_inst.one_natural)) @ V2)))) @ cOption.option.None)))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ (V2 @ ((cProduct_Type.Pair @ V1) @ (^[V4]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V1))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int)))))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V0) @ V1)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cInt.plus_int_inst.plus_int @ V1) @ cInt.one_int_inst.one_int))))) @ cOption.option.Some) @ (V2 @ ((cProduct_Type.Pair @ V1) @ (^[V4]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V1)))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_sumC_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_integer'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_sumC_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_natural'_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.full_exhaustive_set_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_set_graph @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural))) @ ((V2 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ V5)) @ (((cHOL.If @ ((cHOL.eq @ V5) @ cCode_Numeral.zero_natural_inst.zero_natural)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)) @ (V3 @ ((cProduct_Type.Pair @ (^[V6]: ((cQuickcheck_Exhaustive.orelse @ (V4 @ V6)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (((cHOL.If @ ((cSet.member @ (cProduct_Type.fst @ V7)) @ (cProduct_Type.fst @ V6))) @ cOption.option.None) @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V7) @ V6))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets) @ (^[V0]: (^[V1]: (cQuickcheck_Exhaustive.term_syntax.check_all_subsets_sumC @ ((cProduct_Type.Pair @ V0) @ V1))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_def,((c== @ cQuickcheck_Exhaustive.three_valued.three_valued_rec) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cHOL.The @ (^[V4]: (((((cQuickcheck_Exhaustive.three_valued.three_valued_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)))))))))
(TQuickcheck_Narrowing.arity_partial_term_of_three_valued,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.equal_property_inst.equal_property,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Narrowing.narrowing_bool_inst.narrowing_bool,((c== @ cQuickcheck_Narrowing.narrowing_bool_inst.narrowing_bool) @ cQuickcheck_Narrowing.narrowing_bool_inst.narrowing_bool))
(TQuickcheck_Narrowing.narrowing_cfun_inst.narrowing_cfun,((c== @ cQuickcheck_Narrowing.narrowing_cfun_inst.narrowing_cfun) @ cQuickcheck_Narrowing.narrowing_cfun_inst.narrowing_cfun))
(TQuickcheck_Narrowing.narrowing_char_inst.narrowing_char,((c== @ cQuickcheck_Narrowing.narrowing_char_inst.narrowing_char) @ cQuickcheck_Narrowing.narrowing_char_inst.narrowing_char))
(TQuickcheck_Narrowing.narrowing_ffun_inst.narrowing_ffun,((c== @ cQuickcheck_Narrowing.narrowing_ffun_inst.narrowing_ffun) @ cQuickcheck_Narrowing.narrowing_ffun_inst.narrowing_ffun))
(TQuickcheck_Narrowing.narrowing_list_inst.narrowing_list,((c== @ cQuickcheck_Narrowing.narrowing_list_inst.narrowing_list) @ cQuickcheck_Narrowing.narrowing_list_inst.narrowing_list))
(TQuickcheck_Narrowing.narrowing_prod_inst.narrowing_prod,((c== @ cQuickcheck_Narrowing.narrowing_prod_inst.narrowing_prod) @ cQuickcheck_Narrowing.narrowing_prod_inst.narrowing_prod))
(TQuickcheck_Narrowing.narrowing_term_inst.narrowing_term,((c== @ cQuickcheck_Narrowing.narrowing_term_inst.narrowing_term) @ cQuickcheck_Narrowing.narrowing_term_inst.narrowing_term))
(TQuickcheck_Narrowing.narrowing_unit_inst.narrowing_unit,((c== @ cQuickcheck_Narrowing.narrowing_unit_inst.narrowing_unit) @ cQuickcheck_Narrowing.narrowing_unit_inst.narrowing_unit))
(TQuickcheck_Narrowing.partial_term_of_lazy_sequence_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TRecord.isomorphic_tuple.iso_tuple_access_update_fst_fst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ V1) @ (V2 @ V3))) @ ((cFun.comp @ V4) @ V1))) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ V4) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0)))))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_access_update_fst_snd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ cFun.id) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_fst @ V0))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_access_update_snd_fst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ cFun.id) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_access_update_snd_snd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ V1) @ (V2 @ V3))) @ ((cFun.comp @ V4) @ V1))) @ ((cHOL.eq @ ((cFun.comp @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0))) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V2) @ V3))) @ ((cFun.comp @ V4) @ ((cFun.comp @ V1) @ (cRecord.iso_tuple_snd @ V0)))))))))))))))))
(TRings.classrel_comm_semiring_0_cancel_semiring_0_cancel,(cRings.semiring_0_cancel_class @ cTYPE))
(TRings.classrel_comm_semiring_1_cancel_semiring_1_cancel,(cRings.semiring_1_cancel_class @ cTYPE))
(TRings.classrel_linordered_ring_ordered_ab_group_add_abs,(cGroups.ordered_ab_group_add_abs_class @ cTYPE))
(TRings.linordered_ring_strict.mult_less_cancel_left_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ ((V7 @ V8) @ V9)) @ ((V7 @ V8) @ V10))) @ ((cHOL.disj @ ((cHOL.conj @ ((V5 @ V3) @ V8)) @ ((V5 @ V9) @ V10))) @ ((cHOL.conj @ ((V5 @ V8) @ V3)) @ ((V5 @ V10) @ V9))))))))))))))))))))))))))))
(TRings.linordered_ring_strict.mult_strict_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((c==> @ ((V5 @ V8) @ V9)) @ ((c==> @ ((V5 @ V10) @ V3)) @ ((V5 @ ((V7 @ V9) @ V10)) @ ((V7 @ V8) @ V10))))))))))))))))))))))))))))
(TRings.linordered_ring_strict_class.mult_le_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V2) @ V0)))))))))))
(TRings.linordered_semiring_class.mult_left_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V2))))))))))
(TRings.linordered_semiring_strict.mult_strict_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((c==> @ ((V3 @ V1) @ V7)) @ ((V3 @ ((V4 @ V5) @ V7)) @ ((V4 @ V6) @ V7))))))))))))))))))))))
(TRings.linordered_semiring_strict_class.mult_strict_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))))
(TRings.ordered_cancel_semiring_class.mult_nonneg_nonpos2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V1) @ V0)) @ cGroups.zero_class.zero))))))))
(TSemiring_Normalization.comm_ring_1.normalizing_ring_ops_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cPure.term @ (V5 @ V6))))))))))))))))))
(TSemiring_Normalization.comm_ring_1.normalizing_ring_ops_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ (cPure.term @ ((V4 @ V6) @ V7))))))))))))))))))))
(TSet_Interval.atLeastPlusOneAtMost_greaterThanAtMost_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)))))))
(TSet_Interval.complete_lattice_class.Inf_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ V0)))))))
(TSet_Interval.linorder_class.greaterThan_Int_greaterThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cSet_Interval.ord_class.lessThan @ V0)) @ (cSet_Interval.ord_class.lessThan @ V1))) @ (cSet_Interval.ord_class.lessThan @ ((cOrderings.ord_class.min @ V0) @ V1))))))))
(TSet_Interval.ord_class.ord_class.greaterThanAtMost_dict,((c== @ cSet_Interval.ord_class.greaterThanAtMost) @ ((cSet_Interval.ord.greaterThanAtMost @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less)))
(TSet_Interval.ordered_ab_group_add.image_uminus_lessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ ((cSet_Interval.ord.lessThan @ V5) @ V6))) @ ((cSet_Interval.ord.greaterThan @ V5) @ (V3 @ V6)))))))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.insert_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ ((cSet.insert @ V2) @ V0))) @ ((cGroups.plus_class.plus @ (V1 @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.neutral_const,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V1]: cGroups.zero_class.zero)) @ V0)) @ cGroups.zero_class.zero))))
(TBig_Operators.comm_monoid_mult.setprod_cartesian_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ (^[V5]: ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ (^[V6]: ((V2 @ V5) @ V6))) @ V3))) @ V4)) @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ (cProduct_Type.prod.prod_case @ (^[V5]: (^[V6]: ((V2 @ V5) @ V6))))) @ ((cProduct_Type.Sigma @ V4) @ (^[V5]: V3))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.strong_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V4]: (V2 @ V4))) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V4]: (V3 @ V4))) @ V1)))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.subset_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.union_inter,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((cHOL.eq @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.inf_class.inf @ V0) @ V1)))) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1))))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.INF_sup,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ V2)))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.Inf_sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: ((cLattices.sup_class.sup @ V2) @ V1)))))))))
(TComplete_Lattices.complete_distrib_lattice_class.SUP_inf,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ V2)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ V2)))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.Sup_inf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: ((cLattices.inf_class.inf @ V2) @ V1)))))))))
(TComplete_Lattices.complete_distrib_lattice_class.inf_SUP,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V3]: ((cLattices.inf_class.inf @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.inf_Sup,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ (cComplete_Lattices.Sup_class.Sup @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V2]: ((cLattices.inf_class.inf @ V0) @ V2)))))))))
(TComplete_Lattices.complete_distrib_lattice_class.sup_INF,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V3]: ((cLattices.sup_class.sup @ V0) @ (V2 @ V3))))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.sup_Inf,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V2]: ((cLattices.sup_class.sup @ V0) @ V2)))))))))
(TComplete_Lattices.complete_lattice.dual_complete_lattice,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cComplete_Lattices.class.complete_lattice @ V1) @ V0) @ V5) @ (^[V8]: (^[V9]: ((V3 @ V9) @ V8)))) @ (^[V8]: (^[V9]: ((V4 @ V9) @ V8)))) @ V2) @ V7) @ V6)))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_inf_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V3]: ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_subset_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V1) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.complete_lattice_class.SUP_sup_distrib,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V1 @ V3)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: (V2 @ V3))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V3]: ((cLattices.sup_class.sup @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TComplete_Lattices.complete_lattice_class.Sup_subset_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.complete_linorder_class.INF_eq_bot_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2)))) @ cOrderings.bot_class.bot)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ cOrderings.bot_class.bot) @ V2)) @ ((cSet.Bex @ V0) @ (^[V3]: ((cOrderings.ord_class.less @ (V1 @ V3)) @ V2))))))))))))
(TComplete_Lattices.complete_linorder_class.Inf_eq_bot_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ cOrderings.bot_class.bot)) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cOrderings.ord_class.less @ cOrderings.bot_class.bot) @ V1)) @ ((cSet.Bex @ V0) @ (^[V2]: ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TComplete_Lattices.complete_linorder_class.SUP_eq_top_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2)))) @ cOrderings.top_class.top)) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V2) @ cOrderings.top_class.top)) @ ((cSet.Bex @ V0) @ (^[V3]: ((cOrderings.ord_class.less @ V2) @ (V1 @ V3)))))))))))))
(TComplete_Lattices.complete_linorder_class.Sup_eq_top_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ cOrderings.top_class.top)) @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cOrderings.top_class.top)) @ ((cSet.Bex @ V0) @ (^[V2]: ((cOrderings.ord_class.less @ V1) @ V2))))))))))
(TFields.division_ring_inverse_zero_class.inverse_minus_eq,(call @ (^[V0]: ((cHOL.eq @ (cFields.inverse_class.inverse @ (cGroups.uminus_class.uminus @ V0))) @ (cGroups.uminus_class.uminus @ (cFields.inverse_class.inverse @ V0))))))
(TFields.field_class.nonzero_mult_divide_mult_cancel_left2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V1) @ V2)) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cFields.inverse_class.divide @ V2) @ V0)))))))))))
(TFields.field_class.nonzero_mult_divide_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cFields.inverse_class.divide @ V2) @ V0)))))))))))
(TFields.linordered_field_inverse_zero.divide_less_0_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V3) @ V12)) @ V5)) @ ((V10 @ V12) @ V5))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.one_divide_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ ((V1 @ V3) @ V12)) @ V5)) @ ((cHOL.eq @ V12) @ V5))))))))))))))))))))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_triangle_ineq2,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))) @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V0) @ V1))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_triangle_ineq3,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1)))) @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V0) @ V1))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_triangle_ineq4,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V0) @ V1))) @ ((cGroups.plus_class.plus @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.le_add_diff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ V2) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V1) @ V2)) @ V0))))))))))
(TGroups.ordered_comm_monoid_add_class.add_nonneg_eq_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))))
(TLattices.linorder_class.max.semilattice_strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0)))))))))
(TLattices.linorder_class.min.semilattice_strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TLattices.semilattice_inf_class.inf.abel_semigroup_axioms,(cGroups.abel_semigroup @ cLattices.inf_class.inf))
(TLattices.semilattice_sup_class.sup.abel_semigroup_axioms,(cGroups.abel_semigroup @ cLattices.sup_class.sup))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (((cLazy_Sequence.lazy_sequence.lazy_sequence_rec_set @ V0) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V1)) @ (V0 @ V1)))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rep_set.intros,(call @ (^[V0]: (cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set @ (cDatatype.Leaf @ V0)))))
(TList.monoid_add_class.interv_listsum_conv_setsum_set_int,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ ((cList.upto @ V1) @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ (cList.set @ ((cList.upto @ V1) @ V2)))))))))))
(TList.monoid_add_class.interv_listsum_conv_setsum_set_nat,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (cList.monoid_add_class.listsum @ ((cList.map @ V0) @ ((cList.upt @ V1) @ V2)))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V0) @ (cList.set @ ((cList.upt @ V1) @ V2)))))))))))
(TNum.neg_numeral_class.neg_numeral_class.neg_numeral_dict,((c== @ cNum.neg_numeral_class.neg_numeral) @ (((cNum.neg_numeral.neg_numeral @ cGroups.plus_class.plus) @ cGroups.uminus_class.uminus) @ cGroups.one_class.one)))
(TPartial_Function.partial_function_definitions.const_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ (((cComplete_Partial_Order.monotone @ V2) @ V0) @ (^[V4]: V3))))))))))))
(TPower.ring_1_no_zero_divisors_class.field_power_not_zero,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ (cHOL.Not @ ((cHOL.eq @ ((cPower.power_class.power @ V0) @ V1)) @ cGroups.zero_class.zero))))))))
(TQuickcheck_Exhaustive.arity_full_exhaustive_three_valued,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_bool_inst.check_all_bool,((c== @ cQuickcheck_Exhaustive.check_all_bool_inst.check_all_bool) @ cQuickcheck_Exhaustive.check_all_bool_inst.check_all_bool))
(TQuickcheck_Exhaustive.check_all_char_inst.check_all_char,((c== @ cQuickcheck_Exhaustive.check_all_char_inst.check_all_char) @ cQuickcheck_Exhaustive.check_all_char_inst.check_all_char))
(TQuickcheck_Exhaustive.check_all_prod_inst.check_all_prod,((c== @ cQuickcheck_Exhaustive.check_all_prod_inst.check_all_prod) @ cQuickcheck_Exhaustive.check_all_prod_inst.check_all_prod))
(TQuickcheck_Exhaustive.check_all_unit_inst.check_all_unit,((c== @ cQuickcheck_Exhaustive.check_all_unit_inst.check_all_unit) @ cQuickcheck_Exhaustive.check_all_unit_inst.check_all_unit))
(TQuickcheck_Exhaustive.exhaustive_fun_inst.exhaustive_fun,((c== @ cQuickcheck_Exhaustive.exhaustive_fun_inst.exhaustive_fun) @ cQuickcheck_Exhaustive.exhaustive_fun_inst.exhaustive_fun))
(TQuickcheck_Exhaustive.exhaustive_int_inst.exhaustive_int,((c== @ cQuickcheck_Exhaustive.exhaustive_int_inst.exhaustive_int) @ cQuickcheck_Exhaustive.exhaustive_int_inst.exhaustive_int))
(TQuickcheck_Exhaustive.exhaustive_nat_inst.exhaustive_nat,((c== @ cQuickcheck_Exhaustive.exhaustive_nat_inst.exhaustive_nat) @ cQuickcheck_Exhaustive.exhaustive_nat_inst.exhaustive_nat))
(TQuickcheck_Exhaustive.exhaustive_set_inst.exhaustive_set,((c== @ cQuickcheck_Exhaustive.exhaustive_set_inst.exhaustive_set) @ cQuickcheck_Exhaustive.exhaustive_set_inst.exhaustive_set))
(TQuickcheck_Exhaustive.full_exhaustive_fun'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((cQuickcheck_Exhaustive.full_exhaustive_fun'_graph @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((c==> @ ((c==> @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V7]: (V4 @ (cQuickcheck_Exhaustive.valtermify_absdummy @ V7)))) @ V6)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.one_natural_inst.one_natural) @ V5)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V8]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (^[V9]: (V4 @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V7) @ V8) @ V9)))) @ V6))) @ V6))) @ ((cProduct_Type.Pair @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)) @ V6)))) @ cOption.option.None)))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_int'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_int'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cInt.ord_int_inst.less_int @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cInt.ord_int_inst.less_int @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cInt.plus_int_inst.plus_int @ V6) @ cInt.one_int_inst.one_int))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_int_inst.term_of_int @ V6)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_graph_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_integer'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6)))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((cHOL.induct_implies @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V5))))) @ cOption.option.None)) @ V2))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V4) @ cCode_Numeral.one_integer_inst.one_integer))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ ((cHOL.conj @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V3) @ V4))) @ ((cHOL.eq @ (V2 @ ((cProduct_Type.Pair @ V4) @ (^[V5]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V4))))) @ cOption.option.None))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_graph_def,((c== @ cQuickcheck_Exhaustive.full_exhaustive_natural'_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V6))))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((cHOL.induct_implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((V0 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ V2)))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V4) @ cCode_Numeral.one_natural_inst.one_natural))))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V3) @ V4)))) @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V3) @ V4))))))))))))))))
(TQuickcheck_Exhaustive.random_unknown_inst.random_unknown,((c== @ cQuickcheck_Exhaustive.random_unknown_inst.random_unknown) @ cQuickcheck_Exhaustive.random_unknown_inst.random_unknown))
(TQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Exhaustive.term_syntax.valtermify_fun_upd @ V0) @ V1) @ V2)) @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cFun.fun_upd) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V0)) @ V1)) @ V2)))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_case_def,((c== @ cQuickcheck_Exhaustive.three_valued.three_valued_case) @ (^[V0]: (^[V1]: (^[V2]: (((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ V0) @ (^[V3]: (V1 @ V3))) @ V2))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_size_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Exhaustive.three_valued.three_valued_size @ V0)) @ (((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V1]: ((cNat.plus_nat_inst.plus_nat @ (V0 @ V1)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))) @ cNat.zero_nat_inst.zero_nat)))))
(TQuickcheck_Narrowing.arity_partial_term_of_lazy_sequence,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.mutual_random_auxnarrowing_term_def,((c== @ cQuickcheck_Narrowing.mutual_random_auxnarrowing_term) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ ((cProduct_Type.Pair @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V1)) @ (^[V3]: ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V1)) @ (^[V4]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_term.Narrowing_variable) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V3)) @ V4)))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil))) @ V2))))) @ (^[V1]: (^[V2]: ((cProduct_Type.Pair @ (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_integer_inst.random_integer @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ ((cProduct_Type.snd @ V2) @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ ((cProduct_Type.scomp @ (cQuickcheck_Random.random_class.random @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ (cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_term.Narrowing_variable) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ cList.list.Nil)))) @ V4)))) @ (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ ((cProduct_Type.fst @ V2) @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ ((cProduct_Type.snd @ V2) @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V4))))))) @ V0))))
(TQuickcheck_Narrowing.mutual_random_auxnarrowing_type_def,((c== @ cQuickcheck_Narrowing.mutual_random_auxnarrowing_type) @ (^[V0]: (((cCode_Numeral.natural.natural_rec @ ((cProduct_Type.Pair @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ cList.list.Nil)) @ V2)))) @ ((cProduct_Type.Pair @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))))))) @ cList.list.Nil))) @ V2)))) @ (^[V1]: (^[V2]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V3]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil))) @ V2)))))) @ (^[V1]: (^[V2]: ((cProduct_Type.Pair @ (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ ((cProduct_Type.fst @ (cProduct_Type.snd @ V2)) @ V3)) @ (^[V5]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products) @ (^[V6]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ V5)))))) @ cList.list.Nil))) @ V4)))) @ ((cProduct_Type.Pair @ (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ (cCode_Numeral.Suc @ V1)) @ ((cProduct_Type.scomp @ ((cProduct_Type.snd @ (cProduct_Type.snd @ V2)) @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ ((cProduct_Type.fst @ (cProduct_Type.snd @ V2)) @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V4)))) @ (^[V3]: (^[V4]: ((cQuickcheck_Random.collapse @ (cRandom.select_weight @ ((cList.list.Cons @ ((cProduct_Type.Pair @ ((cQuickcheck_Random.beyond @ cCode_Numeral.one_natural_inst.one_natural) @ (cCode_Numeral.Suc @ V1))) @ ((cProduct_Type.scomp @ ((cProduct_Type.fst @ V2) @ V3)) @ (^[V5]: ((cProduct_Type.scomp @ ((cProduct_Type.snd @ (cProduct_Type.snd @ V2)) @ V3)) @ (^[V6]: (cProduct_Type.Pair @ ((cCode_Evaluation.valapp @ ((cCode_Evaluation.valapp @ ((cProduct_Type.Pair @ cList.list.Cons) @ (^[V7]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))))) @ V5)) @ V6)))))))) @ ((cList.list.Cons @ ((cProduct_Type.Pair @ cCode_Numeral.one_natural_inst.one_natural) @ (cProduct_Type.Pair @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V5]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))))))) @ cList.list.Nil)))) @ V4)))))))) @ V0))))
(TQuickcheck_Narrowing.narrowing_dummy_partial_term_of_def,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_dummy_partial_term_of) @ cQuickcheck_Narrowing.partial_term_of_class.partial_term_of))
(TQuickcheck_Narrowing.partial_term_of_narrowing_cons_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_class.partial_term_of @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_narrowing_term_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_narrowing_term_inst.partial_term_of_narrowing_term @ V0) @ V1)) @ cHOL.undefined))))))
(TQuickcheck_Narrowing.partial_term_of_narrowing_type_triv,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.partial_term_of_narrowing_type_inst.partial_term_of_narrowing_type @ V0) @ V1)) @ cHOL.undefined))))))
(TRecord.isomorphic_tuple.iso_tuple_update_compose_fst_fst,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ (V5 @ ((cFun.comp @ V2) @ V4)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V3) @ V4))) @ (((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V5) @ ((cFun.comp @ V2) @ V4))))))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_update_compose_snd_snd,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cHOL.eq @ ((cFun.comp @ (V1 @ V2)) @ (V3 @ V4))) @ (V5 @ ((cFun.comp @ V2) @ V4)))) @ ((cHOL.eq @ ((cFun.comp @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1) @ V2)) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V3) @ V4))) @ (((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V5) @ ((cFun.comp @ V2) @ V4))))))))))))))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cRecord.tuple_isomorphism.tuple_isomorphism_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V2) @ ((V0 @ V4) @ V5))) @ V3))))))) @ V3)))))))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cRecord.tuple_isomorphism.tuple_isomorphism_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V3) @ V4))) @ ((cHOL.eq @ V2) @ ((V0 @ V3) @ V4)))))))))))))))
(TRings.class.linordered_comm_semiring_strict_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ V3) @ V4)) @ ((c==> @ ((V0 @ V1) @ V5)) @ ((V0 @ ((V2 @ V5) @ V3)) @ ((V2 @ V5) @ V4))))))))))) @ (((cRings.class.linordered_comm_semiring_strict_axioms @ V0) @ V1) @ V2)))))))))
(TRings.classrel_ordered_cancel_semiring_semiring_0_cancel,(cRings.semiring_0_cancel_class @ cTYPE))
(TRings.linordered_ring_strict.mult_less_cancel_right_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cRings.class.linordered_ring_strict @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ ((V7 @ V8) @ V9)) @ ((V7 @ V10) @ V9))) @ ((cHOL.disj @ ((cHOL.conj @ ((V5 @ V3) @ V9)) @ ((V5 @ V8) @ V10))) @ ((cHOL.conj @ ((V5 @ V9) @ V3)) @ ((V5 @ V10) @ V8))))))))))))))))))))))))))))
(TRings.linordered_ring_strict_class.mult_less_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V1)))))))))))
(TRings.linordered_semidom_class.linordered_semidom_axioms,((((((cRings.class.linordered_semidom @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TRings.linordered_semiring_1_strict_class.convex_bound_lt,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V4)) @ ((c==> @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V3) @ V4)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V3) @ V0)) @ ((cGroups.times_class.times @ V4) @ V2))) @ V1)))))))))))))))))
(TRings.linordered_semiring_class.mult_right_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TRings.linordered_semiring_strict.mult_less_imp_less_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ ((V4 @ V5) @ V6)) @ ((V4 @ V5) @ V7))) @ ((c==> @ ((V2 @ V1) @ V5)) @ ((V3 @ V6) @ V7)))))))))))))))))))))
(TRings.linordered_semiring_strict_class.mult_strict_mono',(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))))
(TSMT.full_exhaustive_pattern_inst.full_exhaustive_pattern,((c== @ cSMT.full_exhaustive_pattern_inst.full_exhaustive_pattern) @ cSMT.full_exhaustive_pattern_inst.full_exhaustive_pattern))
(TSMT.partial_term_of_pattern_inst.partial_term_of_pattern,((c== @ cSMT.partial_term_of_pattern_inst.partial_term_of_pattern) @ cSMT.partial_term_of_pattern_inst.partial_term_of_pattern))
(TSemiring_Normalization.field_class.normalizing_field_ops_2,(call @ (^[V0]: (cPure.term @ (cFields.inverse_class.inverse @ V0)))))
(TSemiring_Normalization.field_class.normalizing_field_ops_1,(call @ (^[V0]: (call @ (^[V1]: (cPure.term @ ((cFields.inverse_class.divide @ V0) @ V1)))))))
(TBig_Operators.comm_monoid_add_class.setsum.UNION_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ V0) @ (^[V4]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V1 @ V4))) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ (V1 @ V3)))) @ V0))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ V2)))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (cBig_Operators.comm_monoid_add_class.setsum @ V1)) @ V0)))))))))
(TBig_Operators.comm_monoid_add_class.setsum.union_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ V2)))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (cBig_Operators.comm_monoid_add_class.setsum @ V1)) @ V0)))))))))
(TBig_Operators.comm_monoid_mult_class.setprod_reindex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ ((cSet.image @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ V3) @ ((cFun.comp @ V4) @ V0))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V4) @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1))))))))))))))))
(TBig_Operators.linorder_class.min_max.dual_distrib_lattice,((((cLattices.class.distrib_lattice @ cOrderings.ord_class.max) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cOrderings.ord_class.min))
(TBig_Operators.linordered_ab_semigroup_add.add_Max_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.linordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ V4) @ ((cBig_Operators.linorder.Max @ V1) @ V3))) @ ((cBig_Operators.linorder.Max @ V1) @ (cSet.Collect @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V5) @ ((V0 @ V4) @ V6))) @ ((cSet.member @ V6) @ V3))))))))))))))))))))))
(TBig_Operators.linordered_ab_semigroup_add.add_Min_commute,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (((cGroups.class.linordered_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ (cFinite_Set.finite @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((V0 @ V4) @ ((cBig_Operators.linorder.Min @ V1) @ V3))) @ ((cBig_Operators.linorder.Min @ V1) @ (cSet.Collect @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V5) @ ((V0 @ V4) @ V6))) @ ((cSet.member @ V6) @ V3))))))))))))))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.insert_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cSet.insert @ V1) @ V0))) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cLattices.inf_class.inf @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.insert_remove,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cSet.insert @ V1) @ V0))) @ (((cHOL.If @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))) @ cOrderings.bot_class.bot)) @ V1) @ ((cLattices.sup_class.sup @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V1) @ cOrderings.bot_class.bot))))))))))))
(TFields.classrel_linordered_field_unbounded_dense_linorder,(cOrderings.unbounded_dense_linorder_class @ cTYPE))
(TFields.division_ring_inverse_zero_class.inverse_eq_iff_eq,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TFields.division_ring_inverse_zero_class.inverse_eq_imp_eq,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TFields.field_class.nonzero_mult_divide_mult_cancel_right2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cFields.inverse_class.divide @ V2) @ V0)))))))))))
(TFields.field_inverse_zero.mult_divide_mult_cancel_left_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((((((((cFields.class.field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V1 @ ((V2 @ V8) @ V9)) @ ((V2 @ V8) @ V10))) @ (((cHOL.If @ ((cHOL.eq @ V8) @ V5)) @ V5) @ ((V1 @ V9) @ V10)))))))))))))))))))))))))))
(TFields.field_inverse_zero_class.field_inverse_zero_axioms,((((((((cFields.class.field_inverse_zero @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TFields.linordered_field_class.divide_strict_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V2) @ V0)) @ ((cFields.inverse_class.divide @ V2) @ V1))))))))))))
(TFields.linordered_field_inverse_zero.divide_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V9 @ V14) @ V5)) @ ((c==> @ ((V10 @ V5) @ ((V2 @ V12) @ V13))) @ ((V9 @ ((V1 @ V14) @ V12)) @ ((V1 @ V14) @ V13)))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_less_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V13) @ V12)) @ V3)) @ ((V10 @ V12) @ V13)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.divide_less_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V10 @ ((V1 @ V13) @ V12)) @ V3)) @ ((V10 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.less_divide_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V12) @ V5)) @ ((cHOL.eq @ ((V10 @ V3) @ ((V1 @ V13) @ V12))) @ ((V10 @ V13) @ V12)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.less_divide_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V10 @ V5) @ V12)) @ ((cHOL.eq @ ((V10 @ V3) @ ((V1 @ V13) @ V12))) @ ((V10 @ V12) @ V13)))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.one_less_inverse_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V3) @ (V0 @ V12))) @ ((cHOL.conj @ ((V10 @ V5) @ V12)) @ ((V10 @ V12) @ V3)))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.zero_eq_1_divide_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((cHOL.eq @ V5) @ ((V1 @ V3) @ V12))) @ ((cHOL.eq @ V12) @ V5))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.zero_le_divide_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ V5) @ ((V1 @ V3) @ V12))) @ ((V9 @ V5) @ V12))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.zero_less_divide_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V5) @ ((V1 @ V12) @ V13))) @ ((cHOL.disj @ ((cHOL.conj @ ((V10 @ V5) @ V12)) @ ((V10 @ V5) @ V13))) @ ((cHOL.conj @ ((V10 @ V12) @ V5)) @ ((V10 @ V13) @ V5))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.divide_eq_eq_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V1) @ V0))))))))
(TFields.linordered_field_inverse_zero_class.divide_le_eq_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)))))))))
(TFields.linordered_field_inverse_zero_class.divide_less_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ V2)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ ((cGroups.times_class.times @ V2) @ V1))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V2) @ V1)) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)))))))))))
(TFields.linordered_field_inverse_zero_class.eq_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ V1) @ V0))))))))
(TFields.linordered_field_inverse_zero_class.inverse_le_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))))
(TFields.linordered_field_inverse_zero_class.le_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))))
(TFields.linordered_field_inverse_zero_class.less_divide_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ ((cFields.inverse_class.divide @ V1) @ V2))) @ (((cHOL.If @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)) @ (((cHOL.If @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))))))))
(TGroups.ab_semigroup_mult_class.mult.abel_semigroup_axioms,(cGroups.abel_semigroup @ cGroups.times_class.times))
(TGroups.class.ordered_ab_semigroup_add_imp_le_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V1 @ V2) @ V4))) @ ((V0 @ V3) @ V4))))))))) @ ((cGroups.class.ordered_ab_semigroup_add_imp_le_axioms @ V1) @ V0)))))))
(TGroups.class.ordered_cancel_comm_monoid_diff_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((V0 @ V2) @ V3)) @ (cHOL.Ex @ (^[V4]: ((cHOL.eq @ V3) @ ((V1 @ V2) @ V4)))))))))) @ ((cGroups.class.ordered_cancel_comm_monoid_diff_axioms @ V1) @ V0)))))))
(TGroups.ordered_ab_semigroup_add_imp_le.add_le_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5))) @ ((V1 @ V4) @ V5))))))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.add_le_imp_le_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5))) @ ((V1 @ V4) @ V5))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff.le_imp_diff_is_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cGroups.class.ordered_cancel_comm_monoid_diff @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((c==> @ ((V3 @ V5) @ V6)) @ ((cHOL.eq @ ((cHOL.eq @ ((V2 @ V6) @ V5)) @ V7)) @ ((cHOL.eq @ V6) @ ((V0 @ V7) @ V5)))))))))))))))))))))))
(TLazy_Sequence.lazy_sequence.lazy_sequence_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cLazy_Sequence.lazy_sequence.lazy_sequence_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.Leaf @ V2))))) @ (V1 @ V0))))))))
(TList.linorder_class.linorder_class.insort_insert_key_dict,((c== @ cList.linorder_class.insort_insert_key) @ (cList.linorder.insort_insert_key @ cOrderings.ord_class.less_eq)))
(TMain.full_exhaustive_sumbool_inst.full_exhaustive_sumbool,((c== @ cMain.full_exhaustive_sumbool_inst.full_exhaustive_sumbool) @ cMain.full_exhaustive_sumbool_inst.full_exhaustive_sumbool))
(TMain.partial_term_of_sumbool_inst.partial_term_of_sumbool,((c== @ cMain.partial_term_of_sumbool_inst.partial_term_of_sumbool) @ cMain.partial_term_of_sumbool_inst.partial_term_of_sumbool))
(TPartial_Function.partial_function_definitions.leq_antisym,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ ((V0 @ V2) @ V3)) @ ((c==> @ ((V0 @ V3) @ V2)) @ ((cHOL.eq @ V2) @ V3)))))))))))))
(TQuickcheck_Exhaustive.arity_full_exhaustive_lazy_sequence,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Exhaustive.check_all_fun_inst.enum_term_of_fun,((c== @ cQuickcheck_Exhaustive.check_all_fun_inst.enum_term_of_fun) @ cQuickcheck_Exhaustive.check_all_fun_inst.enum_term_of_fun))
(TQuickcheck_Exhaustive.check_all_set_inst.enum_term_of_set,((c== @ cQuickcheck_Exhaustive.check_all_set_inst.enum_term_of_set) @ cQuickcheck_Exhaustive.check_all_set_inst.enum_term_of_set))
(TQuickcheck_Exhaustive.check_all_sum_inst.enum_term_of_sum,((c== @ cQuickcheck_Exhaustive.check_all_sum_inst.enum_term_of_sum) @ cQuickcheck_Exhaustive.check_all_sum_inst.enum_term_of_sum))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V5))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ (V2 @ ((cProduct_Type.Pair @ V1) @ (^[V3]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V1))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_rel @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.nibble.full_exhaustive_nibble.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_nibble_inst.full_exhaustive_nibble @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble0) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble0)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble1) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble2) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble3) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble4) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble5) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble6) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble7) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble7)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble8) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble8)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.Nibble9) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble9)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleA) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleB) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleC) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleD) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleE) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cString.nibble.NibbleF) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble6)) @ cList.list.Nil))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))))))))))))))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.option.full_exhaustive_option.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cOption.option.None) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cOption.option.Some @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ cList.list.Nil))) @ V1)))) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V2) @ ((cList.list.Cons @ V3) @ V4)))) @ V1)))))))) @ V1)))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.elims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ V1)) @ V2)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ V3)))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6))) @ V3)))))))))) @ V3))))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.simps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V3]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V3))) @ cOption.option.Some) @ (V0 @ V3)))) @ V2)))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.simps_1,(call @ (^[V0]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ cList.list.Nil)) @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))
(TQuickcheck_Exhaustive.three_valued.Abs_three_valued_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.Abs_three_valued @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set))) @ V1))))) @ V1))))))
(TQuickcheck_Exhaustive.three_valued.Rep_three_valued_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Exhaustive.Rep_three_valued @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Exhaustive.unknown.unknown_size_overloaded_def,((c== @ cNat.size_class.size) @ ((cQuickcheck_Exhaustive.unknown.unknown_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Narrowing.arity_full_exhaustive_narrowing_cons,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Narrowing.arity_full_exhaustive_narrowing_term,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Narrowing.arity_full_exhaustive_narrowing_type,(cQuickcheck_Exhaustive.full_exhaustive_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_narrowing_cons,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_narrowing_term,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.arity_partial_term_of_narrowing_type,(cQuickcheck_Narrowing.partial_term_of_class @ cTYPE))
(TQuickcheck_Narrowing.random_property_inst.random_property,((c== @ cQuickcheck_Narrowing.random_property_inst.random_property) @ cQuickcheck_Narrowing.random_property_inst.random_property))
(TRecord.tuple_isomorphism.tuple_isomorphism_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((cRecord.tuple_isomorphism.tuple_isomorphism_rec_set @ V0) @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V1) @ V2)) @ ((V0 @ V1) @ V2)))))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRecord.tuple_isomorphism.tuple_isomorphism_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))) @ (V1 @ V0))))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rep_set.intros,(call @ (^[V0]: (call @ (^[V1]: (cRecord.tuple_isomorphism.tuple_isomorphism_rep_set @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1)))))))))
(TRings.linordered_idom_class.linorder_neqE_linordered_idom,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ V2)) @ ((c==> @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V0)) @ V2)) @ V2))))))))))
(TRings.linordered_ring_strict_class.mult_less_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V0)))))))))))
(TRings.linordered_semiring_strict.mult_less_imp_less_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V3 @ ((V4 @ V5) @ V6)) @ ((V4 @ V7) @ V6))) @ ((c==> @ ((V2 @ V1) @ V6)) @ ((V3 @ V5) @ V7)))))))))))))))))))))
(TRings.linordered_semiring_strict_class.zero_less_mult_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))))))))
(TSemiring_Normalization.comm_ring_1.normalizing_ring_rules_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V6) @ V7)) @ ((V2 @ V6) @ (V5 @ V7)))))))))))))))))))))
(TSemiring_Normalization.comm_ring_1.normalizing_ring_rules_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ (V5 @ V6)) @ ((V0 @ (V5 @ V1)) @ V6))))))))))))))))))
(TSemiring_Normalization.idom_class.normalizing_idom_axioms,((((((cRings.class.idom @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TSet_Interval.complete_lattice_class.Sup_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ V1)))))))
(TSet_Interval.dense_linorder.greaterThanLessThan_empty_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V2) @ V3)) @ cOrderings.bot_class.bot)) @ ((V0 @ V3) @ V2))))))))))))
(TSet_Interval.ord_class.ord_class.greaterThanLessThan_dict,((c== @ cSet_Interval.ord_class.greaterThanLessThan) @ (cSet_Interval.ord.greaterThanLessThan @ cOrderings.ord_class.less)))
(TBig_Operators.comm_monoid_add_class.setsum_reindex_nonzero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cSet.member @ V3) @ V0)) @ ((c==> @ ((cSet.member @ V4) @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((c==> @ ((cHOL.eq @ (V1 @ V3)) @ (V1 @ V4))) @ ((cHOL.eq @ (V2 @ (V1 @ V3))) @ cGroups.zero_class.zero)))))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cSet.image @ V1) @ V0))) @ ((cBig_Operators.comm_monoid_add_class.setsum @ ((cFun.comp @ V2) @ V1)) @ V0)))))))))))
(TBig_Operators.comm_monoid_mult.strong_setprod_reindex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cGroups.class.comm_monoid_mult @ V0) @ V1)) @ ((c==> @ ((cFun.inj_on @ V2) @ V3)) @ ((c==> @ ((cHOL.eq @ V4) @ ((cSet.image @ V2) @ V3))) @ ((c==> @ (call @ (^[V7]: ((c==> @ ((cSet.member @ V7) @ V3)) @ ((cHOL.eq @ (V5 @ V7)) @ (((cFun.comp @ V6) @ V2) @ V7)))))) @ ((cHOL.eq @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V6) @ V4)) @ ((((cBig_Operators.comm_monoid_mult.setprod @ V0) @ V1) @ V5) @ V3)))))))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.insert_remove,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ ((cSet.insert @ V2) @ V0))) @ ((cGroups.times_class.times @ (V1 @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ ((cGroups.minus_class.minus @ V0) @ ((cSet.insert @ V2) @ cOrderings.bot_class.bot)))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.neutral_const,(call @ (^[V0]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V1]: cGroups.one_class.one)) @ V0)) @ cGroups.one_class.one))))
(TComplete_Lattices.complete_lattice_class.INF_superset_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V0)) @ ((cOrderings.ord_class.less_eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cOrderings.ord_class.less_eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ V1) @ (^[V4]: (V2 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V3 @ V4)))))))))))))))
(TComplete_Lattices.complete_lattice_class.Inf_superset_mono,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Inf_class.Inf @ V1)) @ (cComplete_Lattices.Inf_class.Inf @ V0))))))))
(TComplete_Lattices.complete_lattice_class.Inf_union_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Inf_class.Inf @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ V1))))))))
(TComplete_Lattices.complete_lattice_class.Sup_inter_less_eq,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ (cComplete_Lattices.Sup_class.Sup @ ((cLattices.inf_class.inf @ V0) @ V1))) @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.complete_lattice_class.Sup_union_distrib,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ (cComplete_Lattices.Sup_class.Sup @ V1))))))))
(TComplete_Lattices.complete_lattice_class.less_eq_Inf_inter,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ (cComplete_Lattices.Inf_class.Inf @ V1))) @ (cComplete_Lattices.Inf_class.Inf @ ((cLattices.inf_class.inf @ V0) @ V1))))))))
(TComplete_Lattices.complete_linorder.dual_complete_linorder,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cComplete_Lattices.class.complete_linorder @ V1) @ V0) @ V5) @ (^[V8]: (^[V9]: ((V3 @ V9) @ V8)))) @ (^[V8]: (^[V9]: ((V4 @ V9) @ V8)))) @ V2) @ V7) @ V6)))))))))))))))))))
(TComplete_Partial_Order.ccpo_class.ccpo_class.iterates_dict,((c== @ cComplete_Partial_Order.ccpo_class.iterates) @ ((cComplete_Partial_Order.ccpo.iterates @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq)))
(TFields.division_ring_inverse_zero_class.inverse_inverse_eq,(call @ (^[V0]: ((cHOL.eq @ (cFields.inverse_class.inverse @ (cFields.inverse_class.inverse @ V0))) @ V0))))
(TFields.linordered_field_class.divide_strict_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V1) @ V2)) @ ((cFields.inverse_class.divide @ V0) @ V2)))))))))))
(TFields.linordered_field_inverse_zero.divide_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: (call @ (^[V14]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ ((V9 @ V12) @ V13)) @ ((c==> @ ((V9 @ V14) @ V5)) @ ((V9 @ ((V1 @ V13) @ V14)) @ ((V1 @ V12) @ V14))))))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.divide_le_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.add_le_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V1 @ ((V0 @ V3) @ V4)) @ ((V0 @ V5) @ V4))) @ ((V1 @ V3) @ V5))))))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.add_le_imp_le_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((c==> @ ((V1 @ ((V0 @ V3) @ V4)) @ ((V0 @ V5) @ V4))) @ ((V1 @ V3) @ V5))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.le_diff_conv2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V2) @ V0)) @ V1))))))))))
(TGroups.ordered_comm_monoid_add_class.add_strict_increasing,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))))
(TLazy_Sequence.equal_lazy_sequence_inst.equal_lazy_sequence,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TList.linorder_class.linorder_class.sorted_list_of_set_dict,((c== @ cList.linorder_class.sorted_list_of_set) @ (cList.linorder.sorted_list_of_set @ cOrderings.ord_class.less_eq)))
(TPartial_Function.partial_function_definitions.fixp_rule_uc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ (call @ (^[V6]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ V0)) @ V0) @ (^[V7]: ((V2 @ (V3 @ (V4 @ V7))) @ V6)))))) @ ((c==> @ ((c== @ V5) @ (V4 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ V1)) @ (cPartial_Function.fun_ord @ V0)) @ (^[V6]: (V2 @ (V3 @ (V4 @ V6)))))))) @ ((c==> @ (call @ (^[V6]: ((cHOL.eq @ (V4 @ (V2 @ V6))) @ V6)))) @ ((cHOL.eq @ V5) @ (V3 @ V5)))))))))))))))))))
(TPower.linordered_ring_strict_class.sum_squares_eq_zero_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cGroups.times_class.times @ V1) @ V1))) @ cGroups.zero_class.zero)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))
(TPower.linordered_ring_strict_class.sum_squares_gt_zero_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cGroups.times_class.times @ V1) @ V1)))) @ ((cHOL.disj @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)))))))))
(TPower.linordered_ring_strict_class.sum_squares_le_zero_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cGroups.times_class.times @ V1) @ V1))) @ cGroups.zero_class.zero)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))
(TPower.linordered_semidom_class.power_strict_increasing_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((cNat.ord_nat_inst.less_nat @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.exhaustive_prod_inst.exhaustive_prod,((c== @ cQuickcheck_Exhaustive.exhaustive_prod_inst.exhaustive_prod) @ cQuickcheck_Exhaustive.exhaustive_prod_inst.exhaustive_prod))
(TQuickcheck_Exhaustive.full_exhaustive_integer'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V2) @ V3))) @ ((c==> @ ((cHOL.eq @ (V1 @ ((cProduct_Type.Pair @ V3) @ (^[V4]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V3))))) @ cOption.option.None)) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V3) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0)))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_integer'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5)) @ cOption.option.None) @ (((cOption.option.option_case @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer))))) @ cOption.option.Some) @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V5)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((cHOL.implies @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V5))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V5))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V5) @ cCode_Numeral.one_integer_inst.one_integer)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V2) @ V3))) @ ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V3) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V1) @ ((cProduct_Type.Pair @ V2) @ V3)))) @ V0))))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.full_exhaustive_natural'_rel) @ V1))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V6))))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ V2)))))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V3 @ ((cProduct_Type.Pair @ V5) @ (^[V6]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V5))))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))))))) @ ((cHOL.implies @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural))))))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V4) @ V5))) @ ((V2 @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V5) @ cCode_Numeral.one_natural_inst.one_natural)))) @ ((cProduct_Type.Pair @ V3) @ ((cProduct_Type.Pair @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.term_of_unknown_inst.term_of_unknown,((c== @ cQuickcheck_Exhaustive.term_of_unknown_inst.term_of_unknown) @ cQuickcheck_Exhaustive.term_of_unknown_inst.term_of_unknown))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (call @ (^[V3]: ((V0 @ V3) @ cList.list.Nil)))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((V0 @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((V0 @ V3) @ ((cList.list.Cons @ V4) @ V5)))))))))) @ ((V0 @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.pelims,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ V1)) @ V2)) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V2) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil))) @ V3))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ V4)) @ ((c==> @ ((cHOL.eq @ V1) @ ((cList.list.Cons @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ V2) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6))) @ ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ V3))))))))))) @ V3)))))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.psimps_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2)))) @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ (^[V3]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V3))) @ cOption.option.Some) @ (V0 @ V3)))) @ V2))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.psimps_1,(call @ (^[V0]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil))) @ ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets @ V0) @ cList.list.Nil)) @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset))))))
(TQuickcheck_Exhaustive.three_valued.Abs_three_valued_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set))) @ (V0 @ (cQuickcheck_Exhaustive.Abs_three_valued @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Exhaustive.three_valued.Abs_three_valued_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.Abs_three_valued @ V0)) @ (cQuickcheck_Exhaustive.Abs_three_valued @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Exhaustive.three_valued.Rep_three_valued_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Exhaustive.Rep_three_valued @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.Rep_three_valued_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Exhaustive.Rep_three_valued @ V0)) @ (cQuickcheck_Exhaustive.Rep_three_valued @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Exhaustive.three_valued.arity_size_three_valued,(cNat.size_class @ cTYPE))
(TQuickcheck_Exhaustive.typerep_unknown_inst.typerep_unknown,((c== @ cQuickcheck_Exhaustive.typerep_unknown_inst.typerep_unknown) @ cQuickcheck_Exhaustive.typerep_unknown_inst.typerep_unknown))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_def,((c== @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec) @ (^[V0]: (^[V1]: (cHOL.The @ (^[V2]: (((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set @ V0) @ V1) @ V2)))))))
(TQuickcheck_Narrowing.narrowing_term.Narrowing_variable_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V0) @ V1)) @ (cQuickcheck_Narrowing.Abs_narrowing_term @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V0)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V1))))))))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cRecord.tuple_isomorphism.tuple_isomorphism_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))) @ (V1 @ V0))))))))
(TRings.classrel_linordered_semiring_ordered_cancel_semiring,(cRings.ordered_cancel_semiring_class @ cTYPE))
(TRings.classrel_linordered_semiring_ordered_comm_monoid_add,(cGroups.ordered_comm_monoid_add_class @ cTYPE))
(TRings.linordered_ring_strict_class.mult_le_cancel_left_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ V2) @ V1))))))))))
(TRings.linordered_ring_strict_class.mult_le_cancel_left_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TRings.linordered_semiring_class.linordered_semiring_axioms,(((((cRings.class.linordered_semiring @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.linordered_semiring_strict_class.mult_left_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V2))))))))))
(TRings.linordered_semiring_strict_class.zero_less_mult_pos2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0))))))))
(TSemiring_Normalization.field_class.normalizing_field_rules_2,(call @ (^[V0]: ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0)))))
(TSemiring_Normalization.field_class.normalizing_field_rules_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ (cFields.inverse_class.inverse @ V1))))))))
(TSet_Interval.complete_lattice_class.Sup_greaterThanAtLeast,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cOrderings.top_class.top)) @ ((cHOL.eq @ (cComplete_Lattices.Sup_class.Sup @ (cSet_Interval.ord_class.greaterThan @ V0))) @ cOrderings.top_class.top)))))
(TSet_Interval.dense_linorder.greaterThanLessThan_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V2) @ V3))) @ ((V0 @ V3) @ V2))))))))))))
(TSet_Interval.ordered_ab_group_add.image_uminus_greaterThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ ((cSet_Interval.ord.greaterThan @ V5) @ V6))) @ ((cSet_Interval.ord.lessThan @ V5) @ (V3 @ V6)))))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.UNION_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: (cFinite_Set.finite @ (V1 @ V3))))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V3]: ((cSet.Ball @ V0) @ (^[V4]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (V1 @ V3)) @ (V1 @ V4))) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ V1))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ (V1 @ V3)))) @ V0))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ V2)))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (cBig_Operators.comm_monoid_mult_class.setprod @ V1)) @ V0)))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.union_disjoint,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod_Union_disjoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: (cFinite_Set.finite @ V2)))) @ ((c==> @ ((cSet.Ball @ V0) @ (^[V2]: ((cSet.Ball @ V0) @ (^[V3]: ((cHOL.implies @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3))) @ ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V3)) @ cOrderings.bot_class.bot))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V1) @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (cBig_Operators.comm_monoid_mult_class.setprod @ V1)) @ V0)))))))))
(TBig_Operators.linorder_class.min_max.distrib_lattice_axioms,((((cLattices.class.distrib_lattice @ cOrderings.ord_class.min) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cOrderings.ord_class.max))
(TBig_Operators.linorder_class.min_max.semilattice_inf_axioms,(((cLattices.class.semilattice_inf @ cOrderings.ord_class.min) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TBig_Operators.linorder_class.min_max.semilattice_sup_axioms,(((cLattices.class.semilattice_sup @ cOrderings.ord_class.max) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TBig_Operators.semilattice_inf_class.Inf_fin.insert_not_elem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_inf_class.Inf_fin @ ((cSet.insert @ V1) @ V0))) @ ((cLattices.inf_class.inf @ V1) @ (cBig_Operators.semilattice_inf_class.Inf_fin @ V0)))))))))))
(TBig_Operators.semilattice_sup_class.Sup_fin.insert_not_elem,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cSet.member @ V1) @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cBig_Operators.semilattice_sup_class.Sup_fin @ ((cSet.insert @ V1) @ V0))) @ ((cLattices.sup_class.sup @ V1) @ (cBig_Operators.semilattice_sup_class.Sup_fin @ V0)))))))))))
(TComplete_Lattices.class.complete_distrib_lattice_axioms_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V3 @ V4) @ (V0 @ V5))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V5) @ (^[V6]: ((V3 @ V4) @ V6))))))))) @ (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((V2 @ V4) @ (V1 @ V5))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V5) @ (^[V6]: ((V2 @ V4) @ V6)))))))))))))))))))
(TComplete_Lattices.classrel_complete_lattice_bounded_lattice,(cLattices.bounded_lattice_class @ cTYPE))
(TComplete_Lattices.complete_boolean_algebra_class.uminus_INF,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (cGroups.uminus_class.uminus @ (V1 @ V2))))))))))
(TComplete_Lattices.complete_boolean_algebra_class.uminus_Inf,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cComplete_Lattices.Inf_class.Inf @ V0))) @ (cComplete_Lattices.Sup_class.Sup @ ((cSet.image @ cGroups.uminus_class.uminus) @ V0))))))
(TComplete_Lattices.complete_boolean_algebra_class.uminus_SUP,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V2]: (V1 @ V2))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V2]: (cGroups.uminus_class.uminus @ (V1 @ V2))))))))))
(TComplete_Lattices.complete_boolean_algebra_class.uminus_Sup,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cComplete_Lattices.Sup_class.Sup @ V0))) @ (cComplete_Lattices.Inf_class.Inf @ ((cSet.image @ cGroups.uminus_class.uminus) @ V0))))))
(TComplete_Lattices.complete_distrib_lattice.INF_sup_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V5 @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V12]: (V9 @ V12)))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V10) @ (^[V12]: (V11 @ V12))))) @ (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V8) @ (^[V12]: (((cComplete_Lattices.complete_lattice.INFI @ V0) @ V10) @ (^[V13]: ((V5 @ (V9 @ V12)) @ (V11 @ V13)))))))))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.SUP_inf_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((V2 @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: (V9 @ V12)))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V10) @ (^[V12]: (V11 @ V12))))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V8) @ (^[V12]: (((cComplete_Lattices.complete_lattice.SUPR @ V1) @ V10) @ (^[V13]: ((V2 @ (V9 @ V12)) @ (V11 @ V13)))))))))))))))))))))))))))))))))
(TComplete_Partial_Order.ccpo_class.ccpo_class.iteratesp_dict,((c== @ cComplete_Partial_Order.ccpo_class.iteratesp) @ ((cComplete_Partial_Order.ccpo.iteratesp @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq)))
(TFields.linordered_field_class.inverse_negative_imp_negative,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ cGroups.zero_class.zero)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero))))))
(TFields.linordered_field_class.inverse_positive_imp_positive,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cFields.inverse_class.inverse @ V0))) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0))))))
(TFields.linordered_field_class.negative_imp_inverse_negative,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ cGroups.zero_class.zero)))))
(TFields.linordered_field_class.positive_imp_inverse_positive,(call @ (^[V0]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cFields.inverse_class.inverse @ V0))))))
(TFields.linordered_field_inverse_zero.zero_less_divide_1_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V5) @ ((V1 @ V3) @ V12))) @ ((V10 @ V5) @ V12))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.divide_le_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cFields.inverse_class.divide @ V2) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V2) @ V0)))))))))))
(TFields.linordered_field_inverse_zero_class.divide_less_eq_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ V0))) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)))))))))
(TFields.linordered_field_inverse_zero_class.inverse_le_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V0)) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ V0))))))
(TFields.linordered_field_inverse_zero_class.inverse_less_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ (cFields.inverse_class.inverse @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cOrderings.ord_class.less @ V1) @ V0))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ V1)))))))))
(TFields.linordered_field_inverse_zero_class.less_divide_eq_1,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V1) @ V0))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ V1)))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.add_less_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5))) @ ((V2 @ V4) @ V5))))))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.max_add_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ (((cOrderings.ord.max @ V1) @ V3) @ V4)) @ V5)) @ (((cOrderings.ord.max @ V1) @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V5)))))))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.min_add_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ (((cOrderings.ord.min @ V1) @ V3) @ V4)) @ V5)) @ (((cOrderings.ord.min @ V1) @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V5)))))))))))))))))
(TGroups.ordered_cancel_ab_semigroup_add.add_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ ((V0 @ V5) @ V3)) @ ((V0 @ V5) @ V4)))))))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.add_diff_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V2) @ V1)) @ V0))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.diff_add_assoc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V2) @ V1)) @ V0)) @ ((cGroups.plus_class.plus @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0)))))))))))
(TGroups.ordered_comm_monoid_add_class.add_strict_increasing2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ V1) @ V2)) @ ((cOrderings.ord_class.less @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2)))))))))))
(TLattices.semilattice_inf_class.inf.semilattice_order_axioms,(((cLattices.semilattice_order @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TLattices.semilattice_sup_class.sup.semilattice_order_axioms,(((cLattices.semilattice_order @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TPartial_Function.option.partial_function_definitions_axioms,((cPartial_Function.partial_function_definitions @ (cPartial_Function.flat_ord @ cOption.option.None)) @ (cPartial_Function.flat_lub @ cOption.option.None)))
(TQuickcheck_Exhaustive.check_all_bool_inst.enum_term_of_bool,((c== @ cQuickcheck_Exhaustive.check_all_bool_inst.enum_term_of_bool) @ cQuickcheck_Exhaustive.check_all_bool_inst.enum_term_of_bool))
(TQuickcheck_Exhaustive.check_all_char_inst.enum_term_of_char,((c== @ cQuickcheck_Exhaustive.check_all_char_inst.enum_term_of_char) @ cQuickcheck_Exhaustive.check_all_char_inst.enum_term_of_char))
(TQuickcheck_Exhaustive.check_all_prod_inst.enum_term_of_prod,((c== @ cQuickcheck_Exhaustive.check_all_prod_inst.enum_term_of_prod) @ cQuickcheck_Exhaustive.check_all_prod_inst.enum_term_of_prod))
(TQuickcheck_Exhaustive.check_all_unit_inst.enum_term_of_unit,((c== @ cQuickcheck_Exhaustive.check_all_unit_inst.enum_term_of_unit) @ cQuickcheck_Exhaustive.check_all_unit_inst.enum_term_of_unit))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ V1))) @ ((c==> @ ((cHOL.eq @ (V2 @ ((cProduct_Type.Pair @ V1) @ (^[V4]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V1))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V0) @ V1)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V1) @ cCode_Numeral.one_integer_inst.one_integer))))) @ cOption.option.Some) @ (V2 @ ((cProduct_Type.Pair @ V1) @ (^[V4]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V1)))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V6))))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_graph.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1))) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ V1))) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V0) @ V1)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V2 @ ((cProduct_Type.Pair @ V1) @ (^[V4]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V1))))) @ (V3 @ ((cProduct_Type.Pair @ V2) @ ((cProduct_Type.Pair @ V0) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.pinduct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V0) @ V1))) @ ((c==> @ (call @ (^[V3]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V3) @ cList.list.Nil))) @ ((V2 @ V3) @ cList.list.Nil))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((c==> @ ((V2 @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((V2 @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5))) @ ((cHOL.eq @ V2) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5))))))))))))))))
(TQuickcheck_Exhaustive.three_valued.Abs_three_valued_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set))) @ ((cHOL.eq @ (cQuickcheck_Exhaustive.Rep_three_valued @ (cQuickcheck_Exhaustive.Abs_three_valued @ V0))) @ V0)))))
(TQuickcheck_Exhaustive.three_valued.Rep_three_valued_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Exhaustive.Abs_three_valued @ (cQuickcheck_Exhaustive.Rep_three_valued @ V0))) @ V0))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_set_def,((c== @ cQuickcheck_Exhaustive.three_valued.three_valued_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (cInductive.complete_lattice_class.lfp @ (^[V3]: (^[V4]: (^[V5]: ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((cHOL.eq @ V5) @ V0))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V4) @ (cQuickcheck_Exhaustive.three_valued.Value @ V6))) @ ((cHOL.eq @ V5) @ (V1 @ V6)))))) @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ ((cHOL.eq @ V5) @ V2)))))))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rep_set_def,((c== @ cQuickcheck_Exhaustive.three_valued.three_valued_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: ((cHOL.disj @ ((cHOL.eq @ V1) @ (cDatatype.In0 @ cHOL.undefined))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.Leaf @ V2))))))) @ ((cHOL.eq @ V1) @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))))))))
(TQuickcheck_Exhaustive.unknown.full_exhaustive_unknown.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.unknown.Unknown) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cQuickcheck_Exhaustive.unknown.Known @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case_def,((c== @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_case) @ (^[V0]: (cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec @ (^[V1]: (^[V2]: ((V0 @ V1) @ V2)))))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_size_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_size @ V0)) @ (cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec @ (^[V1]: (^[V2]: cNat.zero_nat_inst.zero_nat)))))))
(TQuickcheck_Narrowing.narrowing_nibble_inst.narrowing_nibble,((c== @ cQuickcheck_Narrowing.narrowing_nibble_inst.narrowing_nibble) @ cQuickcheck_Narrowing.narrowing_nibble_inst.narrowing_nibble))
(TQuickcheck_Narrowing.narrowing_option_inst.narrowing_option,((c== @ cQuickcheck_Narrowing.narrowing_option_inst.narrowing_option) @ cQuickcheck_Narrowing.narrowing_option_inst.narrowing_option))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_case_def,((c== @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_case) @ (^[V0]: (^[V1]: ((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ (^[V2]: (^[V3]: ((V0 @ V2) @ V3)))) @ (^[V2]: (^[V3]: (^[V4]: ((V1 @ V2) @ V3))))) @ cHOL.undefined) @ cHOL.undefined)))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_size_def,((c== @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_size) @ ((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat))) @ (^[V0]: (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_case_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_case) @ (^[V0]: (((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1 @ (^[V1]: (^[V2]: (V0 @ V1)))) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_size_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_size) @ (((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1 @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TQuickcheck_Narrowing.term_of_property_inst.term_of_property,((c== @ cQuickcheck_Narrowing.term_of_property_inst.term_of_property) @ cQuickcheck_Narrowing.term_of_property_inst.term_of_property))
(TQuickcheck_Narrowing.typerep_property_inst.typerep_property,((c== @ cQuickcheck_Narrowing.typerep_property_inst.typerep_property) @ cQuickcheck_Narrowing.typerep_property_inst.typerep_property))
(TRecord.equal_tuple_isomorphism_inst.equal_tuple_isomorphism,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TRings.classrel_linordered_idom_linordered_semiring_1_strict,(cRings.linordered_semiring_1_strict_class @ cTYPE))
(TRings.classrel_linordered_ring_strict_ring_no_zero_divisors,(cRings.ring_no_zero_divisors_class @ cTYPE))
(TRings.classrel_linordered_semiring_strict_semiring_0_cancel,(cRings.semiring_0_cancel_class @ cTYPE))
(TRings.linordered_semiring_strict_class.mult_right_le_imp_le,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less_eq @ V0) @ V2))))))))))
(TSemiring_Normalization.field_class.normalizing_field_axioms,((((((((cFields.class.field @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TSet_Interval.atLeastPlusOneLessThan_greaterThanLessThan_int,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastLessThan @ ((cInt.plus_int_inst.plus_int @ V0) @ cInt.one_int_inst.one_int)) @ V1)) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)))))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_atMost,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ (cSet_Interval.ord_class.atMost @ V0))) @ (cSet_Interval.ord_class.atLeast @ (cGroups.uminus_class.uminus @ V0))))))
(TBig_Operators.comm_monoid_add_class.setsum.cartesian_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ (V0 @ V3)) @ V1))) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (cProduct_Type.prod.prod_case @ V0)) @ ((cProduct_Type.Sigma @ V2) @ (^[V3]: V1)))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.mono_neutral_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum_cartesian_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V3]: ((cBig_Operators.comm_monoid_add_class.setsum @ (^[V4]: ((V0 @ V3) @ V4))) @ V1))) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4))))) @ ((cProduct_Type.Sigma @ V2) @ (^[V3]: V1)))))))))))
(TBig_Operators.linordered_ab_group_add_class.minus_Max_eq_Min,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cBig_Operators.linorder_class.Max @ V0))) @ (cBig_Operators.linorder_class.Min @ ((cSet.image @ cGroups.uminus_class.uminus) @ V0))))))))
(TBig_Operators.linordered_ab_group_add_class.minus_Min_eq_Max,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ (cGroups.uminus_class.uminus @ (cBig_Operators.linorder_class.Min @ V0))) @ (cBig_Operators.linorder_class.Max @ ((cSet.image @ cGroups.uminus_class.uminus) @ V0))))))))
(TComplete_Lattices.complete_lattice_class.INF_foundation_dual,((cHOL.eq @ (cComplete_Lattices.complete_lattice.SUPR @ cComplete_Lattices.Inf_class.Inf)) @ cComplete_Lattices.complete_lattice_class.INFI))
(TComplete_Lattices.complete_lattice_class.SUP_foundation_dual,((cHOL.eq @ (cComplete_Lattices.complete_lattice.INFI @ cComplete_Lattices.Sup_class.Sup)) @ cComplete_Lattices.complete_lattice_class.SUPR))
(TFields.field_inverse_zero_class.mult_divide_mult_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cFields.inverse_class.divide @ V1) @ V2))))))))))
(TFields.linordered_field_inverse_zero_class.divide_le_0_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)))))
(TFields.linordered_field_inverse_zero_class.divide_less_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ cGroups.zero_class.zero)) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)))))))))
(TFields.linordered_field_inverse_zero_class.divide_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V0) @ V2)) @ ((cFields.inverse_class.divide @ V1) @ V2)))))))))))
(TGroups.classrel_cancel_ab_semigroup_add_cancel_semigroup_add,(cGroups.cancel_semigroup_add_class @ cTYPE))
(TGroups.classrel_ordered_ab_group_add_ordered_comm_monoid_add,(cGroups.ordered_comm_monoid_add_class @ cTYPE))
(TGroups.ordered_ab_group_add_abs_class.abs_diff_triangle_ineq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cOrderings.ord_class.less_eq @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V3)))) @ ((cGroups.plus_class.plus @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V0) @ V2))) @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V1) @ V3)))))))))))))
(TGroups.ordered_ab_group_add_abs_class.abs_triangle_ineq2_sym,(call @ (^[V0]: (call @ (^[V1]: ((cOrderings.ord_class.less_eq @ ((cGroups.minus_class.minus @ (cGroups.abs_class.abs @ V0)) @ (cGroups.abs_class.abs @ V1))) @ (cGroups.abs_class.abs @ ((cGroups.minus_class.minus @ V1) @ V0))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.add_less_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V3) @ V4)) @ ((V0 @ V5) @ V4))) @ ((V2 @ V3) @ V5))))))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.max_add_distrib_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ (((cOrderings.ord.max @ V1) @ V4) @ V5))) @ (((cOrderings.ord.max @ V1) @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5)))))))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le.min_add_distrib_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((cHOL.eq @ ((V0 @ V3) @ (((cOrderings.ord.min @ V1) @ V4) @ V5))) @ (((cOrderings.ord.min @ V1) @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5)))))))))))))))))
(TGroups.ordered_cancel_ab_semigroup_add.add_strict_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_cancel_ab_semigroup_add @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ V3) @ V4)) @ ((V2 @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V5)))))))))))))))))
(TGroups.ordered_cancel_ab_semigroup_add_class.add_strict_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3)))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.add_diff_assoc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V1) @ V0)) @ V2)) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V1) @ V2)) @ V0))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.diff_add_assoc2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V1) @ V2)) @ V0)) @ ((cGroups.plus_class.plus @ ((cGroups.minus_class.minus @ V1) @ V0)) @ V2))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.diff_diff_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V2) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ ((cGroups.minus_class.minus @ ((cGroups.plus_class.plus @ V2) @ V0)) @ V1))))))))))
(TNitpick.full_exhaustive_fun_box_inst.full_exhaustive_fun_box,((c== @ cNitpick.full_exhaustive_fun_box_inst.full_exhaustive_fun_box) @ cNitpick.full_exhaustive_fun_box_inst.full_exhaustive_fun_box))
(TNitpick.partial_term_of_fun_box_inst.partial_term_of_fun_box,((c== @ cNitpick.partial_term_of_fun_box_inst.partial_term_of_fun_box) @ cNitpick.partial_term_of_fun_box_inst.partial_term_of_fun_box))
(TOrderings.order_class.dual_order.not_eq_order_implies_strict,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TPartial_Function.partial_function_definitions.fixp_induct_uc,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ (call @ (^[V7]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ V0)) @ V0) @ (^[V8]: ((V2 @ (V3 @ (V4 @ V8))) @ V7)))))) @ ((c==> @ ((c== @ V5) @ (V4 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ V1)) @ (cPartial_Function.fun_ord @ V0)) @ (^[V7]: (V2 @ (V3 @ (V4 @ V7)))))))) @ ((c==> @ (call @ (^[V7]: ((cHOL.eq @ (V2 @ (V4 @ V7))) @ V7)))) @ ((c==> @ (((cComplete_Partial_Order.ccpo.admissible @ (cPartial_Function.fun_lub @ V1)) @ (cPartial_Function.fun_ord @ V0)) @ V6)) @ ((c==> @ (call @ (^[V7]: ((c==> @ (V6 @ (V2 @ V7))) @ (V6 @ (V2 @ (V3 @ V7))))))) @ (V6 @ (V2 @ V5)))))))))))))))))))))))
(TPartial_Function.partial_function_definitions.mono_body_fixp,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cPartial_Function.partial_function_definitions @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (((cComplete_Partial_Order.monotone @ (cPartial_Function.fun_ord @ V0)) @ V0) @ (^[V4]: ((V2 @ V4) @ V3)))))) @ ((cHOL.eq @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ V1)) @ (cPartial_Function.fun_ord @ V0)) @ V2)) @ (V2 @ (((cComplete_Partial_Order.ccpo.fixp @ (cPartial_Function.fun_lub @ V1)) @ (cPartial_Function.fun_ord @ V0)) @ V2))))))))))))
(TPartial_Function.tailrec.partial_function_definitions_axioms,((cPartial_Function.partial_function_definitions @ (cPartial_Function.flat_ord @ cHOL.undefined)) @ (cPartial_Function.flat_lub @ cHOL.undefined)))
(TQuickcheck_Exhaustive.check_all_nibble_inst.check_all_nibble,((c== @ cQuickcheck_Exhaustive.check_all_nibble_inst.check_all_nibble) @ cQuickcheck_Exhaustive.check_all_nibble_inst.check_all_nibble))
(TQuickcheck_Exhaustive.check_all_option_inst.check_all_option,((c== @ cQuickcheck_Exhaustive.check_all_option_inst.check_all_option) @ cQuickcheck_Exhaustive.check_all_option_inst.check_all_option))
(TQuickcheck_Exhaustive.full_exhaustive_integer'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6))) @ ((c==> @ ((cHOL.eq @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6))))) @ cOption.option.None)) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer)))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_integer_inst.less_integer @ V5) @ V6)) @ cOption.option.None) @ (((cOption.option.option_case @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_integer_inst.plus_integer @ V6) @ cCode_Numeral.one_integer_inst.one_integer))))) @ cOption.option.Some) @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_integer_inst.term_of_integer @ V6)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_natural'_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((cQuickcheck_Exhaustive.full_exhaustive_natural'_graph @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((c==> @ ((c==> @ (cHOL.Not @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural))))))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ V6))) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ V5) @ V6)) @ cOption.option.None) @ ((cQuickcheck_Exhaustive.orelse @ (V4 @ ((cProduct_Type.Pair @ V6) @ (^[V7]: (cCode_Evaluation.term_of_natural_inst.term_of_natural @ V6))))) @ (V3 @ ((cProduct_Type.Pair @ V4) @ ((cProduct_Type.Pair @ V5) @ ((cCode_Numeral.plus_natural_inst.plus_natural @ V6) @ cCode_Numeral.one_natural_inst.one_natural)))))))))))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_sumC_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_sumC) @ (^[V0]: ((cFunDef.THE_default @ cHOL.undefined) @ (^[V1]: ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1))))))
(TQuickcheck_Exhaustive.unknown.size_unknown_inst.size_unknown,((c== @ cQuickcheck_Exhaustive.unknown.size_unknown_inst.size_unknown) @ cQuickcheck_Exhaustive.unknown.size_unknown_inst.size_unknown))
(TQuickcheck_Narrowing.narrowing_cons.Abs_narrowing_cons_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Abs_narrowing_cons @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set))) @ V1))))) @ V1))))))
(TQuickcheck_Narrowing.narrowing_cons.Rep_narrowing_cons_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Rep_narrowing_cons @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_term.Abs_narrowing_term_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Abs_narrowing_term @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1))) @ V1))))) @ V1))))))
(TQuickcheck_Narrowing.narrowing_term.Rep_narrowing_term_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Rep_narrowing_term @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_Rep_1_def,((c== @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_Rep_1) @ ((cList.list.list_rec @ (cDatatype.In0 @ cHOL.undefined)) @ (^[V0]: (^[V1]: (^[V2]: (cDatatype.In1 @ ((cDatatype.Scons @ (cQuickcheck_Narrowing.Rep_narrowing_term @ V0)) @ V2))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1_def,((c== @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (cHOL.The @ (^[V5]: ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2_def,((c== @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_2) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (cHOL.The @ (^[V5]: ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5))))))))))
(TQuickcheck_Narrowing.narrowing_type.Abs_narrowing_type_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Abs_narrowing_type @ V2))) @ ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1))) @ V1))))) @ V1))))))
(TQuickcheck_Narrowing.narrowing_type.Rep_narrowing_type_cases,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1))) @ ((c==> @ (call @ (^[V2]: ((c==> @ ((cHOL.eq @ V0) @ (cQuickcheck_Narrowing.Rep_narrowing_type @ V2))) @ V1)))) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_Rep_1_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_Rep_1) @ ((cList.list.list_rec @ (cDatatype.In0 @ cHOL.undefined)) @ (^[V0]: (^[V1]: (^[V2]: (cDatatype.In1 @ ((cDatatype.Scons @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_Rep_2 @ V0)) @ V2))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_Rep_2_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_Rep_2) @ ((cList.list.list_rec @ (cDatatype.In0 @ cHOL.undefined)) @ (^[V0]: (^[V1]: (^[V2]: (cDatatype.In1 @ ((cDatatype.Scons @ (cQuickcheck_Narrowing.Rep_narrowing_type @ V0)) @ V2))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (cHOL.The @ (^[V6]: (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_2) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (cHOL.The @ (^[V6]: (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_3) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (^[V5]: (cHOL.The @ (^[V6]: (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)))))))))))
(TRings.classrel_comm_semiring_1_cancel_comm_semiring_0_cancel,(cRings.comm_semiring_0_cancel_class @ cTYPE))
(TRings.linordered_ring_strict_class.mult_less_cancel_left_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cOrderings.ord_class.less @ V2) @ V1))))))))))
(TRings.linordered_ring_strict_class.mult_less_cancel_left_pos,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cOrderings.ord_class.less @ V1) @ V2))))))))))
(TRings.linordered_ring_strict_class.mult_strict_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V2) @ V1)) @ ((cGroups.times_class.times @ V2) @ V0)))))))))))
(TRings.linordered_semiring_strict_class.mult_le_less_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))))
(TRings.linordered_semiring_strict_class.mult_less_le_imp_less,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3)))))))))))))))
(TRings.linordered_semiring_strict_class.mult_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V2) @ V0)) @ ((cGroups.times_class.times @ V2) @ V1)))))))))))
(TSet_Interval.bounded_lattice_class.atLeastAtMost_eq_UNIV_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ cOrderings.top_class.top)) @ ((cHOL.conj @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot)) @ ((cHOL.eq @ V1) @ cOrderings.top_class.top))))))))
(TSet_Interval.ordered_ab_group_add.image_uminus_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ (((cSet_Interval.ord.atLeastAtMost @ V4) @ V6) @ V7))) @ (((cSet_Interval.ord.atLeastAtMost @ V4) @ (V3 @ V7)) @ (V3 @ V6)))))))))))))))))))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_atLeast,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ (cSet_Interval.ord_class.atLeast @ V0))) @ (cSet_Interval.ord_class.atMost @ (cGroups.uminus_class.uminus @ V0))))))
(TBig_Operators.comm_monoid_add_class.setsum.mono_neutral_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1))))))))))))
(TBig_Operators.linorder_class.Max.semilattice_order_set_axioms,(((cBig_Operators.semilattice_order_set @ cOrderings.ord_class.max) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TBig_Operators.linorder_class.Min.semilattice_order_set_axioms,(((cBig_Operators.semilattice_order_set @ cOrderings.ord_class.min) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TComplete_Lattices.class.complete_distrib_lattice_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((V0 @ V4) @ (V1 @ V5))) @ (((cComplete_Lattices.complete_lattice.INFI @ V1) @ V5) @ (^[V6]: ((V0 @ V4) @ V6))))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((V2 @ V4) @ (V3 @ V5))) @ (((cComplete_Lattices.complete_lattice.SUPR @ V3) @ V5) @ (^[V6]: ((V2 @ V4) @ V6))))))))) @ ((((cComplete_Lattices.class.complete_distrib_lattice_axioms @ V1) @ V3) @ V2) @ V0))))))))))))
(TComplete_Lattices.complete_distrib_lattice.Inf_sup_eq_top_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V5 @ (V0 @ V8)) @ V9)) @ V7)) @ ((cSet.Ball @ V8) @ (^[V10]: ((cHOL.eq @ ((V5 @ V10) @ V9)) @ V7))))))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.Sup_inf_eq_bot_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ ((V2 @ (V1 @ V8)) @ V9)) @ V6)) @ ((cSet.Ball @ V8) @ (^[V10]: ((cHOL.eq @ ((V2 @ V10) @ V9)) @ V6))))))))))))))))))))))))))
(TComplete_Lattices.complete_lattice_class.INF_UNIV_bool_expand,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.INFI @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1)))) @ ((cLattices.inf_class.inf @ (V0 @ cHOL.True)) @ (V0 @ cHOL.False))))))
(TComplete_Lattices.complete_lattice_class.SUP_UNIV_bool_expand,(call @ (^[V0]: ((cHOL.eq @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V1]: (V0 @ V1)))) @ ((cLattices.sup_class.sup @ (V0 @ cHOL.True)) @ (V0 @ cHOL.False))))))
(TComplete_Lattices.complete_linorder.complete_linorder_inf_min,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ V2) @ (cOrderings.ord.min @ V3))))))))))))))))))))
(TComplete_Lattices.complete_linorder.complete_linorder_sup_max,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_linorder @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ V5) @ (cOrderings.ord.max @ V3))))))))))))))))))))
(TFields.classrel_field_inverse_zero_division_ring_inverse_zero,(cFields.division_ring_inverse_zero_class @ cTYPE))
(TFields.division_ring_inverse_zero.inverse_nonzero_iff_nonzero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((((((cFields.class.division_ring_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((cHOL.eq @ ((cHOL.eq @ (V0 @ V8)) @ V5)) @ ((cHOL.eq @ V8) @ V5))))))))))))))))))))))
(TFields.field_inverse_zero_class.mult_divide_mult_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V1) @ V0)) @ ((cGroups.times_class.times @ V2) @ V0))) @ ((cFields.inverse_class.divide @ V1) @ V2))))))))))
(TFields.linordered_field_inverse_zero_class.divide_le_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ V0) @ V1))))))))
(TFields.linordered_field_inverse_zero_class.divide_le_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V1) @ V0)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TFields.linordered_field_inverse_zero_class.divide_less_cancel,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V0) @ V1)) @ ((cFields.inverse_class.divide @ V2) @ V1))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))) @ ((cHOL.conj @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V0))) @ (cHOL.Not @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero))))))))))))
(TFields.linordered_field_inverse_zero_class.inverse_less_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ cGroups.one_class.one)) @ ((cHOL.disj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ V0))))))
(TFields.linordered_field_inverse_zero_class.le_divide_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V1) @ V0))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0))))))))
(TFields.linordered_field_inverse_zero_class.le_divide_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V1) @ V0))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1))))))))
(TFields.linordered_field_inverse_zero_class.one_le_inverse_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.one_class.one) @ (cFields.inverse_class.inverse @ V0))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.one_class.one))))))
(TFields.linordered_field_inverse_zero_class.zero_le_divide_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V1) @ cGroups.zero_class.zero)))))))))
(TGroups.cancel_semigroup_add_class.cancel_semigroup_add_axioms,(cGroups.class.cancel_semigroup_add @ cGroups.plus_class.plus))
(TGroups.ordered_ab_group_add_class.ordered_ab_group_add_axioms,((((((cGroups.class.ordered_ab_group_add @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TGroups.ordered_ab_semigroup_add_imp_le.add_less_imp_less_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5))) @ ((V2 @ V4) @ V5))))))))))))))))
(TGroups.ordered_cancel_ab_semigroup_add_class.add_le_less_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ V3)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3)))))))))))))
(TGroups.ordered_cancel_ab_semigroup_add_class.add_less_le_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ V3)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3)))))))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.add_diff_inverse,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.minus_class.minus @ V1) @ V0))) @ V1)))))))
(TLattices.bounded_lattice_bot_class.bounded_lattice_bot_axioms,(((((cLattices.class.bounded_lattice_bot @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot))
(TLattices.bounded_lattice_top_class.bounded_lattice_top_axioms,(((((cLattices.class.bounded_lattice_top @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.top_class.top))
(TLazy_Sequence.lazy_sequence.lazy_sequence_size_overloaded_def,((c== @ cNat.size_class.size) @ (cLazy_Sequence.lazy_sequence.lazy_sequence_rec @ (^[V0]: cNat.zero_nat_inst.zero_nat))))
(TQuickcheck_Exhaustive.finite_1.full_exhaustive_finite_1.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_finite_1_inst.full_exhaustive_finite_1 @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_1.a\<__caret__sub>1) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.finite_2.full_exhaustive_finite_2.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_finite_2_inst.full_exhaustive_finite_2 @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>1) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_2.a\<__caret__sub>2) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.finite_3.full_exhaustive_finite_3.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_finite_3_inst.full_exhaustive_finite_3 @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>1) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>2) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_3.a\<__caret__sub>3) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.finite_4.full_exhaustive_finite_4.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_finite_4_inst.full_exhaustive_finite_4 @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>1) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>2) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>3) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_4.a\<__caret__sub>4) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil))))))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.finite_5.full_exhaustive_finite_5.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_finite_5_inst.full_exhaustive_finite_5 @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>1) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble1)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>2) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>3) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>4) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))) @ (V0 @ ((cProduct_Type.Pair @ cEnum.finite_5.a\<__caret__sub>5) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble3) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))) @ cList.list.Nil)))))))))) @ cOption.option.None)))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph_def,((c== @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil))) @ ((cHOL.eq @ V2) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: (cHOL.Ex @ (^[V6]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((V0 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6))))))))))))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5))) @ ((c==> @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ V2))))))))) @ V2)))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ (^[V5]: (((cOption.option.option_case @ (V2 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V3) @ V5))) @ cOption.option.Some) @ (V2 @ V5)))) @ V4))) @ ((cHOL.eq @ V1) @ ((cProduct_Type.Pair @ V2) @ ((cList.list.Cons @ V3) @ V4))))))))))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((((cQuickcheck_Exhaustive.three_valued.three_valued_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((c==> @ ((cHOL.eq @ V4) @ V0)) @ V5))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V3) @ (cQuickcheck_Exhaustive.three_valued.Value @ V6))) @ ((c==> @ ((cHOL.eq @ V4) @ (V1 @ V6))) @ V5))))) @ ((c==> @ ((c==> @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ ((c==> @ ((cHOL.eq @ V4) @ V2)) @ V5))) @ V5)))))))))))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((cHOL.eq @ (((((cQuickcheck_Exhaustive.three_valued.three_valued_rec_set @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((cHOL.eq @ V4) @ V0))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V3) @ (cQuickcheck_Exhaustive.three_valued.Value @ V5))) @ ((cHOL.eq @ V4) @ (V1 @ V5)))))) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ cQuickcheck_Exhaustive.three_valued.No_value)) @ ((cHOL.eq @ V4) @ V2))))))))))))))))
(TQuickcheck_Narrowing.narrowing_cons.Abs_narrowing_cons_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set))) @ (V0 @ (cQuickcheck_Narrowing.Abs_narrowing_cons @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.narrowing_cons.Abs_narrowing_cons_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_narrowing_cons @ V0)) @ (cQuickcheck_Narrowing.Abs_narrowing_cons @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.narrowing_cons.Rep_narrowing_cons_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Narrowing.Rep_narrowing_cons @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.narrowing_cons.Rep_narrowing_cons_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_narrowing_cons @ V0)) @ (cQuickcheck_Narrowing.Rep_narrowing_cons @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_cons.arity_size_narrowing_cons,(cNat.size_class @ cTYPE))
(TQuickcheck_Narrowing.narrowing_integer_inst.narrowing_integer,((c== @ cQuickcheck_Narrowing.narrowing_integer_inst.narrowing_integer) @ cQuickcheck_Narrowing.narrowing_integer_inst.narrowing_integer))
(TQuickcheck_Narrowing.narrowing_natural_inst.narrowing_natural,((c== @ cQuickcheck_Narrowing.narrowing_natural_inst.narrowing_natural) @ cQuickcheck_Narrowing.narrowing_natural_inst.narrowing_natural))
(TQuickcheck_Narrowing.narrowing_term.Abs_narrowing_term_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1))) @ (V0 @ (cQuickcheck_Narrowing.Abs_narrowing_term @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.narrowing_term.Abs_narrowing_term_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_narrowing_term @ V0)) @ (cQuickcheck_Narrowing.Abs_narrowing_term @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.narrowing_term.Narrowing_constructor_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V0) @ V1)) @ (cQuickcheck_Narrowing.Abs_narrowing_term @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V0))) @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_Rep_1 @ V1))))))))))
(TQuickcheck_Narrowing.narrowing_term.Rep_narrowing_term_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Narrowing.Rep_narrowing_term @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.narrowing_term.Rep_narrowing_term_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_narrowing_term @ V0)) @ (cQuickcheck_Narrowing.Rep_narrowing_term @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_term.arity_size_narrowing_term,(cNat.size_class @ cTYPE))
(TQuickcheck_Narrowing.narrowing_type.Abs_narrowing_type_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cSet.member @ V2) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1))) @ (V0 @ (cQuickcheck_Narrowing.Abs_narrowing_type @ V2)))))) @ (V0 @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.Abs_narrowing_type_inject,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1))) @ ((c==> @ ((cSet.member @ V1) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1))) @ ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_narrowing_type @ V0)) @ (cQuickcheck_Narrowing.Abs_narrowing_type @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))))
(TQuickcheck_Narrowing.narrowing_type.Rep_narrowing_type_induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cQuickcheck_Narrowing.Rep_narrowing_type @ V2))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.narrowing_type.Rep_narrowing_type_inject,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_narrowing_type @ V0)) @ (cQuickcheck_Narrowing.Rep_narrowing_type @ V1))) @ ((cHOL.eq @ V0) @ V1)))))))
(TQuickcheck_Narrowing.narrowing_type.arity_size_narrowing_type,(cNat.size_class @ cTYPE))
(TQuickcheck_Narrowing.narrowing_unknown_inst.narrowing_unknown,((c== @ cQuickcheck_Narrowing.narrowing_unknown_inst.narrowing_unknown) @ cQuickcheck_Narrowing.narrowing_unknown_inst.narrowing_unknown))
(TRecord.random_tuple_isomorphism_inst.random_tuple_isomorphism,((c== @ cRecord.random_tuple_isomorphism_inst.random_tuple_isomorphism) @ cRecord.random_tuple_isomorphism_inst.random_tuple_isomorphism))
(TRings.classrel_linordered_semiring_strict_linordered_semiring,(cRings.linordered_semiring_class @ cTYPE))
(TRings.classrel_ordered_comm_ring_ordered_cancel_comm_semiring,(cRings.ordered_cancel_comm_semiring_class @ cTYPE))
(TRings.linordered_ring_strict_class.mult_less_cancel_left_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V1)))))))))))
(TRings.linordered_ring_strict_class.mult_strict_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V1) @ V2)) @ ((cGroups.times_class.times @ V0) @ V2)))))))))))
(TRings.linordered_semiring_strict_class.mult_strict_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2)))))))))))
(TSemiring_Normalization.comm_ring_1_class.normalizing_ring_ops_2,(call @ (^[V0]: (cPure.term @ (cGroups.uminus_class.uminus @ V0)))))
(TSemiring_Normalization.comm_ring_1_class.normalizing_ring_ops_1,(call @ (^[V0]: (call @ (^[V1]: (cPure.term @ ((cGroups.minus_class.minus @ V0) @ V1)))))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_lessThan,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ (cSet_Interval.ord_class.lessThan @ V0))) @ (cSet_Interval.ord_class.greaterThan @ (cGroups.uminus_class.uminus @ V0))))))
(TBig_Operators.comm_monoid_add_class.setsum.eq_general_reverses,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V0)) @ ((cHOL.conj @ ((cSet.member @ (V1 @ V6)) @ V2)) @ ((cHOL.eq @ (V3 @ (V1 @ V6))) @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V2)) @ ((cHOL.conj @ ((cSet.member @ (V3 @ V6)) @ V0)) @ ((cHOL.conj @ ((cHOL.eq @ (V1 @ (V3 @ V6))) @ V6)) @ ((cHOL.eq @ (V4 @ (V3 @ V6))) @ (V5 @ V6)))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V5) @ V2)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V4) @ V0)))))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.union_inter_neutral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.zero_class.zero)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.plus_class.plus @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V1)))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.cartesian_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cBig_Operators.comm_monoid_mult_class.setprod @ (V0 @ V3)) @ V1))) @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (cProduct_Type.prod.prod_case @ V0)) @ ((cProduct_Type.Sigma @ V2) @ (^[V3]: V1)))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.mono_neutral_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod_cartesian_product,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V3]: ((cBig_Operators.comm_monoid_mult_class.setprod @ (^[V4]: ((V0 @ V3) @ V4))) @ V1))) @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ (cProduct_Type.prod.prod_case @ (^[V3]: (^[V4]: ((V0 @ V3) @ V4))))) @ ((cProduct_Type.Sigma @ V2) @ (^[V3]: V1)))))))))))
(TComplete_Lattices.complete_lattice_class.dual_complete_lattice,((((((((cComplete_Lattices.class.complete_lattice @ cComplete_Lattices.Sup_class.Sup) @ cComplete_Lattices.Inf_class.Inf) @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot))
(TDivides.semiring_numeral_div_class.semiring_numeral_div_axioms,(((((((((cDivides.class.semiring_numeral_div @ cGroups.times_class.times) @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.one_class.one) @ cGroups.minus_class.minus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TFields.linordered_field_inverse_zero_class.divide_less_0_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TFields.linordered_field_inverse_zero_class.one_divide_eq_0_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.ordered_ab_semigroup_add_imp_le.add_less_imp_less_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (((cGroups.class.ordered_ab_semigroup_add_imp_le @ V0) @ V1) @ V2)) @ ((c==> @ ((V2 @ ((V0 @ V3) @ V4)) @ ((V0 @ V5) @ V4))) @ ((V2 @ V3) @ V5))))))))))))))))
(TNitpick.full_exhaustive_pair_box_inst.full_exhaustive_pair_box,((c== @ cNitpick.full_exhaustive_pair_box_inst.full_exhaustive_pair_box) @ cNitpick.full_exhaustive_pair_box_inst.full_exhaustive_pair_box))
(TNitpick.partial_term_of_pair_box_inst.partial_term_of_pair_box,((c== @ cNitpick.partial_term_of_pair_box_inst.partial_term_of_pair_box) @ cNitpick.partial_term_of_pair_box_inst.partial_term_of_pair_box))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ ((cProduct_Type.Pair @ (^[V3]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V3))) @ cOption.option.Some) @ (V0 @ V3)))) @ V2)) @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cQuickcheck_Exhaustive.three_valued.three_valued_rec_set @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.No_value) @ V2))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (((((cQuickcheck_Exhaustive.three_valued.three_valued_rec_set @ V0) @ V1) @ V2) @ (cQuickcheck_Exhaustive.three_valued.Value @ V3)) @ (V1 @ V3)))))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((((cQuickcheck_Exhaustive.three_valued.three_valued_rec_set @ V0) @ V1) @ V2) @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ V0))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Exhaustive.three_valued.three_valued_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.Leaf @ V2))))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))) @ (V1 @ V0))))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rep_set.intros_3,(cQuickcheck_Exhaustive.three_valued.three_valued_rep_set @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rep_set.intros_2,(call @ (^[V0]: (cQuickcheck_Exhaustive.three_valued.three_valued_rep_set @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.Leaf @ V0)))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rep_set.intros_1,(cQuickcheck_Exhaustive.three_valued.three_valued_rep_set @ (cDatatype.In0 @ cHOL.undefined)))
(TQuickcheck_Narrowing.narrowing_cons.Abs_narrowing_cons_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set))) @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_narrowing_cons @ (cQuickcheck_Narrowing.Abs_narrowing_cons @ V0))) @ V0)))))
(TQuickcheck_Narrowing.narrowing_cons.Rep_narrowing_cons_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_narrowing_cons @ (cQuickcheck_Narrowing.Rep_narrowing_cons @ V0))) @ V0))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set_def,((c== @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set) @ (^[V0]: (cInductive.complete_lattice_class.lfp @ (^[V1]: (^[V2]: (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V4) @ V5))) @ ((cHOL.eq @ V3) @ ((V0 @ V4) @ V5))))))))))))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set_def,((c== @ cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.eq @ V1) @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3)))))))))))))
(TQuickcheck_Narrowing.narrowing_term.Abs_narrowing_term_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1))) @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_narrowing_term @ (cQuickcheck_Narrowing.Abs_narrowing_term @ V0))) @ V0)))))
(TQuickcheck_Narrowing.narrowing_term.Rep_narrowing_term_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_narrowing_term @ (cQuickcheck_Narrowing.Rep_narrowing_term @ V0))) @ V0))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_def,((c== @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (cInductive.complete_lattice_class.lfp @ (^[V4]: (^[V5]: (^[V6]: (^[V7]: (^[V8]: (^[V9]: ((cHOL.disj @ (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: ((cHOL.conj @ (cHOL.Not @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ V8) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V10) @ V11))) @ ((cHOL.eq @ V9) @ ((V0 @ V10) @ V11))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: (cHOL.Ex @ (^[V12]: ((cHOL.conj @ (cHOL.Not @ V5)) @ ((cHOL.conj @ ((cHOL.eq @ V8) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V12) @ V10))) @ ((cHOL.conj @ ((cHOL.eq @ V9) @ (((V1 @ V12) @ V10) @ V11))) @ (((((V4 @ cHOL.True) @ V10) @ V11) @ cHOL.undefined) @ cHOL.undefined))))))))))) @ ((cHOL.disj @ ((cHOL.conj @ V5) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ cList.list.Nil)) @ ((cHOL.eq @ V7) @ V2)))) @ (cHOL.Ex @ (^[V10]: (cHOL.Ex @ (^[V11]: (cHOL.Ex @ (^[V12]: (cHOL.Ex @ (^[V13]: ((cHOL.conj @ V5) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ ((cList.list.Cons @ V10) @ V12))) @ ((cHOL.conj @ ((cHOL.eq @ V7) @ ((((V3 @ V10) @ V12) @ V11) @ V13))) @ ((cHOL.conj @ (((((V4 @ cHOL.False) @ cHOL.undefined) @ cHOL.undefined) @ V10) @ V11)) @ (((((V4 @ cHOL.True) @ V12) @ V13) @ cHOL.undefined) @ cHOL.undefined)))))))))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_def,((c== @ cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ (cHOL.Not @ V1)) @ ((cHOL.eq @ V2) @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4)))))))))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ (cHOL.Not @ V1)) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V4))) @ V3)))) @ ((V0 @ cHOL.True) @ V3)))))))) @ ((cHOL.disj @ ((cHOL.conj @ V1) @ ((cHOL.eq @ V2) @ (cDatatype.In0 @ cHOL.undefined)))) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ V1) @ ((cHOL.conj @ ((cHOL.eq @ V2) @ (cDatatype.In1 @ ((cDatatype.Scons @ V3) @ V4)))) @ ((cHOL.conj @ ((V0 @ cHOL.False) @ V3)) @ ((V0 @ cHOL.True) @ V4)))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.Abs_narrowing_type_inverse,(call @ (^[V0]: ((c==> @ ((cSet.member @ V0) @ (cSet.Collect @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1))) @ ((cHOL.eq @ (cQuickcheck_Narrowing.Rep_narrowing_type @ (cQuickcheck_Narrowing.Abs_narrowing_type @ V0))) @ V0)))))
(TQuickcheck_Narrowing.narrowing_type.Rep_narrowing_type_inverse,(call @ (^[V0]: ((cHOL.eq @ (cQuickcheck_Narrowing.Abs_narrowing_type @ (cQuickcheck_Narrowing.Rep_narrowing_type @ V0))) @ V0))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: (^[V4]: (cInductive.complete_lattice_class.lfp @ (^[V5]: (^[V6]: (^[V7]: (^[V8]: (^[V9]: (^[V10]: (^[V11]: (^[V12]: (^[V13]: ((cHOL.disj @ (cHOL.Ex @ (^[V14]: (cHOL.Ex @ (^[V15]: ((cHOL.conj @ (cHOL.Not @ V6)) @ ((cHOL.conj @ (cHOL.Not @ V7)) @ ((cHOL.conj @ ((cHOL.eq @ V12) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V14))) @ ((cHOL.conj @ ((cHOL.eq @ V13) @ ((V0 @ V14) @ V15))) @ ((((((((V5 @ cHOL.True) @ cHOL.False) @ cHOL.undefined) @ cHOL.undefined) @ V14) @ V15) @ cHOL.undefined) @ cHOL.undefined)))))))))) @ ((cHOL.disj @ ((cHOL.conj @ V6) @ ((cHOL.conj @ (cHOL.Not @ V7)) @ ((cHOL.conj @ ((cHOL.eq @ V10) @ cList.list.Nil)) @ ((cHOL.eq @ V11) @ V1))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V14]: (cHOL.Ex @ (^[V15]: (cHOL.Ex @ (^[V16]: (cHOL.Ex @ (^[V17]: ((cHOL.conj @ V6) @ ((cHOL.conj @ (cHOL.Not @ V7)) @ ((cHOL.conj @ ((cHOL.eq @ V10) @ ((cList.list.Cons @ V14) @ V16))) @ ((cHOL.conj @ ((cHOL.eq @ V11) @ ((((V2 @ V14) @ V16) @ V15) @ V17))) @ ((cHOL.conj @ ((((((((V5 @ cHOL.False) @ cHOL.True) @ V14) @ V15) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined)) @ ((((((((V5 @ cHOL.True) @ cHOL.False) @ cHOL.undefined) @ cHOL.undefined) @ V16) @ V17) @ cHOL.undefined) @ cHOL.undefined))))))))))))))) @ ((cHOL.disj @ ((cHOL.conj @ (cHOL.Not @ V6)) @ ((cHOL.conj @ V7) @ ((cHOL.conj @ ((cHOL.eq @ V8) @ cList.list.Nil)) @ ((cHOL.eq @ V9) @ V3))))) @ (cHOL.Ex @ (^[V14]: (cHOL.Ex @ (^[V15]: (cHOL.Ex @ (^[V16]: (cHOL.Ex @ (^[V17]: ((cHOL.conj @ (cHOL.Not @ V6)) @ ((cHOL.conj @ V7) @ ((cHOL.conj @ ((cHOL.eq @ V8) @ ((cList.list.Cons @ V14) @ V16))) @ ((cHOL.conj @ ((cHOL.eq @ V9) @ ((((V4 @ V14) @ V16) @ V15) @ V17))) @ ((cHOL.conj @ ((((((((V5 @ cHOL.False) @ cHOL.False) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined) @ V14) @ V15)) @ ((((((((V5 @ cHOL.False) @ cHOL.True) @ V16) @ V17) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined) @ cHOL.undefined)))))))))))))))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_def,((c== @ cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set) @ (cInductive.complete_lattice_class.lfp @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cHOL.disj @ (cHOL.Ex @ (^[V4]: ((cHOL.conj @ (cHOL.Not @ V1)) @ ((cHOL.conj @ (cHOL.Not @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ V4)) @ (((V0 @ cHOL.True) @ cHOL.False) @ V4))))))) @ ((cHOL.disj @ ((cHOL.conj @ V1) @ ((cHOL.conj @ (cHOL.Not @ V2)) @ ((cHOL.eq @ V3) @ (cDatatype.In0 @ cHOL.undefined))))) @ ((cHOL.disj @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ V1) @ ((cHOL.conj @ (cHOL.Not @ V2)) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))) @ ((cHOL.conj @ (((V0 @ cHOL.False) @ cHOL.True) @ V4)) @ (((V0 @ cHOL.True) @ cHOL.False) @ V5)))))))))) @ ((cHOL.disj @ ((cHOL.conj @ (cHOL.Not @ V1)) @ ((cHOL.conj @ V2) @ ((cHOL.eq @ V3) @ (cDatatype.In0 @ cHOL.undefined))))) @ (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ (cHOL.Not @ V1)) @ ((cHOL.conj @ V2) @ ((cHOL.conj @ ((cHOL.eq @ V3) @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))) @ ((cHOL.conj @ (((V0 @ cHOL.False) @ cHOL.False) @ V4)) @ (((V0 @ cHOL.False) @ cHOL.True) @ V5))))))))))))))))))))
(TQuickcheck_Narrowing.three_valued.narrowing_three_valued.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Exhaustive.three_valued.Unknown_value)) @ ((cQuickcheck_Narrowing.sum @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Exhaustive.three_valued.Value)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)) @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Exhaustive.three_valued.No_value)))))
(TRecord.isomorphic_tuple.iso_tuple_surjective_proof_assist_step,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ (((cRecord.iso_tuple_surjective_proof_assist @ V1) @ V2) @ ((cFun.comp @ (cRecord.iso_tuple_fst @ V0)) @ V3))) @ ((c==> @ (((cRecord.iso_tuple_surjective_proof_assist @ V1) @ V4) @ ((cFun.comp @ (cRecord.iso_tuple_snd @ V0)) @ V3))) @ (((cRecord.iso_tuple_surjective_proof_assist @ V1) @ (((cRecord.iso_tuple_cons @ V0) @ V2) @ V4)) @ V3)))))))))))))))
(TRecord.tuple_isomorphism.tuple_isomorphism_size_overloaded_def,((c== @ cNat.size_class.size) @ (cRecord.tuple_isomorphism.tuple_isomorphism_rec @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat)))))
(TRings.linordered_ring_strict_class.mult_less_cancel_right_disj,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V2) @ V0)))))))))))
(TRings.linordered_semiring_1_class.linordered_semiring_1_axioms,((((((cRings.class.linordered_semiring_1 @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.zero_class.zero) @ cGroups.times_class.times) @ cGroups.one_class.one))
(TRings.linordered_semiring_strict_class.mult_less_imp_less_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V2))))))))))
(TRings.ordered_comm_semiring_class.ordered_comm_semiring_axioms,(((((cRings.class.ordered_comm_semiring @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.ring_no_zero_divisors_class.ring_no_zero_divisors_axioms,(((((cRings.class.ring_no_zero_divisors @ cGroups.times_class.times) @ cGroups.zero_class.zero) @ cGroups.plus_class.plus) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TSet_Interval.ordered_ab_group_add.image_uminus_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ ((((cSet_Interval.ord.atLeastLessThan @ V4) @ V5) @ V6) @ V7))) @ ((((cSet_Interval.ord.greaterThanAtMost @ V4) @ V5) @ (V3 @ V7)) @ (V3 @ V6)))))))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.mono_neutral_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1))))))))))))
(TBig_Operators.linordered_ab_semigroup_add_class.add_Max_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V1) @ (cBig_Operators.linorder_class.Max @ V0))) @ (cBig_Operators.linorder_class.Max @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cGroups.plus_class.plus @ V1) @ V3))) @ ((cSet.member @ V3) @ V0)))))))))))))))
(TBig_Operators.linordered_ab_semigroup_add_class.add_Min_commute,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cOrderings.bot_class.bot))) @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V1) @ (cBig_Operators.linorder_class.Min @ V0))) @ (cBig_Operators.linorder_class.Min @ (cSet.Collect @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V2) @ ((cGroups.plus_class.plus @ V1) @ V3))) @ ((cSet.member @ V3) @ V0)))))))))))))))
(TFields.field_inverse_zero_class.mult_divide_mult_cancel_left_if,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cFields.inverse_class.divide @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))) @ (((cHOL.If @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V1) @ V2))))))))))
(TFields.linordered_field_inverse_zero.field_le_mult_one_interval,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: (call @ (^[V13]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((c==> @ (call @ (^[V14]: ((c==> @ ((V10 @ V5) @ V14)) @ ((c==> @ ((V10 @ V14) @ V3)) @ ((V9 @ ((V2 @ V14) @ V12)) @ V13)))))) @ ((V9 @ V12) @ V13))))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.divide_left_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ cGroups.zero_class.zero)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.times_class.times @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V2) @ V0)) @ ((cFields.inverse_class.divide @ V2) @ V1))))))))))))
(TFields.linordered_field_inverse_zero_class.divide_less_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V1) @ V0)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TFields.linordered_field_inverse_zero_class.divide_less_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cFields.inverse_class.divide @ V1) @ V0)) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TFields.linordered_field_inverse_zero_class.less_divide_eq_1_neg,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V1) @ V0))) @ ((cOrderings.ord_class.less @ V1) @ V0))))))))
(TFields.linordered_field_inverse_zero_class.less_divide_eq_1_pos,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ ((cFields.inverse_class.divide @ V1) @ V0))) @ ((cOrderings.ord_class.less @ V0) @ V1))))))))
(TFields.linordered_field_inverse_zero_class.one_less_inverse_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.one_class.one) @ (cFields.inverse_class.inverse @ V0))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.one_class.one))))))
(TFields.linordered_field_inverse_zero_class.zero_eq_1_divide_iff,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0))) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TFields.linordered_field_inverse_zero_class.zero_le_divide_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)))))
(TFields.linordered_field_inverse_zero_class.zero_less_divide_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ V0) @ V1))) @ ((cHOL.disj @ ((cHOL.conj @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V1))) @ ((cHOL.conj @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V1) @ cGroups.zero_class.zero)))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_le_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2)))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_le_imp_le_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cOrderings.ord_class.less_eq @ V1) @ V2)))))))))
(TGroups.ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.eq @ ((cHOL.eq @ ((cGroups.minus_class.minus @ V1) @ V0)) @ V2)) @ ((cHOL.eq @ V1) @ ((cGroups.plus_class.plus @ V2) @ V0))))))))))))
(THilbert_Choice.finite_mono_remains_stable_implies_strict_prefix,(call @ (^[V0]: ((c==> @ (cFinite_Set.finite @ ((cSet.image @ V0) @ cOrderings.top_class.top))) @ ((c==> @ (cOrderings.order_class.mono @ V0)) @ ((c==> @ (cHOL.All @ (^[V1]: ((cHOL.implies @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ (cNat.Suc @ V1)))) @ ((cHOL.eq @ (V0 @ (cNat.Suc @ V1))) @ (V0 @ (cNat.Suc @ (cNat.Suc @ V1)))))))) @ (cHOL.Ex @ (^[V1]: ((cHOL.conj @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V1)) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V1)) @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V3) @ V2)) @ ((cOrderings.ord_class.less @ (V0 @ V3)) @ (V0 @ V2)))))))))) @ (cHOL.All @ (^[V2]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V1) @ V2)) @ ((cHOL.eq @ (V0 @ V1)) @ (V0 @ V2))))))))))))))
(TLattices.bounded_semilattice_inf_top_class.inf_top.comm_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ cOrderings.top_class.top)) @ V0))))
(TLattices.bounded_semilattice_inf_top_class.inf_top.left_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ cOrderings.top_class.top) @ V0)) @ V0))))
(TLattices.bounded_semilattice_sup_bot_class.sup_bot.comm_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ cOrderings.bot_class.bot)) @ V0))))
(TLattices.bounded_semilattice_sup_bot_class.sup_bot.left_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ cOrderings.bot_class.bot) @ V0)) @ V0))))
(TLattices.semilattice_inf_class.inf.semilattice_strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1)))))))))
(TLattices.semilattice_sup_class.sup.semilattice_strict_iff_order,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ (cHOL.Not @ ((cHOL.eq @ V1) @ V0)))))))))
(TQuickcheck_Exhaustive.check_all_nibble_inst.enum_term_of_nibble,((c== @ cQuickcheck_Exhaustive.check_all_nibble_inst.enum_term_of_nibble) @ cQuickcheck_Exhaustive.check_all_nibble_inst.enum_term_of_nibble))
(TQuickcheck_Exhaustive.check_all_option_inst.enum_term_of_option,((c== @ cQuickcheck_Exhaustive.check_all_option_inst.enum_term_of_option) @ cQuickcheck_Exhaustive.check_all_option_inst.enum_term_of_option))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets.termination,(call @ (^[V0]: ((c==> @ (cWellfounded.wf @ V0)) @ ((c==> @ (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cSet.member @ ((cProduct_Type.Pair @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V1 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V2) @ V4))) @ cOption.option.Some) @ (V1 @ V4)))) @ V3)) @ ((cProduct_Type.Pair @ V1) @ ((cList.list.Cons @ V2) @ V3)))) @ V0)))))))) @ (cHOL.All @ (^[V1]: ((cWellfounded.accp @ cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel) @ V1))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil))) @ ((c==> @ ((cHOL.eq @ V1) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))) @ V2))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6)))) @ ((c==> @ ((cHOL.eq @ V1) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ V2)))))))))))) @ V2))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ cList.list.Nil))) @ ((cHOL.eq @ V1) @ (V3 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))))) @ (cHOL.Ex @ (^[V2]: (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: (cHOL.Ex @ (^[V5]: ((cHOL.conj @ ((cHOL.eq @ V0) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))) @ ((cHOL.conj @ ((cHOL.eq @ V1) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ (V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5))))))))))))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_rel @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((V2 @ ((cProduct_Type.Pair @ (^[V6]: (((cOption.option.option_case @ (V3 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V4) @ V6))) @ cOption.option.Some) @ (V3 @ V6)))) @ V5)) @ ((cProduct_Type.Pair @ V3) @ ((cList.list.Cons @ V4) @ V5)))))))))) @ ((V2 @ V0) @ V1))))))))))
(TQuickcheck_Exhaustive.three_valued.three_valued_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Exhaustive.three_valued.three_valued_rep_set @ V0)) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V2]: (V1 @ (cDatatype.In1 @ (cDatatype.In0 @ (cDatatype.Leaf @ V2))))))) @ ((c==> @ (V1 @ (cDatatype.In1 @ (cDatatype.In1 @ cHOL.undefined)))) @ (V1 @ V0))))))))))
(TQuickcheck_Narrowing.narrowing_finite_1_inst.narrowing_finite_1,((c== @ cQuickcheck_Narrowing.narrowing_finite_1_inst.narrowing_finite_1) @ cQuickcheck_Narrowing.narrowing_finite_1_inst.narrowing_finite_1))
(TQuickcheck_Narrowing.narrowing_finite_2_inst.narrowing_finite_2,((c== @ cQuickcheck_Narrowing.narrowing_finite_2_inst.narrowing_finite_2) @ cQuickcheck_Narrowing.narrowing_finite_2_inst.narrowing_finite_2))
(TQuickcheck_Narrowing.narrowing_finite_3_inst.narrowing_finite_3,((c== @ cQuickcheck_Narrowing.narrowing_finite_3_inst.narrowing_finite_3) @ cQuickcheck_Narrowing.narrowing_finite_3_inst.narrowing_finite_3))
(TQuickcheck_Narrowing.narrowing_finite_4_inst.narrowing_finite_4,((c== @ cQuickcheck_Narrowing.narrowing_finite_4_inst.narrowing_finite_4) @ cQuickcheck_Narrowing.narrowing_finite_4_inst.narrowing_finite_4))
(TQuickcheck_Narrowing.narrowing_finite_5_inst.narrowing_finite_5,((c== @ cQuickcheck_Narrowing.narrowing_finite_5_inst.narrowing_finite_5) @ cQuickcheck_Narrowing.narrowing_finite_5_inst.narrowing_finite_5))
(TRecord.isomorphic_tuple.iso_tuple_fst_update_accessor_eq_assist,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ ((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_fst @ V0))) @ (((cRecord.iso_tuple_cons @ V0) @ V3) @ V7)) @ V4) @ (((cRecord.iso_tuple_cons @ V0) @ V5) @ V7)) @ V6))))))))))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_snd_update_accessor_eq_assist,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((((((cRecord.iso_tuple_update_accessor_eq_assist @ ((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_snd @ V0))) @ (((cRecord.iso_tuple_cons @ V0) @ V7) @ V3)) @ V4) @ (((cRecord.iso_tuple_cons @ V0) @ V7) @ V5)) @ V6))))))))))))))))))))
(TRecord.term_of_tuple_isomorphism_inst.term_of_tuple_isomorphism,((c== @ cRecord.term_of_tuple_isomorphism_inst.term_of_tuple_isomorphism) @ cRecord.term_of_tuple_isomorphism_inst.term_of_tuple_isomorphism))
(TRecord.typerep_tuple_isomorphism_inst.typerep_tuple_isomorphism,((c== @ cRecord.typerep_tuple_isomorphism_inst.typerep_tuple_isomorphism) @ cRecord.typerep_tuple_isomorphism_inst.typerep_tuple_isomorphism))
(TRings.linordered_semiring_strict_class.mult_less_imp_less_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((c==> @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V1)) @ ((cOrderings.ord_class.less @ V0) @ V2))))))))))
(TSemiring_Normalization.comm_ring_1_class.normalizing_ring_rules_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.minus_class.minus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ (cGroups.uminus_class.uminus @ V1))))))))
(TSemiring_Normalization.comm_ring_1_class.normalizing_ring_rules_1,(call @ (^[V0]: ((cHOL.eq @ (cGroups.uminus_class.uminus @ V0)) @ ((cGroups.times_class.times @ (cGroups.uminus_class.uminus @ cGroups.one_class.one)) @ V0)))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_ops_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (cPure.term @ V1)))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_ops_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (cPure.term @ V3)))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_ops_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (cPure.term @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_ops_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (cPure.term @ ((V0 @ V4) @ V5))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_ops_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ (cPure.term @ ((V2 @ V4) @ V5))))))))))))))))
(TSet_Interval.dense_linorder_class.greaterThanLessThan_empty_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ cOrderings.bot_class.bot)) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TBig_Operators.comm_monoid_mult_class.setprod.eq_general_reverses,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V0)) @ ((cHOL.conj @ ((cSet.member @ (V1 @ V6)) @ V2)) @ ((cHOL.eq @ (V3 @ (V1 @ V6))) @ V6)))))) @ ((c==> @ (call @ (^[V6]: ((c==> @ ((cSet.member @ V6) @ V2)) @ ((cHOL.conj @ ((cSet.member @ (V3 @ V6)) @ V0)) @ ((cHOL.conj @ ((cHOL.eq @ (V1 @ (V3 @ V6))) @ V6)) @ ((cHOL.eq @ (V4 @ (V3 @ V6))) @ (V5 @ V6)))))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V5) @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V4) @ V0)))))))))))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.union_inter_neutral,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ ((cSet.Ball @ ((cLattices.inf_class.inf @ V0) @ V1)) @ (^[V3]: ((cHOL.eq @ (V2 @ V3)) @ cGroups.one_class.one)))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ ((cLattices.sup_class.sup @ V0) @ V1))) @ ((cGroups.times_class.times @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V1)))))))))))))
(TBig_Operators.comm_monoid_mult_class.strong_setprod_reindex_cong,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((cFun.inj_on @ V0) @ V1)) @ ((c==> @ ((cHOL.eq @ V2) @ ((cSet.image @ V0) @ V1))) @ ((c==> @ (call @ (^[V5]: ((c==> @ ((cSet.member @ V5) @ V1)) @ ((cHOL.eq @ (V3 @ V5)) @ (((cFun.comp @ V4) @ V0) @ V5)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V4) @ V2)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1))))))))))))))))
(TCode_Evaluation.term_of_lazy_sequence_inst.term_of_lazy_sequence,((c== @ cCode_Evaluation.term_of_lazy_sequence_inst.term_of_lazy_sequence) @ cCode_Evaluation.term_of_lazy_sequence_inst.term_of_lazy_sequence))
(TCode_Evaluation.typerep_lazy_sequence_inst.typerep_lazy_sequence,((c== @ cCode_Evaluation.typerep_lazy_sequence_inst.typerep_lazy_sequence) @ cCode_Evaluation.typerep_lazy_sequence_inst.typerep_lazy_sequence))
(TComplete_Lattices.complete_lattice_class.complete_lattice_axioms,((((((((cComplete_Lattices.class.complete_lattice @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))
(TComplete_Lattices.complete_linorder_class.dual_complete_linorder,((((((((cComplete_Lattices.class.complete_linorder @ cComplete_Lattices.Sup_class.Sup) @ cComplete_Lattices.Inf_class.Inf) @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot))
(TFields.linordered_field_inverse_zero_class.divide_right_mono_neg,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V2) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ ((cFields.inverse_class.divide @ V1) @ V2)) @ ((cFields.inverse_class.divide @ V0) @ V2)))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_le_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V2)))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_le_imp_le_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V1))) @ ((cOrderings.ord_class.less_eq @ V0) @ V2)))))))))
(THilbert_Choice.finite_mono_strict_prefix_implies_finite_fixpoint,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((cOrderings.ord_class.less_eq @ (V0 @ V2)) @ V1)))) @ ((c==> @ (cFinite_Set.finite @ V1)) @ ((c==> @ (cHOL.Ex @ (^[V2]: ((cHOL.conj @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V3) @ V2)) @ (cHOL.All @ (^[V4]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V4) @ V2)) @ ((cHOL.implies @ ((cNat.ord_nat_inst.less_nat @ V4) @ V3)) @ ((cOrderings.ord_class.less @ (V0 @ V4)) @ (V0 @ V3)))))))))) @ (cHOL.All @ (^[V3]: ((cHOL.implies @ ((cNat.ord_nat_inst.less_eq_nat @ V2) @ V3)) @ ((cHOL.eq @ (V0 @ V2)) @ (V0 @ V3))))))))) @ ((cHOL.eq @ (V0 @ (cFinite_Set.card @ V1))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ cOrderings.top_class.top) @ (^[V2]: (V0 @ V2))))))))))))
(TInductive.complete_lattice_class.complete_lattice_class.gfp_dict,((c== @ cInductive.complete_lattice_class.gfp) @ ((cInductive.complete_lattice.gfp @ cComplete_Lattices.Sup_class.Sup) @ cOrderings.ord_class.less_eq)))
(TInductive.complete_lattice_class.complete_lattice_class.lfp_dict,((c== @ cInductive.complete_lattice_class.lfp) @ ((cInductive.complete_lattice.lfp @ cComplete_Lattices.Inf_class.Inf) @ cOrderings.ord_class.less_eq)))
(TLattices.bounded_semilattice_inf_top_class.inf_top.monoid_axioms,((cGroups.monoid @ cLattices.inf_class.inf) @ cOrderings.top_class.top))
(TLattices.bounded_semilattice_inf_top_class.inf_top.right_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V0) @ cOrderings.top_class.top)) @ V0))))
(TLattices.bounded_semilattice_sup_bot_class.sup_bot.monoid_axioms,((cGroups.monoid @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot))
(TLattices.bounded_semilattice_sup_bot_class.sup_bot.right_neutral,(call @ (^[V0]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V0) @ cOrderings.bot_class.bot)) @ V0))))
(TQuickcheck_Exhaustive.check_all_finite_1_inst.check_all_finite_1,((c== @ cQuickcheck_Exhaustive.check_all_finite_1_inst.check_all_finite_1) @ cQuickcheck_Exhaustive.check_all_finite_1_inst.check_all_finite_1))
(TQuickcheck_Exhaustive.check_all_finite_2_inst.check_all_finite_2,((c== @ cQuickcheck_Exhaustive.check_all_finite_2_inst.check_all_finite_2) @ cQuickcheck_Exhaustive.check_all_finite_2_inst.check_all_finite_2))
(TQuickcheck_Exhaustive.check_all_finite_3_inst.check_all_finite_3,((c== @ cQuickcheck_Exhaustive.check_all_finite_3_inst.check_all_finite_3) @ cQuickcheck_Exhaustive.check_all_finite_3_inst.check_all_finite_3))
(TQuickcheck_Exhaustive.check_all_finite_4_inst.check_all_finite_4,((c== @ cQuickcheck_Exhaustive.check_all_finite_4_inst.check_all_finite_4) @ cQuickcheck_Exhaustive.check_all_finite_4_inst.check_all_finite_4))
(TQuickcheck_Exhaustive.equal_three_valued_inst.equal_three_valued,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Exhaustive.exhaustive_integer_inst.exhaustive_integer,((c== @ cQuickcheck_Exhaustive.exhaustive_integer_inst.exhaustive_integer) @ cQuickcheck_Exhaustive.exhaustive_integer_inst.exhaustive_integer))
(TQuickcheck_Exhaustive.exhaustive_natural_inst.exhaustive_natural,((c== @ cQuickcheck_Exhaustive.exhaustive_natural_inst.exhaustive_natural) @ cQuickcheck_Exhaustive.exhaustive_natural_inst.exhaustive_natural))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil)) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V4))) @ cOption.option.Some) @ (V0 @ V4)))) @ V2)) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V4))) @ cOption.option.Some) @ (V0 @ V4)))) @ V2)))) @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ V0) @ ((cList.list.Cons @ V1) @ V2))) @ (V3 @ ((cProduct_Type.Pair @ (^[V4]: (((cOption.option.option_case @ (V0 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V1) @ V4))) @ cOption.option.Some) @ (V0 @ V4)))) @ V2)))))))))))))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph.intros_1,(call @ (^[V0]: ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ V0) @ cList.list.Nil)) @ (V0 @ cQuickcheck_Random.term_syntax.valterm_emptyset)))))
(TQuickcheck_Narrowing.lazy_sequence.narrowing_lazy_sequence.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_class.narrowing) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cLazy_Sequence.lazy_sequence.lazy_sequence_of_list)) @ cQuickcheck_Narrowing.narrowing_class.narrowing)))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set @ V0) @ V1) @ V2)) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V4) @ V5))) @ ((c==> @ ((cHOL.eq @ V2) @ ((V0 @ V4) @ V5))) @ V3))))))) @ V3)))))))))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ (((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set @ V0) @ V1) @ V2)) @ (cHOL.Ex @ (^[V3]: (cHOL.Ex @ (^[V4]: ((cHOL.conj @ ((cHOL.eq @ V1) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V3) @ V4))) @ ((cHOL.eq @ V2) @ ((V0 @ V3) @ V4)))))))))))))))
(TQuickcheck_Random.random_lazy_sequence_inst.random_lazy_sequence,((c== @ cQuickcheck_Random.random_lazy_sequence_inst.random_lazy_sequence) @ cQuickcheck_Random.random_lazy_sequence_inst.random_lazy_sequence))
(TRecord.tuple_isomorphism.full_exhaustive_tuple_isomorphism.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cRecord.tuple_isomorphism.Tuple_Isomorphism @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil)))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TRings.comm_semiring_0_cancel_class.comm_semiring_0_cancel_axioms,(((cRings.class.comm_semiring_0_cancel @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TRings.comm_semiring_1_cancel_class.comm_semiring_1_cancel_axioms,((((cRings.class.comm_semiring_1_cancel @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times) @ cGroups.one_class.one))
(TRings.linordered_comm_semiring_strict.comm_mult_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((cRings.class.linordered_comm_semiring_strict @ V0) @ V1) @ V2) @ V3) @ V4)) @ ((c==> @ ((V2 @ V5) @ V6)) @ ((c==> @ ((V2 @ V3) @ V7)) @ ((V2 @ ((V4 @ V7) @ V5)) @ ((V4 @ V7) @ V6))))))))))))))))))))))
(TRings.linordered_ring_strict_class.linordered_ring_strict_axioms,((((((((cRings.class.linordered_ring_strict @ cGroups.abs_class.abs) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.plus_class.plus) @ cGroups.times_class.times))
(TSet_Interval.dense_linorder_class.greaterThanLessThan_empty_iff2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ cOrderings.bot_class.bot) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ ((cOrderings.ord_class.less_eq @ V1) @ V0)))))))
(TSet_Interval.ordered_ab_group_add.image_uminus_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ ((((cSet_Interval.ord.greaterThanAtMost @ V4) @ V5) @ V6) @ V7))) @ ((((cSet_Interval.ord.atLeastLessThan @ V4) @ V5) @ (V3 @ V7)) @ (V3 @ V6)))))))))))))))))))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_greaterThan,(call @ (^[V0]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ (cSet_Interval.ord_class.greaterThan @ V0))) @ (cSet_Interval.ord_class.lessThan @ (cGroups.uminus_class.uminus @ V0))))))
(TBig_Operators.comm_monoid_add_class.setsum.comm_monoid_set_axioms,((cBig_Operators.comm_monoid_set @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TBig_Operators.comm_monoid_add_class.setsum.mono_neutral_cong_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.zero_class.zero)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V3 @ V4)) @ (V2 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)))))))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.INF_sup_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.sup_class.sup @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: (V1 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ (^[V4]: (V3 @ V4))))) @ ((cComplete_Lattices.complete_lattice_class.INFI @ V0) @ (^[V4]: ((cComplete_Lattices.complete_lattice_class.INFI @ V2) @ (^[V5]: ((cLattices.sup_class.sup @ (V1 @ V4)) @ (V3 @ V5))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice_class.SUP_inf_distrib2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cLattices.inf_class.inf @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: (V1 @ V4)))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V2) @ (^[V4]: (V3 @ V4))))) @ ((cComplete_Lattices.complete_lattice_class.SUPR @ V0) @ (^[V4]: ((cComplete_Lattices.complete_lattice_class.SUPR @ V2) @ (^[V5]: ((cLattices.inf_class.inf @ (V1 @ V4)) @ (V3 @ V5))))))))))))))))
(TFields.linordered_field_inverse_zero_class.zero_less_divide_1_iff,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cFields.inverse_class.divide @ cGroups.one_class.one) @ V0))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TGroups.cancel_comm_monoid_add_class.cancel_comm_monoid_add_axioms,((cGroups.class.cancel_comm_monoid_add @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_less_cancel_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cOrderings.ord_class.less @ V1) @ V2)))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.max_add_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cOrderings.ord_class.max @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.max @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.min_add_distrib_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cOrderings.ord_class.min @ V0) @ V1)) @ V2)) @ ((cOrderings.ord_class.min @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TGroups.ordered_cancel_ab_semigroup_add_class.add_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V2) @ V0)) @ ((cGroups.plus_class.plus @ V2) @ V1))))))))))
(TLattices.classrel_bounded_lattice_bot_bounded_semilattice_sup_bot,(cLattices.bounded_semilattice_sup_bot_class @ cTYPE))
(TLattices.classrel_bounded_lattice_top_bounded_semilattice_inf_top,(cLattices.bounded_semilattice_inf_top_class @ cTYPE))
(TQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph.inducts,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ V0) @ V1)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((V2 @ ((cProduct_Type.Pair @ V4) @ cList.list.Nil)) @ (V4 @ cQuickcheck_Random.term_syntax.valterm_emptyset))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((cQuickcheck_Exhaustive.term_syntax.check_all_subsets_graph @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((c==> @ ((V2 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))) @ ((V2 @ ((cProduct_Type.Pair @ V4) @ ((cList.list.Cons @ V5) @ V6))) @ (V3 @ ((cProduct_Type.Pair @ (^[V7]: (((cOption.option.option_case @ (V4 @ ((cQuickcheck_Random.term_syntax.valtermify_insert @ V5) @ V7))) @ cOption.option.Some) @ (V4 @ V7)))) @ V6)))))))))))))) @ ((V2 @ V0) @ V1)))))))))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set.intros,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (((cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec_set @ V0) @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V1) @ V2)) @ ((V0 @ V1) @ V2)))))))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set.intros,(call @ (^[V0]: (call @ (^[V1]: (cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V0))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1)))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set.intros_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V6) @ V7)) @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ ((cList.list.Cons @ V4) @ V6)) @ ((((V3 @ V4) @ V6) @ V5) @ V7)))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ cList.list.Nil) @ V2))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V6) @ V4)) @ (((V1 @ V6) @ V4) @ V5))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V4) @ V5)) @ ((V0 @ V4) @ V5)))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (call @ (^[V4]: (call @ (^[V5]: (V0 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V4)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V5))))))))))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V4)) @ ((c==> @ (V1 @ V4)) @ (V0 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V5))) @ V4)))))))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ V4)) @ ((c==> @ (V0 @ V4)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V5)) @ ((c==> @ (V1 @ V5)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ ((cHOL.conj @ ((cHOL.implies @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ V2)) @ (V0 @ V2))) @ ((cHOL.implies @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V3)) @ (V1 @ V3))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set.intros_4,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ V0)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V1)) @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ (cDatatype.In1 @ ((cDatatype.Scons @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set.intros_3,(cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ (cDatatype.In0 @ cHOL.undefined)))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V0)) @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V1))) @ V0)))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V0)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V1)))))))))))
(TQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products_def,(call @ (^[V0]: ((c== @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V0)) @ (cQuickcheck_Narrowing.Abs_narrowing_type @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_Rep_1 @ V0))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set.induct,(call @ (^[V0]: ((c==> @ V0) @ V0))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set.intros_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V7) @ V8)) @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ ((cList.list.Cons @ V5) @ V7)) @ ((((V4 @ V5) @ V7) @ V6) @ V8)))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set.intros_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ cList.list.Nil) @ V3))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V7) @ V8)) @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ ((cList.list.Cons @ V5) @ V7)) @ ((((V2 @ V5) @ V7) @ V6) @ V8)))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set.intros_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ cList.list.Nil) @ V1))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set.intros_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V5)) @ ((V0 @ V5) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.induct,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (call @ (^[V6]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V6)) @ ((c==> @ (V0 @ V6)) @ (V1 @ V6)))))) @ ((c==> @ (V0 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V6)) @ ((c==> @ (V2 @ V6)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V7)) @ ((c==> @ (V0 @ V7)) @ (V0 @ (cDatatype.In1 @ ((cDatatype.Scons @ V6) @ V7)))))))))))) @ ((c==> @ (V2 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V6)) @ ((c==> @ (V1 @ V6)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V7)) @ ((c==> @ (V2 @ V7)) @ (V2 @ (cDatatype.In1 @ ((cDatatype.Scons @ V6) @ V7)))))))))))) @ ((cHOL.conj @ ((cHOL.implies @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V3)) @ (V1 @ V3))) @ ((cHOL.conj @ ((cHOL.implies @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V4)) @ (V0 @ V4))) @ ((cHOL.implies @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V5)) @ (V2 @ V5))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.intros_5,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V0)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V1)) @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ (cDatatype.In1 @ ((cDatatype.Scons @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.intros_4,(cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ (cDatatype.In0 @ cHOL.undefined)))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.intros_3,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V0)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V1)) @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ (cDatatype.In1 @ ((cDatatype.Scons @ V0) @ V1))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.intros_2,(cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ (cDatatype.In0 @ cHOL.undefined)))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.intros_1,(call @ (^[V0]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V0)) @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V0)))))
(TQuickcheck_Narrowing.partial_term_of_int_inst.partial_term_of_int,((c== @ cQuickcheck_Narrowing.partial_term_of_int_inst.partial_term_of_int) @ cQuickcheck_Narrowing.partial_term_of_int_inst.partial_term_of_int))
(TQuickcheck_Narrowing.partial_term_of_nat_inst.partial_term_of_nat,((c== @ cQuickcheck_Narrowing.partial_term_of_nat_inst.partial_term_of_nat) @ cQuickcheck_Narrowing.partial_term_of_nat_inst.partial_term_of_nat))
(TQuickcheck_Narrowing.partial_term_of_num_inst.partial_term_of_num,((c== @ cQuickcheck_Narrowing.partial_term_of_num_inst.partial_term_of_num) @ cQuickcheck_Narrowing.partial_term_of_num_inst.partial_term_of_num))
(TQuickcheck_Narrowing.partial_term_of_seq_inst.partial_term_of_seq,((c== @ cQuickcheck_Narrowing.partial_term_of_seq_inst.partial_term_of_seq) @ cQuickcheck_Narrowing.partial_term_of_seq_inst.partial_term_of_seq))
(TQuickcheck_Narrowing.partial_term_of_set_inst.partial_term_of_set,((c== @ cQuickcheck_Narrowing.partial_term_of_set_inst.partial_term_of_set) @ cQuickcheck_Narrowing.partial_term_of_set_inst.partial_term_of_set))
(TQuickcheck_Narrowing.partial_term_of_sum_inst.partial_term_of_sum,((c== @ cQuickcheck_Narrowing.partial_term_of_sum_inst.partial_term_of_sum) @ cQuickcheck_Narrowing.partial_term_of_sum_inst.partial_term_of_sum))
(TRecord.isomorphic_tuple.iso_tuple_fst_update_accessor_cong_assist,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V1) @ V2)) @ ((cRecord.iso_tuple_update_accessor_cong_assist @ ((cFun.comp @ (cRecord.iso_tuple_fst_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_fst @ V0))))))))))))
(TRecord.isomorphic_tuple.iso_tuple_snd_update_accessor_cong_assist,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cRecord.isomorphic_tuple @ V0)) @ ((c==> @ ((cRecord.iso_tuple_update_accessor_cong_assist @ V1) @ V2)) @ ((cRecord.iso_tuple_update_accessor_cong_assist @ ((cFun.comp @ (cRecord.iso_tuple_snd_update @ V0)) @ V1)) @ ((cFun.comp @ V2) @ (cRecord.iso_tuple_snd @ V0))))))))))))
(TRings.classrel_linordered_semiring_1_strict_linordered_semiring_1,(cRings.linordered_semiring_1_class @ cTYPE))
(TRings.classrel_ordered_cancel_comm_semiring_ordered_comm_semiring,(cRings.ordered_comm_semiring_class @ cTYPE))
(TSemiring_Normalization.comm_ring_1.normalizing_comm_ring_1_axioms,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((((((cRings.class.comm_ring_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_37,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ V4) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5)))) @ ((V0 @ V4) @ ((V0 @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_36,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ V4) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V5))) @ ((V0 @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_35,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ V4) @ (cNat.Suc @ V5))) @ ((V0 @ V4) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_34,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V2 @ V5) @ V6))) @ ((V2 @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_33,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ V4) @ cNat.one_nat_inst.one_nat)) @ V4)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_32,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ V4) @ cNat.zero_nat_inst.zero_nat)) @ V1)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_31,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)) @ V6)) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ ((cNat.times_nat_inst.times_nat @ V5) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_30,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((((cPower.power.power @ V1) @ V0) @ ((V0 @ V4) @ V5)) @ V6)) @ ((V0 @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V6)) @ ((((cPower.power.power @ V1) @ V0) @ V5) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_29,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V4)) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_28,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)) @ V4)) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ (cNat.Suc @ V5)))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_27,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5))) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ (cNat.Suc @ V5)))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_26,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V5)) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ V6))) @ ((((cPower.power.power @ V1) @ V0) @ V4) @ ((cNat.plus_nat_inst.plus_nat @ V5) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_25,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V4) @ ((V2 @ V5) @ V6))) @ ((V2 @ ((V2 @ V4) @ V5)) @ V6))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_24,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V4) @ V5)) @ ((V2 @ V5) @ V4))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V4) @ V5)) @ V6)) @ ((V2 @ ((V2 @ V4) @ V6)) @ V5))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V4) @ ((V2 @ V5) @ V6))) @ ((V2 @ V5) @ ((V2 @ V4) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V4) @ V5)) @ V6)) @ ((V2 @ V4) @ ((V2 @ V5) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ ((V2 @ V4) @ V5)) @ ((V2 @ V6) @ V7))) @ ((V2 @ ((V2 @ V4) @ V6)) @ ((V2 @ V5) @ V7)))))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ V5) @ ((V0 @ V4) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_18,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ ((V0 @ V4) @ V5)) @ V6))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V4) @ V5)) @ V6)) @ ((V0 @ V4) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V4) @ V5)) @ V6)) @ ((V0 @ ((V0 @ V4) @ V6)) @ V5))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V4) @ V5)) @ ((V0 @ V6) @ V7))) @ ((V0 @ V6) @ ((V0 @ ((V0 @ V4) @ V5)) @ V7)))))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V4) @ V5)) @ ((V0 @ V6) @ V7))) @ ((V0 @ V4) @ ((V0 @ V5) @ ((V0 @ V6) @ V7))))))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V0 @ V4) @ V5)) @ ((V0 @ V6) @ V7))) @ ((V0 @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V7)))))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_12,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V1)) @ V4)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_11,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V1) @ V4)) @ V4)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_10,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V3)) @ V3)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_9,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V3) @ V4)) @ V3)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ ((V2 @ V4) @ V5)) @ V6)) @ ((V2 @ ((V0 @ V4) @ V6)) @ ((V0 @ V5) @ V6)))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_7,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V0 @ V4) @ V5)) @ ((V0 @ V5) @ V4))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_6,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V4) @ V3)) @ V4)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_5,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V3) @ V4)) @ V4)))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_4,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V4) @ V4)) @ ((V0 @ ((V2 @ V1) @ V1)) @ V4))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ V4) @ ((V0 @ V5) @ V4))) @ ((V0 @ ((V2 @ V5) @ V1)) @ V4))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V4) @ V5)) @ V5)) @ ((V0 @ ((V2 @ V4) @ V1)) @ V5))))))))))))))))
(TSemiring_Normalization.comm_semiring_1.normalizing_semiring_rules_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((V2 @ ((V0 @ V4) @ V5)) @ ((V0 @ V6) @ V5))) @ ((V0 @ ((V2 @ V4) @ V6)) @ V5))))))))))))))))))
(TBig_Operators.comm_monoid_add_class.setsum.mono_neutral_cong_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.zero_class.zero)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_add_class.setsum @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_add_class.setsum @ V3) @ V1)))))))))))))))
(TBig_Operators.semilattice_inf_class.Inf_fin.semilattice_set_axioms,(cBig_Operators.semilattice_set @ cLattices.inf_class.inf))
(TBig_Operators.semilattice_sup_class.Sup_fin.semilattice_set_axioms,(cBig_Operators.semilattice_set @ cLattices.sup_class.sup))
(TComplete_Lattices.complete_linorder_class.complete_linorder_axioms,((((((((cComplete_Lattices.class.complete_linorder @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))
(TFields.linordered_field_inverse_zero.inverse_negative_iff_negative,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ (V0 @ V12)) @ V5)) @ ((V10 @ V12) @ V5))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.inverse_positive_iff_positive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V10 @ V5) @ (V0 @ V12))) @ ((V10 @ V5) @ V12))))))))))))))))))))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_less_cancel_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V2)))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.max_add_distrib_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cOrderings.ord_class.max @ V1) @ V2))) @ ((cOrderings.ord_class.max @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.min_add_distrib_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cOrderings.ord_class.min @ V1) @ V2))) @ ((cOrderings.ord_class.min @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TGroups.ordered_cancel_ab_semigroup_add_class.add_strict_right_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_fun_inst.full_exhaustive_fun,((c== @ cQuickcheck_Exhaustive.full_exhaustive_fun_inst.full_exhaustive_fun) @ cQuickcheck_Exhaustive.full_exhaustive_fun_inst.full_exhaustive_fun))
(TQuickcheck_Exhaustive.full_exhaustive_int_inst.full_exhaustive_int,((c== @ cQuickcheck_Exhaustive.full_exhaustive_int_inst.full_exhaustive_int) @ cQuickcheck_Exhaustive.full_exhaustive_int_inst.full_exhaustive_int))
(TQuickcheck_Exhaustive.full_exhaustive_nat_inst.full_exhaustive_nat,((c== @ cQuickcheck_Exhaustive.full_exhaustive_nat_inst.full_exhaustive_nat) @ cQuickcheck_Exhaustive.full_exhaustive_nat_inst.full_exhaustive_nat))
(TQuickcheck_Exhaustive.full_exhaustive_num_inst.full_exhaustive_num,((c== @ cQuickcheck_Exhaustive.full_exhaustive_num_inst.full_exhaustive_num) @ cQuickcheck_Exhaustive.full_exhaustive_num_inst.full_exhaustive_num))
(TQuickcheck_Exhaustive.full_exhaustive_seq_inst.full_exhaustive_seq,((c== @ cQuickcheck_Exhaustive.full_exhaustive_seq_inst.full_exhaustive_seq) @ cQuickcheck_Exhaustive.full_exhaustive_seq_inst.full_exhaustive_seq))
(TQuickcheck_Exhaustive.full_exhaustive_set_inst.full_exhaustive_set,((c== @ cQuickcheck_Exhaustive.full_exhaustive_set_inst.full_exhaustive_set) @ cQuickcheck_Exhaustive.full_exhaustive_set_inst.full_exhaustive_set))
(TQuickcheck_Exhaustive.full_exhaustive_sum_inst.full_exhaustive_sum,((c== @ cQuickcheck_Exhaustive.full_exhaustive_sum_inst.full_exhaustive_sum) @ cQuickcheck_Exhaustive.full_exhaustive_sum_inst.full_exhaustive_sum))
(TQuickcheck_Exhaustive.random_three_valued_inst.random_three_valued,((c== @ cQuickcheck_Exhaustive.random_three_valued_inst.random_three_valued) @ cQuickcheck_Exhaustive.random_three_valued_inst.random_three_valued))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set.inducts,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rep_set @ V0)) @ ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (V1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ V2))) @ (cDatatype.Leaf @ (cSum_Type.Inl @ V3))))))))) @ (V1 @ V0))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((cHOL.eq @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V7) @ V8))) @ ((c==> @ ((cHOL.eq @ V5) @ ((V0 @ V7) @ V8))) @ V6))))))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V9) @ V7))) @ ((c==> @ ((cHOL.eq @ V5) @ (((V1 @ V9) @ V7) @ V8))) @ ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V7) @ V8)) @ V6)))))))))) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.disj @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V6) @ V7))) @ ((cHOL.eq @ V5) @ ((V0 @ V6) @ V7)))))))) @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V8) @ V6))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ (((V1 @ V8) @ V6) @ V7))) @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V6) @ V7))))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V4) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V5) @ V2)) @ V6))) @ ((c==> @ (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: ((c==> @ ((cHOL.eq @ V4) @ ((cList.list.Cons @ V7) @ V9))) @ ((c==> @ ((cHOL.eq @ V5) @ ((((V3 @ V7) @ V9) @ V8) @ V10))) @ ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V7) @ V8)) @ ((c==> @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V9) @ V10)) @ V6))))))))))))) @ V6))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V4) @ cList.list.Nil)) @ ((cHOL.eq @ V5) @ V2))) @ (cHOL.Ex @ (^[V6]: (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: ((cHOL.conj @ ((cHOL.eq @ V4) @ ((cList.list.Cons @ V6) @ V8))) @ ((cHOL.conj @ ((cHOL.eq @ V5) @ ((((V3 @ V6) @ V8) @ V7) @ V9))) @ ((cHOL.conj @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V6) @ V7)) @ ((((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V8) @ V9)))))))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set.inducts_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V0)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (V1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V3)) @ ((c==> @ (V2 @ V3)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V4))) @ V3)))))))))) @ ((c==> @ (V2 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ V3)) @ ((c==> @ (V1 @ V3)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V4)) @ ((c==> @ (V2 @ V4)) @ (V2 @ (cDatatype.In1 @ ((cDatatype.Scons @ V3) @ V4)))))))))))) @ (V2 @ V0)))))))))))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set.inducts_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ V0)) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: (V1 @ (cDatatype.In0 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inr @ V3)))) @ (cDatatype.Leaf @ (cSum_Type.Inr @ (cSum_Type.Inl @ V4))))))))))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V3)) @ ((c==> @ (V2 @ V3)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ (cDatatype.Leaf @ (cSum_Type.Inl @ V4))) @ V3)))))))))) @ ((c==> @ (V2 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_1 @ V3)) @ ((c==> @ (V1 @ V3)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_term.narrowing_term_rep_set_2 @ V4)) @ ((c==> @ (V2 @ V4)) @ (V2 @ (cDatatype.In1 @ ((cDatatype.Scons @ V3) @ V4)))))))))))) @ (V1 @ V0)))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_narrowing_type.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_narrowing_type_inst.narrowing_narrowing_type) @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products)) @ cQuickcheck_Narrowing.narrowing_narrowing_type_list_list)))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((cHOL.eq @ V5) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V8))) @ ((c==> @ ((cHOL.eq @ V6) @ ((V0 @ V8) @ V9))) @ ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V8) @ V9)) @ V7)))))))) @ V7)))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: ((cHOL.conj @ ((cHOL.eq @ V5) @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V7))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ ((V0 @ V7) @ V8))) @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V7) @ V8)))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V6) @ V1)) @ V7))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((cHOL.eq @ V5) @ ((cList.list.Cons @ V8) @ V10))) @ ((c==> @ ((cHOL.eq @ V6) @ ((((V2 @ V8) @ V10) @ V9) @ V11))) @ ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V8) @ V9)) @ ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V10) @ V11)) @ V7))))))))))))) @ V7))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cList.list.Nil)) @ ((cHOL.eq @ V6) @ V1))) @ (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: ((cHOL.conj @ ((cHOL.eq @ V5) @ ((cList.list.Cons @ V7) @ V9))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ ((((V2 @ V7) @ V9) @ V8) @ V10))) @ ((cHOL.conj @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V7) @ V8)) @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_2 @ V0) @ V1) @ V2) @ V3) @ V4) @ V9) @ V10)))))))))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3.cases,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((c==> @ ((c==> @ ((cHOL.eq @ V5) @ cList.list.Nil)) @ ((c==> @ ((cHOL.eq @ V6) @ V3)) @ V7))) @ ((c==> @ (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: ((c==> @ ((cHOL.eq @ V5) @ ((cList.list.Cons @ V8) @ V10))) @ ((c==> @ ((cHOL.eq @ V6) @ ((((V4 @ V8) @ V10) @ V9) @ V11))) @ ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V8) @ V9)) @ ((c==> @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V10) @ V11)) @ V7))))))))))))) @ V7))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3.simps,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((cHOL.eq @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6)) @ ((cHOL.disj @ ((cHOL.conj @ ((cHOL.eq @ V5) @ cList.list.Nil)) @ ((cHOL.eq @ V6) @ V3))) @ (cHOL.Ex @ (^[V7]: (cHOL.Ex @ (^[V8]: (cHOL.Ex @ (^[V9]: (cHOL.Ex @ (^[V10]: ((cHOL.conj @ ((cHOL.eq @ V5) @ ((cList.list.Cons @ V7) @ V9))) @ ((cHOL.conj @ ((cHOL.eq @ V6) @ ((((V4 @ V7) @ V9) @ V8) @ V10))) @ ((cHOL.conj @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_1 @ V0) @ V1) @ V2) @ V3) @ V4) @ V7) @ V8)) @ (((((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_set_3 @ V0) @ V1) @ V2) @ V3) @ V4) @ V9) @ V10)))))))))))))))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.inducts_3,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V0)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V4)) @ ((c==> @ (V1 @ V4)) @ (V2 @ V4)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V4)) @ ((c==> @ (V3 @ V4)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V5)) @ ((c==> @ (V1 @ V5)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ ((c==> @ (V3 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V4)) @ ((c==> @ (V2 @ V4)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V5)) @ ((c==> @ (V3 @ V5)) @ (V3 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ (V3 @ V0))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.inducts_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V0)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V4)) @ ((c==> @ (V1 @ V4)) @ (V2 @ V4)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V4)) @ ((c==> @ (V3 @ V4)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V5)) @ ((c==> @ (V1 @ V5)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ ((c==> @ (V3 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V4)) @ ((c==> @ (V2 @ V4)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V5)) @ ((c==> @ (V3 @ V5)) @ (V3 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ (V1 @ V0))))))))))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set.inducts_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V0)) @ ((c==> @ (call @ (^[V4]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V4)) @ ((c==> @ (V1 @ V4)) @ (V2 @ V4)))))) @ ((c==> @ (V1 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V4)) @ ((c==> @ (V3 @ V4)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_2 @ V5)) @ ((c==> @ (V1 @ V5)) @ (V1 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ ((c==> @ (V3 @ (cDatatype.In0 @ cHOL.undefined))) @ ((c==> @ (call @ (^[V4]: (call @ (^[V5]: ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_1 @ V4)) @ ((c==> @ (V2 @ V4)) @ ((c==> @ (cQuickcheck_Narrowing.narrowing_type.narrowing_type_rep_set_3 @ V5)) @ ((c==> @ (V3 @ V5)) @ (V3 @ (cDatatype.In1 @ ((cDatatype.Scons @ V4) @ V5)))))))))))) @ (V2 @ V0))))))))))))))))
(TRings.classrel_ordered_cancel_comm_semiring_comm_semiring_0_cancel,(cRings.comm_semiring_0_cancel_class @ cTYPE))
(TRings.ordered_cancel_semiring_class.ordered_cancel_semiring_axioms,(((((cRings.class.ordered_cancel_semiring @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.times_class.times))
(TRings.ring_1_no_zero_divisors_class.ring_1_no_zero_divisors_axioms,((((((cRings.class.ring_1_no_zero_divisors @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TSet_Interval.ordered_ab_group_add.image_uminus_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((cGroups.class.ordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((cSet.image @ V3) @ (((cSet_Interval.ord.greaterThanLessThan @ V5) @ V6) @ V7))) @ (((cSet_Interval.ord.greaterThanLessThan @ V5) @ (V3 @ V7)) @ (V3 @ V6)))))))))))))))))))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_atLeastAtMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastAtMost @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TBig_Operators.comm_monoid_mult_class.setprod.comm_monoid_set_axioms,((cBig_Operators.comm_monoid_set @ cGroups.times_class.times) @ cGroups.one_class.one))
(TBig_Operators.comm_monoid_mult_class.setprod.mono_neutral_cong_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.one_class.one)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V3 @ V4)) @ (V2 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)))))))))))))))
(TComplete_Lattices.classrel_complete_distrib_lattice_distrib_lattice,(cLattices.distrib_lattice_class @ cTYPE))
(TComplete_Lattices.complete_distrib_lattice_class.Inf_sup_eq_top_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.sup_class.sup @ (cComplete_Lattices.Inf_class.Inf @ V0)) @ V1)) @ cOrderings.top_class.top)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ ((cLattices.sup_class.sup @ V2) @ V1)) @ cOrderings.top_class.top)))))))))
(TComplete_Lattices.complete_distrib_lattice_class.Sup_inf_eq_bot_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ ((cLattices.inf_class.inf @ (cComplete_Lattices.Sup_class.Sup @ V0)) @ V1)) @ cOrderings.bot_class.bot)) @ ((cSet.Ball @ V0) @ (^[V2]: ((cHOL.eq @ ((cLattices.inf_class.inf @ V2) @ V1)) @ cOrderings.bot_class.bot)))))))))
(TComplete_Lattices.complete_linorder_class.complete_linorder_inf_min,((cHOL.eq @ cLattices.inf_class.inf) @ cOrderings.ord_class.min))
(TComplete_Lattices.complete_linorder_class.complete_linorder_sup_max,((cHOL.eq @ cLattices.sup_class.sup) @ cOrderings.ord_class.max))
(TFields.division_ring_inverse_zero_class.inverse_nonzero_iff_nonzero,(call @ (^[V0]: ((cHOL.eq @ ((cHOL.eq @ (cFields.inverse_class.inverse @ V0)) @ cGroups.zero_class.zero)) @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.cancel_ab_semigroup_add_class.cancel_ab_semigroup_add_axioms,(cGroups.class.cancel_ab_semigroup_add @ cGroups.plus_class.plus))
(TGroups.linordered_ab_group_add_class.linordered_ab_group_add_axioms,((((((cGroups.class.linordered_ab_group_add @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_less_imp_less_left,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V0) @ V2))) @ ((cOrderings.ord_class.less @ V1) @ V2)))))))))
(TGroups.ordered_comm_monoid_add_class.ordered_comm_monoid_add_axioms,((((cGroups.class.ordered_comm_monoid_add @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TQuickcheck_Exhaustive.check_all_finite_1_inst.enum_term_of_finite_1,((c== @ cQuickcheck_Exhaustive.check_all_finite_1_inst.enum_term_of_finite_1) @ cQuickcheck_Exhaustive.check_all_finite_1_inst.enum_term_of_finite_1))
(TQuickcheck_Exhaustive.check_all_finite_2_inst.enum_term_of_finite_2,((c== @ cQuickcheck_Exhaustive.check_all_finite_2_inst.enum_term_of_finite_2) @ cQuickcheck_Exhaustive.check_all_finite_2_inst.enum_term_of_finite_2))
(TQuickcheck_Exhaustive.check_all_finite_3_inst.enum_term_of_finite_3,((c== @ cQuickcheck_Exhaustive.check_all_finite_3_inst.enum_term_of_finite_3) @ cQuickcheck_Exhaustive.check_all_finite_3_inst.enum_term_of_finite_3))
(TQuickcheck_Exhaustive.check_all_finite_4_inst.enum_term_of_finite_4,((c== @ cQuickcheck_Exhaustive.check_all_finite_4_inst.enum_term_of_finite_4) @ cQuickcheck_Exhaustive.check_all_finite_4_inst.enum_term_of_finite_4))
(TQuickcheck_Exhaustive.three_valued.three_valued_size_overloaded_def,((c== @ cNat.size_class.size) @ (((cQuickcheck_Exhaustive.three_valued.three_valued_rec @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: cNat.zero_nat_inst.zero_nat)) @ cNat.zero_nat_inst.zero_nat)))
(TQuickcheck_Narrowing.equal_narrowing_cons_inst.equal_narrowing_cons,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Narrowing.equal_narrowing_term_inst.equal_narrowing_term,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Narrowing.equal_narrowing_type_inst.equal_narrowing_type,((c== @ cHOL.equal_class.equal) @ cHOL.equal_class.equal))
(TQuickcheck_Narrowing.full_exhaustive_cfun_inst.full_exhaustive_cfun,((c== @ cQuickcheck_Narrowing.full_exhaustive_cfun_inst.full_exhaustive_cfun) @ cQuickcheck_Narrowing.full_exhaustive_cfun_inst.full_exhaustive_cfun))
(TQuickcheck_Narrowing.full_exhaustive_ffun_inst.full_exhaustive_ffun,((c== @ cQuickcheck_Narrowing.full_exhaustive_ffun_inst.full_exhaustive_ffun) @ cQuickcheck_Narrowing.full_exhaustive_ffun_inst.full_exhaustive_ffun))
(TQuickcheck_Narrowing.partial_term_of_bool_inst.partial_term_of_bool,((c== @ cQuickcheck_Narrowing.partial_term_of_bool_inst.partial_term_of_bool) @ cQuickcheck_Narrowing.partial_term_of_bool_inst.partial_term_of_bool))
(TQuickcheck_Narrowing.partial_term_of_cfun_inst.partial_term_of_cfun,((c== @ cQuickcheck_Narrowing.partial_term_of_cfun_inst.partial_term_of_cfun) @ cQuickcheck_Narrowing.partial_term_of_cfun_inst.partial_term_of_cfun))
(TQuickcheck_Narrowing.partial_term_of_char_inst.partial_term_of_char,((c== @ cQuickcheck_Narrowing.partial_term_of_char_inst.partial_term_of_char) @ cQuickcheck_Narrowing.partial_term_of_char_inst.partial_term_of_char))
(TQuickcheck_Narrowing.partial_term_of_ffun_inst.partial_term_of_ffun,((c== @ cQuickcheck_Narrowing.partial_term_of_ffun_inst.partial_term_of_ffun) @ cQuickcheck_Narrowing.partial_term_of_ffun_inst.partial_term_of_ffun))
(TQuickcheck_Narrowing.partial_term_of_list_inst.partial_term_of_list,((c== @ cQuickcheck_Narrowing.partial_term_of_list_inst.partial_term_of_list) @ cQuickcheck_Narrowing.partial_term_of_list_inst.partial_term_of_list))
(TQuickcheck_Narrowing.partial_term_of_pred_inst.partial_term_of_pred,((c== @ cQuickcheck_Narrowing.partial_term_of_pred_inst.partial_term_of_pred) @ cQuickcheck_Narrowing.partial_term_of_pred_inst.partial_term_of_pred))
(TQuickcheck_Narrowing.partial_term_of_prod_inst.partial_term_of_prod,((c== @ cQuickcheck_Narrowing.partial_term_of_prod_inst.partial_term_of_prod) @ cQuickcheck_Narrowing.partial_term_of_prod_inst.partial_term_of_prod))
(TQuickcheck_Narrowing.partial_term_of_term_inst.partial_term_of_term,((c== @ cQuickcheck_Narrowing.partial_term_of_term_inst.partial_term_of_term) @ cQuickcheck_Narrowing.partial_term_of_term_inst.partial_term_of_term))
(TQuickcheck_Narrowing.partial_term_of_unit_inst.partial_term_of_unit,((c== @ cQuickcheck_Narrowing.partial_term_of_unit_inst.partial_term_of_unit) @ cQuickcheck_Narrowing.partial_term_of_unit_inst.partial_term_of_unit))
(TRings.classrel_ordered_cancel_comm_semiring_ordered_cancel_semiring,(cRings.ordered_cancel_semiring_class @ cTYPE))
(TBig_Operators.comm_monoid_mult_class.setprod.mono_neutral_cong_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ (cFinite_Set.finite @ V0)) @ ((c==> @ ((cOrderings.ord_class.less_eq @ V1) @ V0)) @ ((c==> @ ((cSet.Ball @ ((cGroups.minus_class.minus @ V0) @ V1)) @ (^[V4]: ((cHOL.eq @ (V2 @ V4)) @ cGroups.one_class.one)))) @ ((c==> @ (call @ (^[V4]: ((c==> @ ((cSet.member @ V4) @ V1)) @ ((cHOL.eq @ (V2 @ V4)) @ (V3 @ V4)))))) @ ((cHOL.eq @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V2) @ V0)) @ ((cBig_Operators.comm_monoid_mult_class.setprod @ V3) @ V1)))))))))))))))
(TGroups.classrel_ordered_ab_group_add_ordered_ab_semigroup_add_imp_le,(cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE))
(TGroups.classrel_ordered_ab_group_add_ordered_cancel_ab_semigroup_add,(cGroups.ordered_cancel_ab_semigroup_add_class @ cTYPE))
(TGroups.ordered_ab_semigroup_add_imp_le_class.add_less_imp_less_right,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V1))) @ ((cOrderings.ord_class.less @ V0) @ V2)))))))))
(TQuickcheck_Exhaustive.full_exhaustive_bool_inst.full_exhaustive_bool,((c== @ cQuickcheck_Exhaustive.full_exhaustive_bool_inst.full_exhaustive_bool) @ cQuickcheck_Exhaustive.full_exhaustive_bool_inst.full_exhaustive_bool))
(TQuickcheck_Exhaustive.full_exhaustive_char_inst.full_exhaustive_char,((c== @ cQuickcheck_Exhaustive.full_exhaustive_char_inst.full_exhaustive_char) @ cQuickcheck_Exhaustive.full_exhaustive_char_inst.full_exhaustive_char))
(TQuickcheck_Exhaustive.full_exhaustive_list_inst.full_exhaustive_list,((c== @ cQuickcheck_Exhaustive.full_exhaustive_list_inst.full_exhaustive_list) @ cQuickcheck_Exhaustive.full_exhaustive_list_inst.full_exhaustive_list))
(TQuickcheck_Exhaustive.full_exhaustive_pred_inst.full_exhaustive_pred,((c== @ cQuickcheck_Exhaustive.full_exhaustive_pred_inst.full_exhaustive_pred) @ cQuickcheck_Exhaustive.full_exhaustive_pred_inst.full_exhaustive_pred))
(TQuickcheck_Exhaustive.full_exhaustive_prod_inst.full_exhaustive_prod,((c== @ cQuickcheck_Exhaustive.full_exhaustive_prod_inst.full_exhaustive_prod) @ cQuickcheck_Exhaustive.full_exhaustive_prod_inst.full_exhaustive_prod))
(TQuickcheck_Exhaustive.full_exhaustive_term_inst.full_exhaustive_term,((c== @ cQuickcheck_Exhaustive.full_exhaustive_term_inst.full_exhaustive_term) @ cQuickcheck_Exhaustive.full_exhaustive_term_inst.full_exhaustive_term))
(TQuickcheck_Exhaustive.full_exhaustive_unit_inst.full_exhaustive_unit,((c== @ cQuickcheck_Exhaustive.full_exhaustive_unit_inst.full_exhaustive_unit) @ cQuickcheck_Exhaustive.full_exhaustive_unit_inst.full_exhaustive_unit))
(TQuickcheck_Exhaustive.term_of_three_valued_inst.term_of_three_valued,((c== @ cQuickcheck_Exhaustive.term_of_three_valued_inst.term_of_three_valued) @ cQuickcheck_Exhaustive.term_of_three_valued_inst.term_of_three_valued))
(TQuickcheck_Exhaustive.typerep_three_valued_inst.typerep_three_valued,((c== @ cQuickcheck_Exhaustive.typerep_three_valued_inst.typerep_three_valued) @ cQuickcheck_Exhaustive.typerep_three_valued_inst.typerep_three_valued))
(TSemiring_Normalization.arity_comm_semiring_1_cancel_crossproduct_nat,(cSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class @ cTYPE))
(TSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_def,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c== @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.conj @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ V0) @ V2))))))))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct.add_0_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ V4) @ ((V0 @ V4) @ V5))) @ ((cHOL.eq @ V5) @ V1))))))))))))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class_def,((c== @ (cSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class @ cTYPE)) @ ((cPure.conjunction @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ ((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_atLeastLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1))) @ ((cSet_Interval.ord_class.greaterThanAtMost @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TBig_Operators.comm_monoid_add_class.comm_monoid_add_class.setsum_dict,((c== @ cBig_Operators.comm_monoid_add_class.setsum) @ ((cBig_Operators.comm_monoid_add.setsum @ cGroups.plus_class.plus) @ cGroups.zero_class.zero)))
(TComplete_Lattices.classrel_complete_linorder_complete_distrib_lattice,(cComplete_Lattices.complete_distrib_lattice_class @ cTYPE))
(TFields.linordered_field_inverse_zero_class.field_le_mult_one_interval,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((c==> @ ((cOrderings.ord_class.less @ V2) @ cGroups.one_class.one)) @ ((cOrderings.ord_class.less_eq @ ((cGroups.times_class.times @ V2) @ V0)) @ V1)))))) @ ((cOrderings.ord_class.less_eq @ V0) @ V1)))))))
(TGroups.ordered_ab_group_add_abs_class.ordered_ab_group_add_abs_axioms,(((((((cGroups.class.ordered_ab_group_add_abs @ cGroups.abs_class.abs) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TGroups.ordered_ab_semigroup_add_class.ordered_ab_semigroup_add_axioms,(((cGroups.class.ordered_ab_semigroup_add @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TLattices.bounded_semilattice_inf_top_class.inf_top.comm_monoid_axioms,((cGroups.comm_monoid @ cLattices.inf_class.inf) @ cOrderings.top_class.top))
(TLattices.bounded_semilattice_sup_bot_class.sup_bot.comm_monoid_axioms,((cGroups.comm_monoid @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot))
(TQuickcheck_Exhaustive.three_valued.full_exhaustive_three_valued.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.Unknown_value) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cQuickcheck_Exhaustive.three_valued.Value @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ (V0 @ ((cProduct_Type.Pair @ cQuickcheck_Exhaustive.three_valued.No_value) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))))))))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.random_narrowing_cons_inst.random_narrowing_cons,((c== @ cQuickcheck_Narrowing.random_narrowing_cons_inst.random_narrowing_cons) @ cQuickcheck_Narrowing.random_narrowing_cons_inst.random_narrowing_cons))
(TQuickcheck_Narrowing.random_narrowing_term_inst.random_narrowing_term,((c== @ cQuickcheck_Narrowing.random_narrowing_term_inst.random_narrowing_term) @ cQuickcheck_Narrowing.random_narrowing_term_inst.random_narrowing_term))
(TQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type,((c== @ cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type) @ cQuickcheck_Narrowing.random_narrowing_type_inst.random_narrowing_type))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_ops_5,(cPure.term @ cGroups.one_class.one))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_ops_4,(cPure.term @ cGroups.zero_class.zero))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_ops_3,(call @ (^[V0]: (call @ (^[V1]: (cPure.term @ ((cPower.power_class.power @ V0) @ V1)))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_ops_2,(call @ (^[V0]: (call @ (^[V1]: (cPure.term @ ((cGroups.times_class.times @ V0) @ V1)))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_ops_1,(call @ (^[V0]: (call @ (^[V1]: (cPure.term @ ((cGroups.plus_class.plus @ V0) @ V1)))))))
(TBig_Operators.semilattice_inf_class.semilattice_inf_class.Inf_fin_dict,((c== @ cBig_Operators.semilattice_inf_class.Inf_fin) @ (cBig_Operators.semilattice_inf.Inf_fin @ cLattices.inf_class.inf)))
(TBig_Operators.semilattice_sup_class.semilattice_sup_class.Sup_fin_dict,((c== @ cBig_Operators.semilattice_sup_class.Sup_fin) @ (cBig_Operators.semilattice_sup.Sup_fin @ cLattices.sup_class.sup)))
(TLazy_Sequence.lazy_sequence.size_lazy_sequence_inst.size_lazy_sequence,((c== @ cLazy_Sequence.lazy_sequence.size_lazy_sequence_inst.size_lazy_sequence) @ cLazy_Sequence.lazy_sequence.size_lazy_sequence_inst.size_lazy_sequence))
(TQuickcheck_Narrowing.narrowing_cons.narrowing_cons_size_overloaded_def,((c== @ cNat.size_class.size) @ (cQuickcheck_Narrowing.narrowing_cons.narrowing_cons_rec @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat)))))
(TQuickcheck_Narrowing.narrowing_term.narrowing_term_size_overloaded_def,((c== @ cQuickcheck_Narrowing.narrowing_term.size_narrowing_term_inst.size_narrowing_term) @ ((((cQuickcheck_Narrowing.narrowing_term.narrowing_term_rec_1 @ (^[V0]: (^[V1]: cNat.zero_nat_inst.zero_nat))) @ (^[V0]: (^[V1]: (^[V2]: ((cNat.plus_nat_inst.plus_nat @ V2) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TQuickcheck_Narrowing.narrowing_type.narrowing_type_size_overloaded_def,((c== @ cQuickcheck_Narrowing.narrowing_type.size_narrowing_type_inst.size_narrowing_type) @ (((((cQuickcheck_Narrowing.narrowing_type.narrowing_type_rec_1 @ (^[V0]: (^[V1]: ((cNat.plus_nat_inst.plus_nat @ V1) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat))))))) @ cNat.zero_nat_inst.zero_nat) @ (^[V0]: (^[V1]: (^[V2]: (^[V3]: ((cNat.plus_nat_inst.plus_nat @ ((cNat.plus_nat_inst.plus_nat @ V2) @ V3)) @ (cNat.Suc @ cNat.zero_nat_inst.zero_nat)))))))))
(TRings.linordered_comm_semiring_strict_class.comm_mult_strict_left_mono,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((c==> @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((c==> @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V2)) @ ((cOrderings.ord_class.less @ ((cGroups.times_class.times @ V2) @ V0)) @ ((cGroups.times_class.times @ V2) @ V1)))))))))))
(TSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct.intro,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ V0) @ V2)) @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3))))))))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.intro,((c==> @ (cRings.comm_semiring_1_cancel_class @ cTYPE)) @ ((c==> @ ((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times)) @ (cSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class @ cTYPE))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.super,((c==> @ (cSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class @ cTYPE)) @ (cRings.comm_semiring_1_cancel_class @ cTYPE)))
(TSet_Interval.dense_linorder.atLeastAtMost_subseteq_atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V2) @ V3)) @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V4) @ V5))) @ ((cHOL.implies @ ((V0 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V1 @ V3) @ V5))))))))))))))))))
(TSet_Interval.dense_linorder.atLeastLessThan_subseteq_atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V2) @ V3)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V4) @ V5))) @ ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V0 @ V3) @ V5))))))))))))))))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_greaterThanAtMost,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1))) @ ((cSet_Interval.ord_class.atLeastLessThan @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TQuickcheck_Exhaustive.lazy_sequence.full_exhaustive_lazy_sequence.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cLazy_Sequence.lazy_sequence.lazy_sequence_of_list @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.NibbleA)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.narrowing_three_valued_inst.narrowing_three_valued,((c== @ cQuickcheck_Narrowing.narrowing_three_valued_inst.narrowing_three_valued) @ cQuickcheck_Narrowing.narrowing_three_valued_inst.narrowing_three_valued))
(TQuickcheck_Narrowing.narrowing_type.narrowing_narrowing_type_list.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_narrowing_type_list) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cList.list.Nil)) @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cList.list.Cons)) @ cQuickcheck_Narrowing.narrowing_narrowing_type_inst.narrowing_narrowing_type)) @ cQuickcheck_Narrowing.narrowing_narrowing_type_list))))
(TQuickcheck_Narrowing.partial_term_of_itself_inst.partial_term_of_itself,((c== @ cQuickcheck_Narrowing.partial_term_of_itself_inst.partial_term_of_itself) @ cQuickcheck_Narrowing.partial_term_of_itself_inst.partial_term_of_itself))
(TQuickcheck_Narrowing.partial_term_of_nibble_inst.partial_term_of_nibble,((c== @ cQuickcheck_Narrowing.partial_term_of_nibble_inst.partial_term_of_nibble) @ cQuickcheck_Narrowing.partial_term_of_nibble_inst.partial_term_of_nibble))
(TQuickcheck_Narrowing.partial_term_of_option_inst.partial_term_of_option,((c== @ cQuickcheck_Narrowing.partial_term_of_option_inst.partial_term_of_option) @ cQuickcheck_Narrowing.partial_term_of_option_inst.partial_term_of_option))
(TQuickcheck_Narrowing.term_of_narrowing_cons_inst.term_of_narrowing_cons,((c== @ cQuickcheck_Narrowing.term_of_narrowing_cons_inst.term_of_narrowing_cons) @ cQuickcheck_Narrowing.term_of_narrowing_cons_inst.term_of_narrowing_cons))
(TQuickcheck_Narrowing.term_of_narrowing_term_inst.term_of_narrowing_term,((c== @ cQuickcheck_Narrowing.term_of_narrowing_term_inst.term_of_narrowing_term) @ cQuickcheck_Narrowing.term_of_narrowing_term_inst.term_of_narrowing_term))
(TQuickcheck_Narrowing.term_of_narrowing_type_inst.term_of_narrowing_type,((c== @ cQuickcheck_Narrowing.term_of_narrowing_type_inst.term_of_narrowing_type) @ cQuickcheck_Narrowing.term_of_narrowing_type_inst.term_of_narrowing_type))
(TQuickcheck_Narrowing.typerep_narrowing_cons_inst.typerep_narrowing_cons,((c== @ cQuickcheck_Narrowing.typerep_narrowing_cons_inst.typerep_narrowing_cons) @ cQuickcheck_Narrowing.typerep_narrowing_cons_inst.typerep_narrowing_cons))
(TQuickcheck_Narrowing.typerep_narrowing_term_inst.typerep_narrowing_term,((c== @ cQuickcheck_Narrowing.typerep_narrowing_term_inst.typerep_narrowing_term) @ cQuickcheck_Narrowing.typerep_narrowing_term_inst.typerep_narrowing_term))
(TQuickcheck_Narrowing.typerep_narrowing_type_inst.typerep_narrowing_type,((c== @ cQuickcheck_Narrowing.typerep_narrowing_type_inst.typerep_narrowing_type) @ cQuickcheck_Narrowing.typerep_narrowing_type_inst.typerep_narrowing_type))
(TSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct.axioms_2,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ V0) @ V2)))))))))))
(TSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct.axioms_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((((cRings.class.comm_semiring_1_cancel @ V0) @ V1) @ V2) @ V3)))))))))))
(TSemiring_Normalization.comm_ring_1_class.normalizing_comm_ring_1_axioms,((((((cRings.class.comm_ring_1 @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.axioms,((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ cGroups.plus_class.plus) @ cGroups.times_class.times))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_37,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1)))) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V1)))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_36,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ ((cNat.times_nat_inst.times_nat @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One))) @ V1))) @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_35,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))) @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_34,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_33,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ cNat.one_nat_inst.one_nat)) @ V0))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_32,(call @ (^[V0]: ((cHOL.eq @ ((cPower.power_class.power @ V0) @ cNat.zero_nat_inst.zero_nat)) @ cGroups.one_class.one))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_31,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPower.power_class.power @ ((cPower.power_class.power @ V0) @ V1)) @ V2)) @ ((cPower.power_class.power @ V0) @ ((cNat.times_nat_inst.times_nat @ V1) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_30,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cPower.power_class.power @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V2)) @ ((cPower.power_class.power @ V1) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_29,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V0)) @ ((cPower.power_class.power @ V0) @ (cNum.numeral_class.numeral @ (cNum.num.Bit0 @ cNum.num.One)))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_28,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V1)) @ V0)) @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_27,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cPower.power_class.power @ V0) @ V1))) @ ((cPower.power_class.power @ V0) @ (cNat.Suc @ V1))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_26,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cPower.power_class.power @ V0) @ V1)) @ ((cPower.power_class.power @ V0) @ V2))) @ ((cPower.power_class.power @ V0) @ ((cNat.plus_nat_inst.plus_nat @ V1) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_25,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_24,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V1) @ V0)))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_23,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_22,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))) @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.plus_class.plus @ V0) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_21,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.plus_class.plus @ V1) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_20,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V1)) @ ((cGroups.plus_class.plus @ V2) @ V3))) @ ((cGroups.plus_class.plus @ ((cGroups.plus_class.plus @ V0) @ V2)) @ ((cGroups.plus_class.plus @ V1) @ V3))))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_19,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V0) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_18,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_17,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_16,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V2)) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V2)) @ V1)))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_15,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V3))) @ ((cGroups.times_class.times @ V2) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ V3))))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_14,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V3))) @ ((cGroups.times_class.times @ V0) @ ((cGroups.times_class.times @ V1) @ ((cGroups.times_class.times @ V2) @ V3)))))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_13,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V3))) @ ((cGroups.times_class.times @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3))))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_12,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.one_class.one)) @ V0))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_11,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.one_class.one) @ V0)) @ V0))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_10,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ cGroups.zero_class.zero)) @ cGroups.zero_class.zero))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_9,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.times_class.times @ cGroups.zero_class.zero) @ V0)) @ cGroups.zero_class.zero))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_8,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V1)) @ V2)) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_7,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V1) @ V0)))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_6,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ cGroups.zero_class.zero)) @ V0))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_5,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ cGroups.zero_class.zero) @ V0)) @ V0))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_4,(call @ (^[V0]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ V0)) @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ cGroups.one_class.one) @ cGroups.one_class.one)) @ V0)))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_3,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ V0) @ ((cGroups.times_class.times @ V1) @ V0))) @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V1) @ cGroups.one_class.one)) @ V0)))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_2,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ V1)) @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ cGroups.one_class.one)) @ V1)))))))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_semiring_rules_1,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V1))) @ ((cGroups.times_class.times @ ((cGroups.plus_class.plus @ V0) @ V2)) @ V1)))))))))
(TBig_Operators.comm_monoid_mult_class.comm_monoid_mult_class.setprod_dict,((c== @ cBig_Operators.comm_monoid_mult_class.setprod) @ ((cBig_Operators.comm_monoid_mult.setprod @ cGroups.times_class.times) @ cGroups.one_class.one)))
(TBig_Operators.semilattice_inf_class.Inf_fin.semilattice_order_set_axioms,(((cBig_Operators.semilattice_order_set @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TBig_Operators.semilattice_sup_class.Sup_fin.semilattice_order_set_axioms,(((cBig_Operators.semilattice_order_set @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TComplete_Lattices.complete_boolean_algebra.dual_complete_boolean_algebra,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: ((c==> @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)) @ ((((((((((cComplete_Lattices.class.complete_boolean_algebra @ V1) @ V0) @ V5) @ (^[V10]: (^[V11]: ((V3 @ V11) @ V10)))) @ (^[V10]: (^[V11]: ((V4 @ V11) @ V10)))) @ V2) @ V7) @ V6) @ (^[V10]: (^[V11]: ((V5 @ V10) @ (V9 @ V11))))) @ V9)))))))))))))))))))))))
(TComplete_Lattices.complete_distrib_lattice.dual_complete_distrib_lattice,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7)) @ ((((((((cComplete_Lattices.class.complete_distrib_lattice @ V1) @ V0) @ V5) @ (^[V8]: (^[V9]: ((V3 @ V9) @ V8)))) @ (^[V8]: (^[V9]: ((V4 @ V9) @ V8)))) @ V2) @ V7) @ V6)))))))))))))))))))
(TFields.linordered_field_inverse_zero.inverse_nonnegative_iff_nonnegative,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ V5) @ (V0 @ V12))) @ ((V9 @ V5) @ V12))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero.inverse_nonpositive_iff_nonpositive,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: (call @ (^[V9]: (call @ (^[V10]: (call @ (^[V11]: (call @ (^[V12]: ((c==> @ ((((((((((((cFields.class.linordered_field_inverse_zero @ V0) @ V1) @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9) @ V10) @ V11)) @ ((cHOL.eq @ ((V9 @ (V0 @ V12)) @ V5)) @ ((V9 @ V12) @ V5))))))))))))))))))))))))))))))
(TFields.linordered_field_inverse_zero_class.inverse_negative_iff_negative,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ (cFields.inverse_class.inverse @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TFields.linordered_field_inverse_zero_class.inverse_positive_iff_positive,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ (cFields.inverse_class.inverse @ V0))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TGroups.linordered_ab_group_add.double_add_le_zero_iff_single_add_le_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ ((V0 @ V6) @ V6)) @ V1)) @ ((V4 @ V6) @ V1))))))))))))))))))
(TGroups.linordered_ab_group_add.zero_le_double_add_iff_zero_le_single_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V4 @ V1) @ ((V0 @ V6) @ V6))) @ ((V4 @ V1) @ V6))))))))))))))))))
(TOrderings.unbounded_dense_linorder_class.unbounded_dense_linorder_axioms,((cOrderings.class.unbounded_dense_linorder @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TQuickcheck_Exhaustive.full_exhaustive_nibble_inst.full_exhaustive_nibble,((c== @ cQuickcheck_Exhaustive.full_exhaustive_nibble_inst.full_exhaustive_nibble) @ cQuickcheck_Exhaustive.full_exhaustive_nibble_inst.full_exhaustive_nibble))
(TQuickcheck_Exhaustive.full_exhaustive_option_inst.full_exhaustive_option,((c== @ cQuickcheck_Exhaustive.full_exhaustive_option_inst.full_exhaustive_option) @ cQuickcheck_Exhaustive.full_exhaustive_option_inst.full_exhaustive_option))
(TQuickcheck_Narrowing.narrowing_cons.full_exhaustive_narrowing_cons.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_inst.full_exhaustive_narrowing_type @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cQuickcheck_Narrowing.narrowing_cons.Narrowing_cons @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil)))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ ((cList.list.Cons @ (cTyperep.typerep_class.typerep @ cTYPE)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.narrowing_term.full_exhaustive_narrowing_term.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_term_inst.full_exhaustive_narrowing_term @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ ((cQuickcheck_Exhaustive.full_exhaustive_class.full_exhaustive @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_inst.full_exhaustive_narrowing_type @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_variable @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ ((cQuickcheck_Exhaustive.full_exhaustive_integer_inst.full_exhaustive_integer @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Narrowing.full_exhaustive_narrowing_term_list @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cQuickcheck_Narrowing.narrowing_term.Narrowing_constructor @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ cList.list.Nil)))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.narrowing_type.full_exhaustive_narrowing_type.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_inst.full_exhaustive_narrowing_type @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_list_list @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: (V0 @ ((cProduct_Type.Pair @ (cQuickcheck_Narrowing.narrowing_type.Narrowing_sum_of_products @ V2)) @ (^[V4]: ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural))) @ cOption.option.None)))))))
(TRings.linordered_semiring_strict_class.linordered_semiring_strict_axioms,(((((cRings.class.linordered_semiring_strict @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.times_class.times))
(TSemiring_Normalization.classrel_idom_comm_semiring_1_cancel_crossproduct,(cSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class @ cTYPE))
(TSet_Interval.dense_linorder.greaterThanAtMost_subseteq_atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V2) @ V3)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V4) @ V5))) @ ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V0 @ V3) @ V5))))))))))))))))))
(TSet_Interval.ordered_ab_group_add_class.image_uminus_greaterThanLessThan,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cSet.image @ cGroups.uminus_class.uminus) @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1))) @ ((cSet_Interval.ord_class.greaterThanLessThan @ (cGroups.uminus_class.uminus @ V1)) @ (cGroups.uminus_class.uminus @ V0))))))))
(TComplete_Lattices.complete_lattice_class.complete_lattice_class.INFI_dict,((c== @ cComplete_Lattices.complete_lattice_class.INFI) @ (cComplete_Lattices.complete_lattice.INFI @ cComplete_Lattices.Inf_class.Inf)))
(TComplete_Lattices.complete_lattice_class.complete_lattice_class.SUPR_dict,((c== @ cComplete_Lattices.complete_lattice_class.SUPR) @ (cComplete_Lattices.complete_lattice.SUPR @ cComplete_Lattices.Sup_class.Sup)))
(TDivides.semiring_numeral_div_class.semiring_numeral_div_class.divmod_dict,((c== @ cDivides.semiring_numeral_div_class.divmod) @ ((((cDivides.semiring_numeral_div.divmod @ cDivides.div_class.div) @ cDivides.div_class.mod) @ cGroups.plus_class.plus) @ cGroups.one_class.one)))
(TFields.division_ring_inverse_zero_class.division_ring_inverse_zero_axioms,((((((((cFields.class.division_ring_inverse_zero @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.one_class.one) @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TQuickcheck_Narrowing.narrowing_lazy_sequence_inst.narrowing_lazy_sequence,((c== @ cQuickcheck_Narrowing.narrowing_lazy_sequence_inst.narrowing_lazy_sequence) @ cQuickcheck_Narrowing.narrowing_lazy_sequence_inst.narrowing_lazy_sequence))
(TQuickcheck_Narrowing.partial_term_of_integer_inst.partial_term_of_integer,((c== @ cQuickcheck_Narrowing.partial_term_of_integer_inst.partial_term_of_integer) @ cQuickcheck_Narrowing.partial_term_of_integer_inst.partial_term_of_integer))
(TQuickcheck_Narrowing.partial_term_of_natural_inst.partial_term_of_natural,((c== @ cQuickcheck_Narrowing.partial_term_of_natural_inst.partial_term_of_natural) @ cQuickcheck_Narrowing.partial_term_of_natural_inst.partial_term_of_natural))
(TQuickcheck_Narrowing.partial_term_of_typerep_inst.partial_term_of_typerep,((c== @ cQuickcheck_Narrowing.partial_term_of_typerep_inst.partial_term_of_typerep) @ cQuickcheck_Narrowing.partial_term_of_typerep_inst.partial_term_of_typerep))
(TQuickcheck_Narrowing.partial_term_of_unknown_inst.partial_term_of_unknown,((c== @ cQuickcheck_Narrowing.partial_term_of_unknown_inst.partial_term_of_unknown) @ cQuickcheck_Narrowing.partial_term_of_unknown_inst.partial_term_of_unknown))
(TRings.classrel_linordered_comm_semiring_strict_linordered_semiring_strict,(cRings.linordered_semiring_strict_class @ cTYPE))
(TSemiring_Normalization.comm_semiring_1.normalizing_comm_semiring_1_axioms,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)) @ ((((cRings.class.comm_semiring_1 @ V0) @ V1) @ V2) @ V3)))))))))))
(TGroups.classrel_linordered_ab_group_add_linordered_cancel_ab_semigroup_add,(cGroups.linordered_cancel_ab_semigroup_add_class @ cTYPE))
(TQuickcheck_Exhaustive.full_exhaustive_integer_inst.full_exhaustive_integer,((c== @ cQuickcheck_Exhaustive.full_exhaustive_integer_inst.full_exhaustive_integer) @ cQuickcheck_Exhaustive.full_exhaustive_integer_inst.full_exhaustive_integer))
(TQuickcheck_Exhaustive.full_exhaustive_natural_inst.full_exhaustive_natural,((c== @ cQuickcheck_Exhaustive.full_exhaustive_natural_inst.full_exhaustive_natural) @ cQuickcheck_Exhaustive.full_exhaustive_natural_inst.full_exhaustive_natural))
(TQuickcheck_Exhaustive.full_exhaustive_unknown_inst.full_exhaustive_unknown,((c== @ cQuickcheck_Exhaustive.full_exhaustive_unknown_inst.full_exhaustive_unknown) @ cQuickcheck_Exhaustive.full_exhaustive_unknown_inst.full_exhaustive_unknown))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct.crossproduct_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.eq @ ((V0 @ ((V2 @ V4) @ V5)) @ ((V2 @ V6) @ V7))) @ ((V0 @ ((V2 @ V4) @ V7)) @ ((V2 @ V6) @ V5)))) @ ((cHOL.disj @ ((cHOL.eq @ V4) @ V6)) @ ((cHOL.eq @ V5) @ V7)))))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.add_0_iff,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cHOL.eq @ V0) @ ((cGroups.plus_class.plus @ V0) @ V1))) @ ((cHOL.eq @ V1) @ cGroups.zero_class.zero)))))))
(TSet_Interval.dense_linorder.greaterThanAtMost_subseteq_atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((((cSet_Interval.ord.greaterThanAtMost @ V0) @ V1) @ V2) @ V3)) @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V4) @ V5))) @ ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V1 @ V3) @ V5))))))))))))))))))
(TSet_Interval.dense_linorder.greaterThanLessThan_subseteq_atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V2) @ V3)) @ (((cSet_Interval.ord.atLeastAtMost @ V0) @ V4) @ V5))) @ ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V0 @ V3) @ V5))))))))))))))))))
(TGroups.linordered_ab_semigroup_add_class.linordered_ab_semigroup_add_axioms,(((cGroups.class.linordered_ab_semigroup_add @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TLattices.bounded_semilattice_inf_top_class.inf_top.semilattice_neutr_axioms,((cLattices.semilattice_neutr @ cLattices.inf_class.inf) @ cOrderings.top_class.top))
(TLattices.bounded_semilattice_sup_bot_class.sup_bot.semilattice_neutr_axioms,((cLattices.semilattice_neutr @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot))
(TQuickcheck_Exhaustive.three_valued.size_three_valued_inst.size_three_valued,((c== @ cQuickcheck_Exhaustive.three_valued.size_three_valued_inst.size_three_valued) @ cQuickcheck_Exhaustive.three_valued.size_three_valued_inst.size_three_valued))
(TQuickcheck_Narrowing.narrowing_narrowing_type_inst.narrowing_narrowing_type,((c== @ cQuickcheck_Narrowing.narrowing_narrowing_type_inst.narrowing_narrowing_type) @ cQuickcheck_Narrowing.narrowing_narrowing_type_inst.narrowing_narrowing_type))
(TQuickcheck_Narrowing.partial_term_of_finite_1_inst.partial_term_of_finite_1,((c== @ cQuickcheck_Narrowing.partial_term_of_finite_1_inst.partial_term_of_finite_1) @ cQuickcheck_Narrowing.partial_term_of_finite_1_inst.partial_term_of_finite_1))
(TQuickcheck_Narrowing.partial_term_of_finite_2_inst.partial_term_of_finite_2,((c== @ cQuickcheck_Narrowing.partial_term_of_finite_2_inst.partial_term_of_finite_2) @ cQuickcheck_Narrowing.partial_term_of_finite_2_inst.partial_term_of_finite_2))
(TQuickcheck_Narrowing.partial_term_of_finite_3_inst.partial_term_of_finite_3,((c== @ cQuickcheck_Narrowing.partial_term_of_finite_3_inst.partial_term_of_finite_3) @ cQuickcheck_Narrowing.partial_term_of_finite_3_inst.partial_term_of_finite_3))
(TQuickcheck_Narrowing.partial_term_of_finite_4_inst.partial_term_of_finite_4,((c== @ cQuickcheck_Narrowing.partial_term_of_finite_4_inst.partial_term_of_finite_4) @ cQuickcheck_Narrowing.partial_term_of_finite_4_inst.partial_term_of_finite_4))
(TQuickcheck_Narrowing.partial_term_of_finite_5_inst.partial_term_of_finite_5,((c== @ cQuickcheck_Narrowing.partial_term_of_finite_5_inst.partial_term_of_finite_5) @ cQuickcheck_Narrowing.partial_term_of_finite_5_inst.partial_term_of_finite_5))
(TQuickcheck_Narrowing.partial_term_of_property_inst.partial_term_of_property,((c== @ cQuickcheck_Narrowing.partial_term_of_property_inst.partial_term_of_property) @ cQuickcheck_Narrowing.partial_term_of_property_inst.partial_term_of_property))
(TRecord.tuple_isomorphism.size_tuple_isomorphism_inst.size_tuple_isomorphism,((c== @ cRecord.tuple_isomorphism.size_tuple_isomorphism_inst.size_tuple_isomorphism) @ cRecord.tuple_isomorphism.size_tuple_isomorphism_inst.size_tuple_isomorphism))
(TRings.classrel_linordered_comm_semiring_strict_ordered_cancel_comm_semiring,(cRings.ordered_cancel_comm_semiring_class @ cTYPE))
(TSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms_def,(call @ (^[V0]: (call @ (^[V1]: ((c== @ ((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ V0) @ V1)) @ (cHOL.All @ (^[V2]: (cHOL.All @ (^[V3]: (cHOL.All @ (^[V4]: (cHOL.All @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V1 @ V4) @ V5))) @ ((V0 @ ((V1 @ V2) @ V5)) @ ((V1 @ V4) @ V3)))) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.eq @ V3) @ V5)))))))))))))))))
(TGroups.linordered_ab_group_add.double_add_less_zero_iff_single_add_less_zero,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ ((V0 @ V6) @ V6)) @ V1)) @ ((V5 @ V6) @ V1))))))))))))))))))
(TGroups.linordered_ab_group_add.zero_less_double_add_iff_zero_less_single_add,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: ((c==> @ ((((((cGroups.class.linordered_ab_group_add @ V0) @ V1) @ V2) @ V3) @ V4) @ V5)) @ ((cHOL.eq @ ((V5 @ V1) @ ((V0 @ V6) @ V6))) @ ((V5 @ V1) @ V6))))))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_finite_1_inst.full_exhaustive_finite_1,((c== @ cQuickcheck_Exhaustive.full_exhaustive_finite_1_inst.full_exhaustive_finite_1) @ cQuickcheck_Exhaustive.full_exhaustive_finite_1_inst.full_exhaustive_finite_1))
(TQuickcheck_Exhaustive.full_exhaustive_finite_2_inst.full_exhaustive_finite_2,((c== @ cQuickcheck_Exhaustive.full_exhaustive_finite_2_inst.full_exhaustive_finite_2) @ cQuickcheck_Exhaustive.full_exhaustive_finite_2_inst.full_exhaustive_finite_2))
(TQuickcheck_Exhaustive.full_exhaustive_finite_3_inst.full_exhaustive_finite_3,((c== @ cQuickcheck_Exhaustive.full_exhaustive_finite_3_inst.full_exhaustive_finite_3) @ cQuickcheck_Exhaustive.full_exhaustive_finite_3_inst.full_exhaustive_finite_3))
(TQuickcheck_Exhaustive.full_exhaustive_finite_4_inst.full_exhaustive_finite_4,((c== @ cQuickcheck_Exhaustive.full_exhaustive_finite_4_inst.full_exhaustive_finite_4) @ cQuickcheck_Exhaustive.full_exhaustive_finite_4_inst.full_exhaustive_finite_4))
(TQuickcheck_Exhaustive.full_exhaustive_finite_5_inst.full_exhaustive_finite_5,((c== @ cQuickcheck_Exhaustive.full_exhaustive_finite_5_inst.full_exhaustive_finite_5) @ cQuickcheck_Exhaustive.full_exhaustive_finite_5_inst.full_exhaustive_finite_5))
(TQuickcheck_Narrowing.narrowing_type.narrowing_narrowing_type_list_list.simps,((cHOL.eq @ cQuickcheck_Narrowing.narrowing_narrowing_type_list_list) @ ((cQuickcheck_Narrowing.sum @ (cQuickcheck_Narrowing.cons @ cList.list.Nil)) @ ((cQuickcheck_Narrowing.apply @ ((cQuickcheck_Narrowing.apply @ (cQuickcheck_Narrowing.cons @ cList.list.Cons)) @ cQuickcheck_Narrowing.narrowing_narrowing_type_list)) @ cQuickcheck_Narrowing.narrowing_narrowing_type_list_list))))
(TRings.linordered_semiring_1_strict_class.linordered_semiring_1_strict_axioms,((((((cRings.class.linordered_semiring_1_strict @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.times_class.times) @ cGroups.one_class.one))
(TRings.ordered_cancel_comm_semiring_class.ordered_cancel_comm_semiring_axioms,(((((cRings.class.ordered_cancel_comm_semiring @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.times_class.times))
(TSet_Interval.dense_linorder.greaterThanLessThan_subseteq_atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((c==> @ ((cOrderings.class.dense_linorder @ V0) @ V1)) @ ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (((cSet_Interval.ord.greaterThanLessThan @ V1) @ V2) @ V3)) @ ((((cSet_Interval.ord.atLeastLessThan @ V0) @ V1) @ V4) @ V5))) @ ((cHOL.implies @ ((V1 @ V2) @ V3)) @ ((cHOL.conj @ ((V0 @ V4) @ V2)) @ ((V0 @ V3) @ V5))))))))))))))))))
(TSet_Interval.dense_linorder_class.atLeastAtMost_subseteq_atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.atLeastAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((cHOL.implies @ ((cOrderings.ord_class.less_eq @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V3)))))))))))))
(TSet_Interval.dense_linorder_class.atLeastLessThan_subseteq_atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.atLeastLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ V3))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))))
(TLattices.bounded_semilattice_inf_top_class.bounded_semilattice_inf_top_axioms,((((cLattices.class.bounded_semilattice_inf_top @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cOrderings.top_class.top))
(TLattices.bounded_semilattice_sup_bot_class.bounded_semilattice_sup_bot_axioms,((((cLattices.class.bounded_semilattice_sup_bot @ cLattices.sup_class.sup) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cOrderings.bot_class.bot))
(TQuickcheck_Narrowing.narrowing_term.full_exhaustive_narrowing_term_list.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_term_list @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_term_inst.full_exhaustive_narrowing_term @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Narrowing.full_exhaustive_narrowing_term_list @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleD)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TQuickcheck_Narrowing.narrowing_type.full_exhaustive_narrowing_type_list.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_list @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))))))) @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_inst.full_exhaustive_narrowing_type @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_list @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms.intro,(call @ (^[V0]: (call @ (^[V1]: ((c==> @ (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: ((cHOL.eq @ ((cHOL.eq @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V1 @ V4) @ V5))) @ ((V0 @ ((V1 @ V2) @ V5)) @ ((V1 @ V4) @ V3)))) @ ((cHOL.disj @ ((cHOL.eq @ V2) @ V4)) @ ((cHOL.eq @ V3) @ V5)))))))))))) @ ((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct_axioms @ V0) @ V1)))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct.add_scale_eq_noteq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: (call @ (^[V8]: ((c==> @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ (cHOL.Not @ ((cHOL.eq @ V4) @ V1))) @ ((c==> @ ((cHOL.conj @ ((cHOL.eq @ V5) @ V6)) @ (cHOL.Not @ ((cHOL.eq @ V7) @ V8)))) @ (cHOL.Not @ ((cHOL.eq @ ((V0 @ V5) @ ((V2 @ V4) @ V7))) @ ((V0 @ V6) @ ((V2 @ V4) @ V8))))))))))))))))))))))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct.crossproduct_noteq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: (call @ (^[V5]: (call @ (^[V6]: (call @ (^[V7]: ((c==> @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((cHOL.eq @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V4) @ V5))) @ (cHOL.Not @ ((cHOL.eq @ V6) @ V7)))) @ (cHOL.Not @ ((cHOL.eq @ ((V0 @ ((V2 @ V4) @ V6)) @ ((V2 @ V5) @ V7))) @ ((V0 @ ((V2 @ V4) @ V7)) @ ((V2 @ V5) @ V6)))))))))))))))))))))))
(TComplete_Lattices.complete_boolean_algebra_class.dual_complete_boolean_algebra,((((((((((cComplete_Lattices.class.complete_boolean_algebra @ cComplete_Lattices.Sup_class.Sup) @ cComplete_Lattices.Inf_class.Inf) @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot) @ (^[V0]: (^[V1]: ((cLattices.sup_class.sup @ V0) @ (cGroups.uminus_class.uminus @ V1))))) @ cGroups.uminus_class.uminus))
(TComplete_Lattices.complete_distrib_lattice_class.dual_complete_distrib_lattice,((((((((cComplete_Lattices.class.complete_distrib_lattice @ cComplete_Lattices.Sup_class.Sup) @ cComplete_Lattices.Inf_class.Inf) @ cLattices.sup_class.sup) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))) @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ cOrderings.bot_class.bot))
(TDivides.semiring_numeral_div_class.semiring_numeral_div_class.divmod_step_dict,((c== @ cDivides.semiring_numeral_div_class.divmod_step) @ (((((cDivides.semiring_numeral_div.divmod_step @ cGroups.times_class.times) @ cGroups.plus_class.plus) @ cGroups.one_class.one) @ cGroups.minus_class.minus) @ cOrderings.ord_class.less_eq)))
(TFields.linordered_field_inverse_zero_class.inverse_nonnegative_iff_nonnegative,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ (cFields.inverse_class.inverse @ V0))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)))))
(TFields.linordered_field_inverse_zero_class.inverse_nonpositive_iff_nonpositive,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ (cFields.inverse_class.inverse @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.classrel_linordered_cancel_ab_semigroup_add_linordered_ab_semigroup_add,(cGroups.linordered_ab_semigroup_add_class @ cTYPE))
(TGroups.linordered_ab_group_add_class.double_add_le_zero_iff_single_add_le_zero,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less_eq @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_ab_group_add_class.zero_le_double_add_iff_zero_le_single_add,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V0))) @ ((cOrderings.ord_class.less_eq @ cGroups.zero_class.zero) @ V0)))))
(TSet_Interval.dense_linorder_class.greaterThanAtMost_subseteq_atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ V3))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))))
(TFields.linordered_field_inverse_zero_class.linordered_field_inverse_zero_axioms,((((((((((((cFields.class.linordered_field_inverse_zero @ cFields.inverse_class.inverse) @ cFields.inverse_class.divide) @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus) @ cGroups.abs_class.abs) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.sgn_class.sgn))
(TRecord.full_exhaustive_tuple_isomorphism_inst.full_exhaustive_tuple_isomorphism,((c== @ cRecord.full_exhaustive_tuple_isomorphism_inst.full_exhaustive_tuple_isomorphism) @ cRecord.full_exhaustive_tuple_isomorphism_inst.full_exhaustive_tuple_isomorphism))
(TRecord.partial_term_of_tuple_isomorphism_inst.partial_term_of_tuple_isomorphism,((c== @ cRecord.partial_term_of_tuple_isomorphism_inst.partial_term_of_tuple_isomorphism) @ cRecord.partial_term_of_tuple_isomorphism_inst.partial_term_of_tuple_isomorphism))
(TSemiring_Normalization.comm_semiring_1_class.normalizing_comm_semiring_1_axioms,((((cRings.class.comm_semiring_1 @ cGroups.times_class.times) @ cGroups.one_class.one) @ cGroups.plus_class.plus) @ cGroups.zero_class.zero))
(TComplete_Lattices.complete_boolean_algebra_class.complete_boolean_algebra_axioms,((((((((((cComplete_Lattices.class.complete_boolean_algebra @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top) @ cGroups.minus_class.minus) @ cGroups.uminus_class.uminus))
(TComplete_Lattices.complete_distrib_lattice_class.complete_distrib_lattice_axioms,((((((((cComplete_Lattices.class.complete_distrib_lattice @ cComplete_Lattices.Inf_class.Inf) @ cComplete_Lattices.Sup_class.Sup) @ cLattices.inf_class.inf) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ cOrderings.top_class.top))
(TQuickcheck_Narrowing.narrowing_cons.size_narrowing_cons_inst.size_narrowing_cons,((c== @ cQuickcheck_Narrowing.narrowing_cons.size_narrowing_cons_inst.size_narrowing_cons) @ cQuickcheck_Narrowing.narrowing_cons.size_narrowing_cons_inst.size_narrowing_cons))
(TQuickcheck_Narrowing.narrowing_term.size_narrowing_term_inst.size_narrowing_term,((c== @ cQuickcheck_Narrowing.narrowing_term.size_narrowing_term_inst.size_narrowing_term) @ cQuickcheck_Narrowing.narrowing_term.size_narrowing_term_inst.size_narrowing_term))
(TQuickcheck_Narrowing.narrowing_type.size_narrowing_type_inst.size_narrowing_type,((c== @ cQuickcheck_Narrowing.narrowing_type.size_narrowing_type_inst.size_narrowing_type) @ cQuickcheck_Narrowing.narrowing_type.size_narrowing_type_inst.size_narrowing_type))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.crossproduct_eq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V1)) @ ((cGroups.times_class.times @ V2) @ V3))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V3)) @ ((cGroups.times_class.times @ V2) @ V1)))) @ ((cHOL.disj @ ((cHOL.eq @ V0) @ V2)) @ ((cHOL.eq @ V1) @ V3))))))))))))
(TSet_Interval.dense_linorder_class.greaterThanAtMost_subseteq_atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.greaterThanAtMost @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less @ V1) @ V3)))))))))))))
(TSet_Interval.dense_linorder_class.greaterThanLessThan_subseteq_atLeastAtMost_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastAtMost @ V2) @ V3))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))))
(TLattices.bounded_semilattice_inf_top_class.inf_top.semilattice_neutr_order_axioms,((((cLattices.semilattice_neutr_order @ cLattices.inf_class.inf) @ cOrderings.top_class.top) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TLattices.bounded_semilattice_sup_bot_class.sup_bot.semilattice_neutr_order_axioms,((((cLattices.semilattice_neutr_order @ cLattices.sup_class.sup) @ cOrderings.bot_class.bot) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less_eq @ V1) @ V0)))) @ (^[V0]: (^[V1]: ((cOrderings.ord_class.less @ V1) @ V0)))))
(TGroups.classrel_linordered_cancel_ab_semigroup_add_ordered_ab_semigroup_add_imp_le,(cGroups.ordered_ab_semigroup_add_imp_le_class @ cTYPE))
(TGroups.linordered_ab_group_add_class.double_add_less_zero_iff_single_add_less_zero,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ ((cGroups.plus_class.plus @ V0) @ V0)) @ cGroups.zero_class.zero)) @ ((cOrderings.ord_class.less @ V0) @ cGroups.zero_class.zero)))))
(TGroups.linordered_ab_group_add_class.zero_less_double_add_iff_zero_less_single_add,(call @ (^[V0]: ((cHOL.eq @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ ((cGroups.plus_class.plus @ V0) @ V0))) @ ((cOrderings.ord_class.less @ cGroups.zero_class.zero) @ V0)))))
(TQuickcheck_Narrowing.narrowing_type.full_exhaustive_narrowing_type_list_list.simps,(call @ (^[V0]: (call @ (^[V1]: ((cHOL.eq @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_list_list @ V0) @ V1)) @ (((cHOL.If @ ((cCode_Numeral.ord_natural_inst.less_natural @ cCode_Numeral.zero_natural_inst.zero_natural) @ V1)) @ ((cQuickcheck_Exhaustive.orelse @ (V0 @ ((cProduct_Type.Pair @ cList.list.Nil) @ (^[V2]: ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ cList.list.Nil))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))))))) @ ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_list @ (cProduct_Type.prod.prod_case @ (^[V2]: (^[V3]: ((cQuickcheck_Narrowing.full_exhaustive_narrowing_type_list_list @ (cProduct_Type.prod.prod_case @ (^[V4]: (^[V5]: (V0 @ ((cProduct_Type.Pair @ ((cList.list.Cons @ V2) @ V4)) @ (^[V6]: ((cCode_Evaluation.App @ ((cCode_Evaluation.App @ ((cCode_Evaluation.Const @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ cList.list.Nil)))))))))))))))) @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble6)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ cList.list.Nil))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleC)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ cList.list.Nil))))))))))) @ ((cList.list.Cons @ ((cTyperep.typerep.Typerep @ (cString.STR @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble8)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble3)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleB)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble4) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble2) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble1)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble2)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.NibbleE)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble7)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble5) @ cString.nibble.NibbleF)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble4)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble9)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble7) @ cString.nibble.Nibble0)) @ ((cList.list.Cons @ ((cString.char.Char @ cString.nibble.Nibble6) @ cString.nibble.Nibble5)) @ cList.list.Nil))))))))))))))))))))))))))))))))))))) @ cList.list.Nil)) @ cList.list.Nil))) @ cList.list.Nil))) @ cList.list.Nil)))) @ cList.list.Nil))))) @ (V3 @ cProduct_Type.Unity))) @ (V5 @ cProduct_Type.Unity))))))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))))) @ ((cCode_Numeral.minus_natural_inst.minus_natural @ V1) @ cCode_Numeral.one_natural_inst.one_natural)))) @ cOption.option.None)))))))
(TRings.linordered_comm_semiring_strict_class.linordered_comm_semiring_strict_axioms,(((((cRings.class.linordered_comm_semiring_strict @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less) @ cGroups.zero_class.zero) @ cGroups.times_class.times))
(TSet_Interval.dense_linorder_class.greaterThanLessThan_subseteq_atLeastLessThan_iff,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cOrderings.ord_class.less_eq @ ((cSet_Interval.ord_class.greaterThanLessThan @ V0) @ V1)) @ ((cSet_Interval.ord_class.atLeastLessThan @ V2) @ V3))) @ ((cHOL.implies @ ((cOrderings.ord_class.less @ V0) @ V1)) @ ((cHOL.conj @ ((cOrderings.ord_class.less_eq @ V2) @ V0)) @ ((cOrderings.ord_class.less_eq @ V1) @ V3)))))))))))))
(TGroups.ordered_ab_semigroup_add_imp_le_class.ordered_ab_semigroup_add_imp_le_axioms,(((cGroups.class.ordered_ab_semigroup_add_imp_le @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TGroups.ordered_cancel_ab_semigroup_add_class.ordered_cancel_ab_semigroup_add_axioms,(((cGroups.class.ordered_cancel_ab_semigroup_add @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TGroups.ordered_cancel_comm_monoid_diff_class.ordered_cancel_comm_monoid_diff_axioms,(((((cGroups.class.ordered_cancel_comm_monoid_diff @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.minus_class.minus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TQuickcheck_Narrowing.partial_term_of_three_valued_inst.partial_term_of_three_valued,((c== @ cQuickcheck_Narrowing.partial_term_of_three_valued_inst.partial_term_of_three_valued) @ cQuickcheck_Narrowing.partial_term_of_three_valued_inst.partial_term_of_three_valued))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.add_scale_eq_noteq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: (call @ (^[V4]: ((c==> @ (cHOL.Not @ ((cHOL.eq @ V0) @ cGroups.zero_class.zero))) @ ((c==> @ ((cHOL.conj @ ((cHOL.eq @ V1) @ V2)) @ (cHOL.Not @ ((cHOL.eq @ V3) @ V4)))) @ (cHOL.Not @ ((cHOL.eq @ ((cGroups.plus_class.plus @ V1) @ ((cGroups.times_class.times @ V0) @ V3))) @ ((cGroups.plus_class.plus @ V2) @ ((cGroups.times_class.times @ V0) @ V4)))))))))))))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.crossproduct_noteq,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((cHOL.eq @ ((cHOL.conj @ (cHOL.Not @ ((cHOL.eq @ V0) @ V1))) @ (cHOL.Not @ ((cHOL.eq @ V2) @ V3)))) @ (cHOL.Not @ ((cHOL.eq @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V2)) @ ((cGroups.times_class.times @ V1) @ V3))) @ ((cGroups.plus_class.plus @ ((cGroups.times_class.times @ V0) @ V3)) @ ((cGroups.times_class.times @ V1) @ V2))))))))))))))
(TQuickcheck_Exhaustive.full_exhaustive_three_valued_inst.full_exhaustive_three_valued,((c== @ cQuickcheck_Exhaustive.full_exhaustive_three_valued_inst.full_exhaustive_three_valued) @ cQuickcheck_Exhaustive.full_exhaustive_three_valued_inst.full_exhaustive_three_valued))
(TQuickcheck_Narrowing.partial_term_of_lazy_sequence_inst.partial_term_of_lazy_sequence,((c== @ cQuickcheck_Narrowing.partial_term_of_lazy_sequence_inst.partial_term_of_lazy_sequence) @ cQuickcheck_Narrowing.partial_term_of_lazy_sequence_inst.partial_term_of_lazy_sequence))
(TQuickcheck_Exhaustive.full_exhaustive_lazy_sequence_inst.full_exhaustive_lazy_sequence,((c== @ cQuickcheck_Exhaustive.full_exhaustive_lazy_sequence_inst.full_exhaustive_lazy_sequence) @ cQuickcheck_Exhaustive.full_exhaustive_lazy_sequence_inst.full_exhaustive_lazy_sequence))
(TQuickcheck_Narrowing.full_exhaustive_narrowing_cons_inst.full_exhaustive_narrowing_cons,((c== @ cQuickcheck_Narrowing.full_exhaustive_narrowing_cons_inst.full_exhaustive_narrowing_cons) @ cQuickcheck_Narrowing.full_exhaustive_narrowing_cons_inst.full_exhaustive_narrowing_cons))
(TQuickcheck_Narrowing.full_exhaustive_narrowing_term_inst.full_exhaustive_narrowing_term,((c== @ cQuickcheck_Narrowing.full_exhaustive_narrowing_term_inst.full_exhaustive_narrowing_term) @ cQuickcheck_Narrowing.full_exhaustive_narrowing_term_inst.full_exhaustive_narrowing_term))
(TQuickcheck_Narrowing.full_exhaustive_narrowing_type_inst.full_exhaustive_narrowing_type,((c== @ cQuickcheck_Narrowing.full_exhaustive_narrowing_type_inst.full_exhaustive_narrowing_type) @ cQuickcheck_Narrowing.full_exhaustive_narrowing_type_inst.full_exhaustive_narrowing_type))
(TQuickcheck_Narrowing.partial_term_of_narrowing_cons_inst.partial_term_of_narrowing_cons,((c== @ cQuickcheck_Narrowing.partial_term_of_narrowing_cons_inst.partial_term_of_narrowing_cons) @ cQuickcheck_Narrowing.partial_term_of_narrowing_cons_inst.partial_term_of_narrowing_cons))
(TQuickcheck_Narrowing.partial_term_of_narrowing_term_inst.partial_term_of_narrowing_term,((c== @ cQuickcheck_Narrowing.partial_term_of_narrowing_term_inst.partial_term_of_narrowing_term) @ cQuickcheck_Narrowing.partial_term_of_narrowing_term_inst.partial_term_of_narrowing_term))
(TQuickcheck_Narrowing.partial_term_of_narrowing_type_inst.partial_term_of_narrowing_type,((c== @ cQuickcheck_Narrowing.partial_term_of_narrowing_type_inst.partial_term_of_narrowing_type) @ cQuickcheck_Narrowing.partial_term_of_narrowing_type_inst.partial_term_of_narrowing_type))
(TGroups.linordered_cancel_ab_semigroup_add_class.linordered_cancel_ab_semigroup_add_axioms,(((cGroups.class.linordered_cancel_ab_semigroup_add @ cGroups.plus_class.plus) @ cOrderings.ord_class.less_eq) @ cOrderings.ord_class.less))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.comm_semiring_1_cancel_crossproduct_axioms,((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times) @ cGroups.one_class.one))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct.normalizing_comm_semiring_1_cancel_crossproduct_axioms,(call @ (^[V0]: (call @ (^[V1]: (call @ (^[V2]: (call @ (^[V3]: ((c==> @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)) @ ((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ V0) @ V1) @ V2) @ V3)))))))))))
(TSemiring_Normalization.comm_semiring_1_cancel_crossproduct_class.normalizing_comm_semiring_1_cancel_crossproduct_axioms,((((cSemiring_Normalization.class.comm_semiring_1_cancel_crossproduct @ cGroups.plus_class.plus) @ cGroups.zero_class.zero) @ cGroups.times_class.times) @ cGroups.one_class.one))